Ise viii-system modeling and simulation [10 cs82]-notes

OITALUMISDNAGNILLEDOMMETSYS N 01 28SC
SUBALLYS
TRAP – A
TINU – 1 oH8 u sr
:noitcudortnI nehW noitalumis si eht etairporppa loot dna nehw it is ton rporppa iate;
segatnavdA dna segatnavdasid fo ;noitalumiS saerA fo ;noitacilppa S smetsy dna s etsy m
e ;tnemnorivn enopmoC n st fo a s sy t ;me csiD r ete dna suounitnoc s sy t ;sme ledoM fo a s ;metsy
T sepy of ;sledoM csiD r ete - tnevE S metsy ;noitalumiS spetS ni a noitalumiS utS dy. ehT scisab of
teehsdaerpS ,noitalumis noitalumiS ex :elpma noitalumiS fo gniueuq s metsy s ni a teehsdaerps .
TINU – 2 oH6 u sr
lareneG ,selpicnirP noitalumiS oS ftw :era stpecnoC ni csiD r ete -Ev ne t :noitalumiS ehT tnevE -
gniludehcS / emiT - ecnavdA Al ,mhtirog dlroW ,sweiV launaM noitalumis gnisU tnevE
;gniludehcS tsiL gnissecorp . noitalumiS ni J ;ava iS mula it no ni GP SS
TINU – 3 6 oH u sr
lacitsitatS sledoM ni talumiS ion: weiveR of olonimret gy dna oc n ;stpec lufesU lacitsitats
sledom ; rcsid ete di ts r ubi it no s; uounitnoC s sid t tubir i sno ; Po ossi n corp e ;ss iripmE cal
rtsid i noitub s.
Q gniueu oM d :sle scitsiretcarahC fo gniueuq s sy t ;sme gniueuQ ;noitaton oL ng- nur saem u ser fo
amrofrep n ec fo iueuq ng s ;smetsy aetS dy-st eta b roivahe of 1/G/M euq u ;e skrowteN of euq u se ;
hguoR - tuc iledom n :g An il ul ts noitar ..
TRAP – B
TINU – 5 oH8 u sr
modnaR - rebmuN ,noitareneG modnaR - etairaV :noitareneG seitreporP fo modnar srebmun ;
noitareneG fo oduesp - ar n mod ;srebmun seuqinhceT rof itareneg ng modnar ;srebmun seT ts rof
modnaR srebmuN modnaR - etairaV :noitareneG esrevnI mrofsnart ;euqinhcet natpeccA ce-
cejeR noit ;euqinhcet laicepS seitreporp .
TINU – 6 oH6 u sr
tupnI oM de nil g : ataD ;noitcelloC itnedI f iy ng the noitubirtsid htiw ;atad retemaraP ;noitamitse
ssendooG fo tiF ;stseT Fi gnitt a non - anoitats ry oP i noss ;ssecorp itceleS ng tupni sledom uohtiw t
;atad etairavitluM dna Ti em - seireS tupni sledom .
noitamitsE fo etulosbA :ecnamrofreP T sepy fo snoitalumis htiw tcepser ot tuptuo ana l sisy ;
citsahcotS erutan fo tuo p tu ;atad etulosbA serusaem fo namrofrep ce dna th rie ;noitamitse uO t up t
ana ly sis rof gnitanimret ;snoitalumis tuptuO sisylana rof aets dy- etats umis l snoita .
,noitacifireV ,noitarbilaC dna ;noitadilaV pO mit iza oit n: ledoM ,gnidliub acifirev t noi dna
;noitadilav noitacifireV of noitalumis ;sledom tarbilaC i no dna av li ad t noi fo ,sledom itpo miza it no
aiv noitalumiS
ESIfo.tpeD , TIBJS 1

txeT B oo ks:
1. yrreJ ,sknaB J Snho . nosraC yrraB,II L. ,nosleN vaD id M. :lociN ercsiD te- tnevE S metsy
,noitalumiS ht5 ,noitidE P nosrae E ud cat ,noi 0102 .
detsiL( scipot no ly morf C pah t 1sre to 21 )
ecnerefeR skooB :
1. L Mecnerwa . ,simeeL nehpetS K. :kraP etercsiD – tnevE :noitalumiS A tsriF C ,esruo P nosrae
,noitacudE 02 01 .
2. llirevA M. :waL noitalumiS gniledoM dna Analys ,si ht4 ,noitidE aT ta rGcM aw- liH l, 7002 .

LBAT E OF NOC ET TN S
ITCUDORTNI ON
nehW noitalumis si eht etairporppa loot dna when it si
ton irporppa ;eta
segatnavdA dna avdasid n segat fo noitalumiS ; saerA fo
;noitacilppa
smetsyS dna s metsy vne i ;tnemnor stnenopmoC fo a
s metsy ;
etercsiD dna suounitnoc s ;smetsy ledoM fo a s sy t ;me
sepyT fo ;sledoM etercsiD - tnevE S metsy ;noitalumiS
spetS alumiSani it no S ut dy.
noitalumiS ex :selpma noitalumiS fo gniueuq s sy t ;sme
noitalumiS fo yrotnevni ys s ;smet rehtO ex elpma s fo
umis lat oi n.
GE LAREN RP I CN I ,SELP NOITALUMIS SOFT RAW E
stpecnoC ni etercsiD -Ev tne iS m alu t :noi 64 - 36
ehT tnevE - iludehcS ng / emiT - ecnavdA Al tirog h ,m
dlroW ,sweiV
launaM noitalumis gnisU tnevE ;gniludehcS siL t
nissecorp g. noitalumiS ni J ;ava miS ula it no ni GPSS
LACITSITATS MODE SL NI S UMI L NOITA
weiveR fo lonimret go y dna ;stpecnoc . 46 - 08
lufesU lacitsitats ;sledom
etercsiD tubirtsid i no s
egaP oN .
7- 54
TINU - 1
1.1
2.1
3.1
4.1
5.1
6.1
7.1
TINU - 2
1.2
2.2
4.2
5.2
TINU -3
1.3
2.3
3.3

3.4 suounitnoC ;snoitubirtsid
.3 5 nossioP secorp ;s
.3 6 laciripmE ubirtsid it sno
TINU – 4 : GNIUEUQ DOM E SL
scitsiretcarahC fo gniueuq s ;smetsy
gniueuQ on t ;noita
gnoL - nur saem u ser fo p ecnamrofre fo qu gniue sys ;smet
ydaetS etats b roivahe of 1/G/M ;eueuq skrowteN fo
seueuq
ydaetS etats b roivahe of 1/G/M ;eueuq skrowteN fo
seueuq
DNAR OM- REBMUN ,NOITARENEG
MODNAR - TAIRAV E NOITARENEG
treporP sei fo modnar ;srebmun 79 - 931
noitareneG fo aroduesp n mod srebmun ;
seuqinhceT rof gnitareneg modnar ;srebmun
stseT rof modnaR uN mb sre .
modnaR - etairaV areneG t :noi
esrevnI mrofsnart ;euqinhcet
peccA t ecna - noitcejeR ;euqinhcet laicepS seitreporp
TUPNI GNILEDOM
ataD noitcelloC . 041 - 841
itnedI f iy ng the noitubirtsid htiw
data;
retemaraP ;noitamitse
gnittiF a non -st anoita ry nossioP
4
1.4
2.4
3.4
4.4
5.4
TINU – 5
18 - 69
1.5
2.5
3.5
4.5
5.5
6.5
7.5
TINU - 6
1.6
2.6
3.6
4.6 ssendooG fo ;stseTtiF
De tp . fo ,ESC TIBJS

OITALUMISDNAGNILLEDOMMETSYS N 01 CS82
ssecorp , gnitceleS tupni ledom s wi tuoht ;atad
etairavitluM dna emiT -
seireS tupni sledom .
TINU - 7 TUPTUO SISYLANA ROF A IS NGLE MOD LE :
.7 1 sepyT of alumis snoit htiw tcepser ot tuptuo ana lysi ;s 941 - 451
.7 2 citsahcotS erutan fo tuo put ad ta;.
.7 3 serusaeM fo amrofrep n ec dna rieht ;noitamitse
.7 4 tuptuO sisylana for mret i gnitan ;snoitalumis tuptuO
ana l sisy rof aets dy- etats s snoitalumi . melborP s
TINU - 8 NOITACIFIREV DNA NOITADILAV FO NOITALUMIS SLEDOM
NOITAZIMITPO :
.8 1 ledoM ,gnidliub 551
.8 2 noitacifirev dna v ;noitadila
.8 3 noitacifireV fo alumis t noi m edo ls
.8 4 laC noitarbi dna noitadilav fo m edo sl .. noitazimitpO
aiv S umi la it no

METSYS GNILEDOM DNA NOITALUMIS
buS Co :ed 01 CS 28 AI M skra : 25
eW/srH e :k 40 xE am oH sru : 30
latoT rH s : 52 xE am M skra : 1 00
TRAP – A
TINU – 1 8 oH sru
I itcudortn o :n
-W neh noitalumis si eht etairporppa loot dna nehw ti si ton rporppa iate
- segatnavdA dna dasid v segatna fo iS m noitalu
- saerA fo ilppa c noita ;
- smetsyS dna metsys ivne tnemnor
- stnenopmoC fo a s sy t me
- etercsiD dna suounitnoc smetsys
- afoledoM s metsy
- sepyT fo sledoM
- alumiS it ;no
- spetS ni noitalumiSa utS dy
- ehT scisab fo sdaerpS h tee talumis i no
- noitalumiS ex :elpma noitalumiS fo gniueuq s sy t sme ni a sdaerps h ee t

TINU :1
I TCUDORTN I SOTNO I NOITALUM
miS u tal i no
A noitalumiS si eht noitatimi fo eht noitarepo fo a laer - dlrow rp o ssec ro s sy tem vo er
it me.
feirB pxE lan ita no
• ehT roivaheb fo a s sy t me sa ti sevlove revo emit si deiduts by d poleve i gn a talumis i no
edom l.
• sihT ledom sekat eht mrof fo a tes fo snoitpmussa inrecnoc ng eht oper noita fo eht s sy tem.
ehT snoitpmussa era ex desserp in
 lacitamehtaM spihsnoitaler
 lacigoL spihsnoitaler
 cilobmyS spihsnoitaler
neewteB eht seititne fo the s metsy .
serusaeM fo rep f amro nce
ehT ledom evlos d by lacitamehtam sdohtem s hcu sa di laitnereff clac ul ,su baborp i il ty
,yroeht al eg b ciar m sdohte ah ev eht noitulos lausu ly stsisnoc fo eno ro erom aciremun l
sretemarap hcihw era dellac serusaem fo ecnamrofrep .
1.1 nehW noitalumiS si the A pp or p etair T loo
• noitalumiS selbane eht uts dy fo dna ex noitatnemirep htiw eht lanretni snoitcaretni of a
xelpmoc ,metsys ro fo a s bu s metsy nihtiw a pmoc le sx metsy .
• ,lanoitamrofnI lanoitazinagro dna latnemnorivne ahc n seg ac n eb detalumis dna eht ceffe t
fo esoht snoitanretla no eht s’ledom roivaheb nac eb revresbo .
• ehT egdelwonk deniag in ingised ng a noitalumis ledom nac eb fo taerg eulav rawot d
gnitseggus tnemevorpmi ni eht metsys rednu ni ves noitagit .
• By ignahc ng noitalumis stupni dna gnivresbo eht gnitluser ,stuptuo elbaulav thgisni yam
eb deniatbo otni hcihw v selbaira era tsom tnatropmi dna woh selbairav i tn e car t.
• noitalumiS nac eb desu sa a gadep ogi lac d ecive ot ecrofnier na alyt ci ulos t oi n
seigolodohtem .
• talumiS ion nac eb desu to nemirepxe t iw th en w ised g sn or eicilop s oirp r to
,noitatnemelpmi os sa ot eraperp rof tahw may neppah .
• noitalumiS c na eb desu ot irev fy anal city oitulos ns.
• By gnitalumis fid f tnere seitilibapac rof a enihcam , stnemeriuqer nac eb d te erm deni .
• noitalumiS sledom dengised rof ,gniniart wolla l nrae ing wi tuoht eht soc t dna dis noitpur
fo no - eht - boj gninrael .
fo.tpeD ESI , TIBJS 7

• noitaminA swohs a s metsy ni detalumis noitarepo os taht eht pl na nac eb vis au zil de .
• ehT nredom s ,yrotcaf(metsy aw t re rbaf i noitac ,tnalp ecivres ,noitazinagro )cte si os
xelpmoc taht eht retni snoitca nac eb detaert no ly t hguorh noitalumis .
nehW noitalumiS si toN pA p or pri ta e
• noitalumiS dluohs eb desu nehw eht melborp nac not eb devlos gnisu oc mm no nes se.
• noitalumiS dluohs ton eb desu fi eht melborp nac eb devlos ana l lacity ly.
• italumiS no dluohs ton eb ,desu fi ti si reisae ot ep r rof m cerid t ex stnemirep .
• noitalumiS dluohs ton eb ,desu fi eht stsoc ex eec ds vas i sgn .
• noitalumiS dluohs ton eb ,demrofrep if eht oser u secr ro emit era ton ava li ab el .
• fI on atad si av ,elbalia not neve se etamit umis la it no si ton desivda .
• fI ereht si ton one u hg it me ro eht nosrep are ton av ,elbalia is mulat noi si ton rporppa iate.
• fI m sregana evah nu r elbanosae ex noitatcep ,yas oot hcum noos – ro eht rewop of
noitalumis si revo ,detamitse noitalumis yam ton eb rporppa i eta .
• fI s sy t me roivaheb si oot elpmoc x ro tonnac eb ed f ,deni noitalumis si ton airporppa te.
2.1 segatnavdA of miS lu oita n
• noitalumiS nac osla eb desu ot uts dy s smetsy ni eht sngised ta eg .
• noitalumiS sledom era nur rehtar naht solver.
• weN seicilop , gnitarepo ,serudecorp noisiced lur e ,s noitamrofni wolf , cte nac eb expl dero
tuohtiw gnitpursid eht iogno ng snoitarepo fo eht laer syst me .
• weN h erawdra d se i ,sng ph acisy l la ,stuoy snart p noitatro s smetsy nac be detset tuohtiw
ttimmoc gni secruoser of r rieht uqca is ti noi .
• sesehtopyH tuoba woh ro yhw niatrec anemonehp rucco nac eb set t de rof f ilibisae ty.
• emiT nac be desserpmoc ro ex dednap gniwolla rof a udeeps p ro ls ow nwod fo ht e
anemonehp rednu noitagitsevni .
• snI i thg nac eb tbo denia tuoba eht noitcaretni fo selbairav .
• snI i thg nac be eniatbo d tuoba eht ecnatropmi fo selbairav ot eht ecnamrofrep fo eht
etsys m.
• kcenelttoB sisylana nac eb demrofrep tacidni i no erehw krow - ni p ,ssecor noitamrofni
slairetam dna os no era gnieb xe evissec ly led a dey .
• A noitalumis uts dy nac pleh ni gnidnatsrednu how eht s metsy setarepo r rehta naht woh
slaudividni kniht eht s sy t me setarepo .
• tahw“ - ”fi snoitseuq nac eb derewsna . Us lufe ni eht ngised fo n we s smetsy .
segatnavdasiD fo noitalumis
• ledoM gnidliub seriuqer laiceps iniart ng.
• noitalumiS stluser yam be tluciffid ot terpretni .
• noitalumiS gniledom dna ana l sisy nac eb emit oc n gnimus dna ex evisnep .

• noitalumiS si desu ni emos sesac nehw na ana l lacity noitulos si elbissop ro neve
referp a lb e.
snoitacilppA fo talumiS ion
gnirutcafunaM lppA i oitac ns
1. anA l sisy fo nortcele i sc bmessa ly po e snoitar
2. ngiseD dna noitaulave fo a evitceles messa bly st noita rof rphgih eci nois llorcs
rosserpmoc sllehs .
3. nosirapmoC fo gnihctapsid ur l se rof dnocimes uct ro gnirutcafunam gnisu l egra ilicaf ty
edom ls.
4. noitaulavE fo retsulc oot l tuphguorht for niht - mlif daeh cudorp it no .
5. gninimreteD lamitpo tol ezis rof a otcudnocimes r dnekcab otcaf ry.
6. noitazimitpO fo elcyc ti em dna noitazilitu ni rotcudnocimes tset m funa act ru i gn .
7. anA l sisy fo ots r ega dna r laveirte getarts i se ni a wa esuoher .
8. noitagitsevnI fo dyn scima ni a ecivres o detneir su pp ly ch nia .
9. ledoM rof na rA my ehc m laci snoitinum lasopsid ilicaf ty.
rotcudnocimeS gnirutcafunaM
1. nosirapmoC fo gnihctapsid selur gnisu egral - icaf lity sledom .
2. ehT gnitpurroc ecneulfni fo ilibairav ty.
3. A wen tol - esaeler elur for refaw sbaf .
4. tnemssessA fo laitnetop sniag in dorp u ivitc ty eud ot evitcaorp deiter tnemeganam .
5. nosirapmoC fo a 002 mm dna 003 mm X-ray htil o parg hy llec .
6. yticapaC gninnalp htiw emit stniartsnoc neewteb snoitarepo .
7. 003 mm citsigol s metsy r ksi noitcuder .
noitcurtsnoC ignE n iree ng
1. tsnoC noitcur fo a mad tnemknabme .
2. hcnerT ssel lawener fo dnuorgrednu nabru serutcurtsarfni .
3. ivitcA ty gniludehcs ni a dyn ,cima tcejorpitlum gnittes .
4. nI v noitagitse fo eht larutcurts leets noitcere rp o ssec .
5. laicepS esoprup pmet l eta rof ilitu ty nnut le noc s curt it no .
yratiliM ppA il oitac ns
1. gniledoM pihsredael stceffe dna tiurcer epyt ni a rA my gnitiurcer st noita .

2. ngiseD dna tset fo na tnegilletni rellortnoc rof suomonotua u retawredn v selcihe .
3. gniledoM yratilim stnemeriuqer rof frawnon i gnithg snoitarepo .
4. yrotcejartitluM ecnamrofrep rof av r iy ng oiranecs sezis .
5. gnisU evitpada stnega ni S.U . riA ecroF noitneter .
,scitsigoL noitatropsnarT dna noitubirtsiD oitacilppA ns
1. gnitaulavE eht op t laitne stifeneb fo a liar - ciffart p gninnal al mhtirog .
2. gnitaulavE seigetarts ot evorpmi daorliar ecnamrofrep .
3. cirtemaraP gniledoM ni liar - yticapac gninnalp .
4. anA l sisy fo p essa n reg lf o sw ni na tropria ret m lani .
5. vitcaorP e thgilf - udehcs le noitaulave .
6. Lo citsig seussi ni otua n suomo doof noitcudorp s metsy s of r ext dedne noitarud caps e
oitarolpxe n.
7. gniziS lairtsudni liar - rac steelf .
8. noitcudorP noitubirtsid ni repapswen yrtsudni .
9. ngiseD o llotaf alp za
10. oohC gnis neewteb latner - rac snoitacol .
11. kciuQ esnopser tnemhsinelper .
ssenisuB ssecorP Si um l oita n
1. tcapmI fo noitcennoc ab nk seder i ng no pria o tr etag tnemngissa .
2. tcudorP tnempoleved margorp gninnalp .
3. noitailicnoceR fo ssenisub dna metsys ledom ing.
4. lanosreP gnitsacerof dna cigetarts ecrofkrow nalp n gni .
namuH tsyS ems
1. gniledoM namuh ofrep r ecnam ni elpmoc x s smetsy .
2. utS d iy ng eht uh m na tnemele ni tuo ciffart rtnoc ol.
tsyS3.1 e sm
A s metsy si denifed sa na noitagergga ro messa b egal fo o stcejb denioj ni emos uger lar
noitcaretni ro retni d epe n ecned drawot eht mocca p tnemhsil fo os me oprup se.

Ex elpma : noitcudorP S sy tem
nI eht oba ve s metsy ereht era rec niat tcnitsid ,stcejbo hcae of hcihw sessessop eitreporp s
fo tseretni . erehT era osla niatrec snoitcaretni gnirrucco ni eht s metsy taht esuac ahc n seg ni eht
sy mets .
Co stnenopm fo a S metsy
Enti yt : nA itne ty si na o tcejb fo anitseretni s etsy m.
:xE In eht otcaf ry sys t ,me ,stnemtraped dro e ,sr strap dna stcudorp era ehT seititne .
etubirttA
nA etubirtta setoned eht reporp ty fo na ytitne .
:xE seititnauQ rof hcae ,redro epyt fo ,trap ro rebmun fo senihcam ni a tnemtrapeD era setubirtta
fo yrotcaf s etsy m.
ytivitcA
ynA ssecorp gnisuac segnahc ni a s sy t me si ellac d ivitcanasa ty.
:xE gnirutcafunaM ssecorp fo eht tnemtraped .
etatS of eht S tsy em
ehT etats fo a s metsy si denifed sa the itcelloc on fo bairav l se assecen ry ot ebircsed a
metsys ta any ,emit evitaler ot eht evitcejbo fo ts du y. nI rehto ,sdrow etats fo eht s metsy naem a
noitpircsed fo lla eht tne i ,seit setubirtta dna seitivitca sa ht ey exi ts ta eno op int ni t mi e.
tnevE
nA tneve si denifed sa na suoenatsni ecnerrucco th ta yam ahc n eg eht tats e of eht s sy t me .
metsyS tnemnorivnE
ehT lanretxe stnenopmoc hcihw tcaretni htiw eht s metsy dna dorp u ec assecen ry ahc n seg
era s dia ot etutitsnoc eht s sy tem tnemnorivne . nI gniledom s ,smetsy ti si assecen ry ot ediced on
eht adnuob ry neewteb the s metsy a dn sti tnemnorivne . sihT noisiced yam dneped no eht esoprup
ydutsehtfo .

:xE nI a otcaf ry s ,metsy eht srotcaf illortnoc ng ar lavir fo sredro may eb co deredisn ot eb edistuo
eht otcaf ry tub tey a rap t fo eht s metsy norivne m tne . ,nehW ew redisnoc eht dnamed dna ppus ly
fo ,sdoog eht re si iatrec nly a er l pihsnoita neewteb eht otcaf ry tuptuo dna lavirra of ro d .sre ihT s
pihsnoitaler si deredisnoc sa na ivitca ty fo eht s sy t me .
suonegodnE Sy mets
ehT mret dne o suoneg si desu ot ebircsed seitivitca dna stneve cco u irr ng w nihti a s sy t me .
Ex: gniwarD hsac ni a ba kn .
suonegoxE metsyS
ehT mret ex suonego si desu ot ebircsed seitivitca dna stneve ni eht envi tnemnor t ah t
tceffa eht s metsy . Ex: irrA lav otsucfo m sre .
desolC metsyS
A metsys rof hcihw ereht si on ex suonego ytivitca dna tneve si dias ot eb a .desolc :xE
retaW ni na detalusni ksalf .
nepO s metsy
A metsys rof hcihw ereht si ex suonego ivitca ty dna tneve si dias ot eb a .nepo :xE knaB
sy mets .
4.1 ercsiD te dna suounitnoC S smetsy
suounitnoC smetsyS
S smetsy ni hcihw eht ch segna era tnanimoderp ly htooms era dellac tnoc i suoun s metsy .
Ex: daeH fo a retaw heb i dn a ad m.

ISDNAGNILLEDOMMETSYS OITALUM N 01 28SC
etercsiD metsyS s
S smetsy ni hcihw eht segnahc era tnanimoderp ly suounitnocsid are dellac tercsid e
sy smets . Ex: knaB – eht rebmun fo s’remotsuc segnahc no ly nehw a remotsuc irra v se ro ehw n
eht ecivres dedivorp a cu remots si detelpmoc .
5.1 ledoM fo a ys s met
A ledom si denifed sa a neserper t noita fo a s sy t me rof eht pu esopr of uts dyi gn ht e s sy t me .
tI si assecen ry ot redisnoc no ly esoht stcepsa fo eht s metsy taht tceffa eht melborp ednu r
oitagitsevni n. Th ese cepsa st era per r detnese in a ,ledom dna by fed i tin i no ti is a is lpm i acif it no of
seht y mets .
sepyT of oM dels
ehT suoirav t sepy edom ls era
• lacitamehtaM ro lacisyhP ledoM
• citatS edoM l
• cimanyD edoM l
• citsinimreteD ledoM
• citsahcotS ledoM
• etercsiD ledoM
• suounitnoC M ledo
lacitamehtaM ledoM
sesU cilobmys noitaton dna eht lacitamehtam snoitauqe ot tneserper a s sy t me .

citatS edoM l
stneserpeR a s metsy at a p ralucitra tniop fo t emi dna osla wonk n as noM te- olraC
talumis ion.
cimanyD edoM l
stneserpeR s smetsy sa th ye ahc n eg revo emit . Ex: talumiS i no fo a knab
citsinimreteD edoM l
sniatnoC on modnar var .selbai hT ey h eva a nk o nw tes fo stupni hw i hc will user lt in a
euqinu tes fo uo t up ts. :xE lavirrA fo stneitap ot the tsitneD ta eht udehcs led nioppa mt ne t it me.
citsahcotS edoM l
saH eno ro erom odnar m elbairav sa upni ts. modnaR stupni sdael to odnar m uo t stup . Ex:
noitalumiS fo a knab sevlovni modnar avirraretni l dna ivres ce t emi s.
ercsiD te dna suounitnoC edoM l
desU ni na suogolana .rennam noitalumiS sledom yam be im x de htob htiw etercsid na d
uounitnoc s. ehT eciohc si desab no eht scitsiretcarahc fo eht s metsy and eht evitcejbo fo eht
duts y.
etercsiD - tnevE metsyS noitalumiS
gniledoM fo s smetsy ni hcihw eht etats v elbaira c segnah no ly ta a id s eterc tes fo niop ts in
it me. ehT noitalumis sledom era ana lyz de yb laciremun rehtar naht yb ana l lacity .sdohtem
anA l lacity sdohtem me ploy eht evitcuded saer o gnin fo scitamehtam ot los ev eht m edo l. Eg:
laitnereffiD suluclac nac eb desu ot enimreted eht muminim tsoc ycilop rof emos otnevni ry
ledom s.
laciremuN sdohtem esu lanoitatupmoc serudecorp dna era ,’snur‘ hcihw si etareneg d
desab no eht ledom ssa u snoitpm dna snoitavresbo era oc detcell ot eb ana lyz de dna ot itse m ta e
eht eurt metsys ecnamrofrep .serusaem laeR - dlrow noitalumis si os ,tsav ohw se snur era
detcudnoc htiw eht pleh fo upmoc t .re hcuM thgisni nac eb deniatbo by noitalumis launam ly
hcihw si elbacilppa for s llam s metsy s.
6.1 spetS ni a noitalumiS ts du y
1. melborP f talumro i no
evE ry uts dy snigeb htiw a tnemetats fo eht ,melborp dedivorp yb ilop cy srekam . tsylanA
serusne sti raelc ly rednu s doot . fI ti si depoleved yb anal tsy ycilop m sreka s dluoh dnatsrednu na d
eerga htiw ti .
2. gnitteS fo sevitcejbo dna llarevo p tcejor lp an

ehT sevitcejbo etacidni eht snoitseuq ot eb derewsna by .noitalumis tA siht tniop a
noitanimreted dluohs eb edam oc n inrec ng hw te h re noitalumis si eht etairporppa em t lodoh og .y
gnimussA ti si airporppa t ,e eht llarevo tcejorp plan uohs ld cni l edu
• A tnemetats fo eht evitanretla smetsys
• A dohtem rof gnitaulave eht ssenevitceffe fo th ese evitanretla s
• snalP rof eht uts dy ni et r sm fo eht forebmun ep ople i devlovn
• tsoC fo eht uts dy
• ehT rebmun fo da sy req deriu ot hsilpmocca cae h esahp fo eht krow htiw eht apicitna t de
tluser s.
3. ledoM noitazilautpecnoc
ehT noitcurtsnoc fo a ledom fo a sys t me si baborp ly sa hcum tra sa ics .ecne ehT tra fo
gniledom si decnahne by na iliba ty
 oT� tcartsba eht laitnesse serutaef of a elborp m
 oT tceles dna yfidom cisab snoitpmussa taht eziretcarahc eht s metsy
 oT� hcirne dna arobale te eht ledom litnu a ufesu l orppa xima it no user l st
suhT , ti si tseb ot trats htiw a elpmis ledom dna dliub drawot gr retae elpmoc xity. edoM l
noitazilautpecnoc ecnahne eht ilauq ty fo eht gnitluser ledom dna esaercni eht ecnedifnoc fo ht e
ledom resu ni eht noitacilppa fo eht ledom .
4. ataD oitcelloc n
erehT si a tnatsnoc yalpretni neewteb eht snoc t noitcur fo ledom dna eht noitcelloc fo
dedeen adtupni ta. enoD ni eht rae ly segats .
evitcejbO dnik fo atad era ot loceb l detce .
5. ledoM oitalsnart n
laeR - dlrow s smetsy tluser ni sledom taht eriuqer a taerg laed fo rofni m noita egarots dna
oitatupmoc n. tI nac eb demmargorp yb gnisu noitalumis segaugnal ro ceps i la esoprup noitalumis
rawtfos e.
umiS la it on egaugnal s era ufrewop l na d elf x lbi e. oitalumiS n rawtfos e edom sl
tnempoleved emit nac eb decuder .
6. deifireV
It p sniatre to eh retupmoc rp o marg na d ikcehc ng t eh ep r amrof n ec . fI the in tup emarap t re s
dna lacigol erutcurts dna yltcerroc ,detneserper noitacifirev si detelpmoc .

7. detadilaV
tI si eht d noitanimrete t tah a ledom si na cca u etar er p neser t noita fo the laer s sy tem.
deveihcA orht u hg noitarbilac fo eht ,ledom na evitareti ssecorp fo rapmoc i gn eht edom l to autca l
s metsy eb h roiva dna eht apercsid n seic neewteb the owt .
8. latnemirepxE D ngise
ehT sevitanretla th ta are ot be is mulat de must eb det denimre . hcihW retla n sevita ot
etalumis yam eb a uf n noitc fo snur . For cae h s etsy m sed i ,ng snoisiced deen to eb m da e
gninrecnoc
 � htgneL fo eht noitazilaitini doirep
 eL n htg of noitalumis nur s
 rebmuN fo noitacilper ot eb edam fo hcae ur n
9. noitcudorP snur dna anal sy is
yehT are desu ot amitse te serusaem fo amrofrep n ec rof eht s metsy sed i ng s taht era b gnie
etalumis d.
10. eroM snur
desaB no eht ana l sisy fo snur taht evah eeb n .detelpmoc ehT ana l tsy senimreted fi
lanoitidda snur era n dedee dna tahw sed i ng esoht idda t lanoi ex irep m ne ts dluohs of l wol .
11. coD u noitatnem dna nitroper g
owT t sepy of atnemucod t noi .
margorP�� d noitatnemuco
ssecorP�� noitatnemucod
margorP cod u itatnem on
naC eb desu niaga by t eh emas ro tnereffid anal stsy ot dnatsrednu how eht rp ogram
repo ates. rehtruF fidom i noitac lliw eb e .reisa M ledo sresu c na chan eg the tupni arap m srete for
retteb amrofrep ecn .
ssecorP noitatnemucod
seviG eht otsih ry of a is mula it no orp j .tce ehT tluser fo lla anal sy is uohs ld eb r trope ed
raelc ly dna esicnoc ly in a lanif .troper sihT selbane ot r weive the lanif noitalumrof na d
,sevitanretla stluser fo the ex stnemirep dna the dednemmocer ulos t noi to t eh melborp . The anif l
troper sedivorp a elcihev fo ifitrec c noita .
12. noitatnemelpmI

sseccuS ed p sdne on eht suoiverp st .spe fI the m ledo esu r sah b ee n roht o hgu ly i evlovn d
dna dnatsrednu s eht tan u er fo the ledom na d its uo t ,stup l doohileki fo a suorogiv pmi lem ne tat oi n
cnahnesi ed.
ehT noitalumis ledom gnidliub nac be nekorb tni o 4 esahp s.
I sahP e
• sisnoC ts fo spets 1 dna 2
• tI si doirep fo evocsid ry/ ro noitatnei
• ehT ana l tsy may ah ve ot tratser eht rp o ssec fi ti si ton enif - enut d
• snoitarbilaceR dna snoitacifiralc yam o cc ur ni siht esahp ro tona h re ahp se.
II ahP es
• stsisnoC fo spets dna6,5,4,3 7
• A gniunitnoc lpretni ay si deriuqer gnoma the ets ps
• Ex noisulc fo ledom resu stluser ni snoitacilpmi rud i gn i oitatnemelpm n
sahPIII e
• sisnoC ts fo spets 9,8 dna 01
• seviecnoC a oroht u hg nalp rof ex nemirep it gn
• etercsiD - tneve cots h citsa si a lacitsitats ex tnemirep
• ehT tuptuo selbairav era mitse seta taht noc t nia modnar rre or na d eht r ofe er eporp r
lacitsitats sisylana si qer u deri .
VI P esah
• sisnoC ts fo spets 11 dna 21
• lufsseccuS noitatnemelpmi sdneped no eht tnemevlovni fo resu dna yreve pets s
lufsseccus noitelpmoc .
D ESIfo.tpe , TIBJS 71

7.1 NOITALUMIS ELPMAXE S
• noitalumiS� si netfo desu ni eht ana l sisy fo ieueuq ng .sledom nI a elpmis pyt i lac
ieueuq ng ,ledom wohs n ni gif 1, remotsuc s evirra f mor emit to it me dna join a ueuq e or
gnitiaw ,enil era lautneve ly ,devres dna lanif ly el a ev eht s sy t me .

• ehT mret "remotsuc" srefer ot yna t epy fo itne ty taht nac eb eweiv d sa er gnitseuq
"ecivres" morf a s metsy .
scitsiretcarahC fo gnieueuQ metsyS s
• ehT key ,stnemele of a euq u gnie s metsy era eht otsuc m re s na d es r .srev ehT t re m
"remotsuc" nac refer to ,elpoep ,senihcam ,skcurt ,scinahcem p tneita s—an ihty ng aht t
sevirra ta a f ilica ty dna seriuqer ecivres .
• ehT mret s" e "revr hgim t refer ot ,stsinoitpecer ,snosrepriaper sUPC ni a ,retupmoc ro
gnihsaw a.…senihcam ny ecruoser ,nosrep( ,enihcam .cte hcihw sedivorp eht etseuqer d
es r iv ec .
• elbaT 1 stsil a rebmun fo tnereffid qu ue gni s etsy ms.
elbaT :1 selpmaxE of gnieueuQ S metsy s
 ehT stnemele fo a iueuq ng s metsy :era -
ehT�� gnillaC upoP l oita n:-
 ehT noitalupop fo laitnetop ,sremotsuc rrefer ed ot sa eht gnillac ,noitalupop yam
demussaeb ot eb etinif or nifni ti e.
 roF ex ,elpma edisnoc r a knab fo 5 senihcam th ta are cu gnir ti er s. retfA na retni v la of
,emit a enihcam lacitamotua ly op sne dna tsum eb dednetta by a row k re who sevomer ht e
erit dna stup na ucnu red erit otni eht m .enihca ehT senihcam era eht c" u ,"sremots hw o
"evirra" ta the tnatsni yeht lacitamotua ly nepo . The row k re si eht "s "revre , ohw res" v "se
na nepo m enihca sa oos n sa ssop ible. The gnillac noitalupop is fi ,etin dna isnoc sts fo ht e
senihcamevif .

 nI s smetsy htiw a egral noitalupop fo laitnetop ,sremotsuc eht gnillac noitalupop is
lausu ly demussa ot eb etinif ro inifni t .e Ex selpma fo etinifni snoitalupop i cn l edu t eh
laitnetop sremotsuc fo a ,tnaruatser ,knab etc.
 ehT niam ereffid n ec eb t neew etinif dna etinifni noitalupop sledom si woh eht rra i av l tar e
si denifed . nI na etinifni - noitalupop ,ledom eht lavirra etar si ton detceffa by eht rebmun
fo sremotsuc ohw h eva l tfe eht gnillac oitalupop n dna denioj eht euq u gnie s metsy . nO ht e
rehto dnah , for etinif ac l gnil noitalupop ,sledom eht lavirra etar ot eht qu ieue ng syst me
seod dneped no eht mun b re fo sremotsuc ieb ng es r dev dna aw i it ng.
�� etsyS m :yticapaC -
 In am ny qu ieue ng s smetsy ereht is a timil ot eht rebmun of remotsuc s that may be ni ht e
gnitiaw enil ro s metsy . roF ex ,elpma na citamotua rac hsaw may ah ve ro mo rof no ly 10
srac ot tiaw ni enil to ne t re eht cem h ina sm.
 nA ivirra gn remotsuc who sdnif eht s metsy lluf seod ton retne tub snruter etaidemmi ly ot
eht gnillac noitalupop .
 emoS ,smetsys hcus sa trecnoc tekcit selas rof ,stneduts yam eb deredisnoc sa ivah ng
detimilnu icapac ty. There era on stimil no t eh n rebmu fo stud stne allow de ot aw it to
esahcrup cit k ste .
 nehW a s metsy h sa detimil icapac t ,y a noitcnitsid si edam wteb e ne the a rr lavi ar et .e.i( ,
eht rebmun fo slavirra rep emit )tinu dna eht evitceffe lavirra ar te ,.e.i( eht rebmun ohw
evirra dna retne the s sy tem )tinuemitrep .
�� ehT lavirrA :ssecorP -
 lavirrA p secor s rof fni i etin - noitalupop sledom si lausu ly carahc t dezire ni t re ms of
avirraretni l semit fo evisseccus sremotsuc . A irr v sla may o rucc ta s dehc u del it m se ro at
modnar ti sem . nehW ta modnar ,semit eht lavirraretni semit era yllausu deziretcarahc yb
a ilibaborp ty noitubirtsid
 ehT tsom tnatropmi ledom rof modnar lavirra s si eht P sio s no avirra l ecorp s .s fI An
erper s stne eht lavirraretni emit neewteb motsuc er n-1 dna uc ts mo er n (A1 si eht ca t au l
lavirra emit fo eht tsrif ,)remotsuc t neh rof a Po si nos lavirra rp o ec ss. nA is ex aitnenop lly
detubirtsid htiw naem λ/I emit .stinU ehT lavirra etar si λ sremotsuc rep ti em .tinu ehT
rebmun fo slavirra ni a emit lavretni fo htgnel ,t yas (N t ) , sah eht nossioP ubirtsid it no
htiw naem tλ remotsuc s.
 ehT nossioP lavirra rp o ssec sah b ee n yllufsseccus lpme o dey sa a ledom fo eht irra v la of
elpoep ot uatser r ,stna rd i ev - ni ,sknab dna rehto ecivres f lica ti sei .

DNAGNILLEDOMMETSYS OITALUMIS N 01 28SC
 A dnoces tnatropmi ssalc fo slavirra si eht cs h delude irra v ,sla hcus as ap ti ne ts to a
ph aicisy n s' of ecif ro s deludehc enilria lf i thg ar slavir ot na ai ropr t. nI siht ,esac eht
lavirraretni semit [ nA , n = .,2,1 . . } yam eb atsnoc ,tn ro tnatsnoc sulp ro sunim a llams
modnar tnuoma ot erper s tne rae ly ro l eta avirra ls.
 A driht noitautis srucco nehw ta tsael one otsuc m re si demussa ot wla a sy be tneserp ni t eh
,eueuq os taht eht res ver si reven eldi esuaceb fo a kcal fo motsuc e .sr For ex ,elpma t eh
"sremotsuc" may tneserper war lairetam rof a ,tcudorp dna ciffus i tne war lairetam is
demussa ot eb wla a sy av elbalia .
 roF etinif - noitalupop ,sledom eht lavirra ssecorp si carahc t dezire ni a etelpmoc ly nereffid t
oihsaf n. enifeD a suc ot m re sa idnep ng wh ne taht remotsuc si edistuo eht ieueuq ng s sy t me
dna a rebmem of eht laitnetop gnillac upop la it no .
 emitnuR fo a nevig suc t remo si denifed sa eht l htgne fo emit morf ed p erutra morf t eh
gnieueuq s sy t me litnu taht s’remotsuc txen avirra l ot eht eueuq .
 teL Ai A, 2 , ... eb eht evisseccus semitnur of remotsuc ,/ dna tel S(i)
1
,S(i)
2
... eb t eh
idnopserroc ng evisseccus s metsy ;semit taht ,si S )i(
si eht latot emit tneps ni t eh s sy tem
by remotsuc i du gnir eht htn vis ti . erugiF 2 setartsulli eseht stpecnoc rof enihcam 3 in t eh
erit - gniruc elpmaxe . ehT latot lavirra ssecorp si eht noitisoprepus fo eht lavirra it m se fo
lla sremotsuc .
giF 2 hs o sw eht tsrif dna rradnoces i av l fo ma enihc 3.
giF :2 lavirrA rp o ssec for a fini et - talupop i no dom el.
tsriF irra v la hcamfo i en 3 dnoceS irra v la fo ihcam ne 3
 enO tnatropmi noitacilppa fo etinif noitalupop mo sled si eht enihcam er pair borp l me . The
senihcam era eht sremotsuc dna a emitnur si osla dellac emit ot eruliaf . nehW a nihcam e
,sliaf ti "sevirra" ta eht q ueu i gn
g sys t me eht( riaper ilicaf t )y dna mer snia ereht litnu ti si evres" d" er( p .)deria semiT ot
eruliaf rof a nevig ssalc fo enihcam evah eeb n carahc t dezire by eht ex ,laitnenop eht
( )i ( )i
n

,llubieW dna eht ammag di rts i .snoitub sledoM htiw na ex laitnenop emitnur era
semitemos yllacitylana elbatcart .
�� eueuQ roivaheB dna eueuQ csiD i ilp n :e -
 eueuQ b oivahe r refer s to remotsuc snoitca elihw in a qu ue e aw ti gni for s re vi ec ot begin.
nI os me ,snoitautis ereht si a ilibissop ty taht cni o gnim sremotsuc may ab lk vael( e ehw n
yeht ees taht eht enil si oot ol ,)gn egener ael( ve retfa ieb ng ni eht enil nehw yeht s ee t ah t
eht enil si gnivom oot wols l ,)y ro jo kc ey om( ve morf eno enil ot ona ther if ht ey kniht
yeht h eva ohc s ne a wols )enil .
 Queue id s pic l ni e refer s to ht e lo ig cal ro ed ring fo remotsuc s in a qu ue e na d
hcihwsenimreted remotsuc lliw eb nesohc rof ecivres nehw a revres semoceb eerf .
• nommoC eueuq senilpicsid edulcni tsrif - ,ni tsrif - tuo (F FI O ;) sal t- ni uotsrif t
;)OFIL( ecivres ni modnar redro (S ;)ORI tsetrohs gnissecorp emit tsrif (| S )TP dna
vres eci gnidrocca ot ytiroirp )RP( .
• In a boj ,pohs qu eue senilpicsid era emos times esab d no eud d eta s dna no
detcepxe gnissecorp it me rof a nevig i t epy of .boj ecitoN taht a FIF O eueuq
enilpicsid seilpmi taht secivres nigeb ni eht emas redro sa avirra l ,s ub t t tah
sremotsuc may evael eht s metsy ni a di tnereff redro esuaceb fo tgneltnereffid h
semitecivres .
• ecivreS iT m se dna eht ecivreS M sinahce m:-
 ehT ecivres semit fo evisseccus slavirra a er d detone by ,1S ,2S yehT…3S am y be
tnatsnoc ro fo ar odn m .noitarud ehT ex ,llubieW,laitnenop ,ammag l rongo mal, na d
detacnurt no lamr birtsid u snoit evah lla b nee us de lufsseccus ly sa sledom of vres ci e it em s
ni tnereffid snoitautis .
 semitemoS secivres yam eb lacitnedi ly detubirtsid rof lla sremotsuc fo a nevig type or
ssalc ro iroirp t ,y elihw sremotsuc fo nereffid t t sepy may ah ve moc p etel ly fid f tnere
ecivres - emit snoitubirtsid . nI ,noitidda ni emos ys s ,smet ecivres semit dneped nopu eht
emit fo day or eht el n htg fo t eh tiaw i gn li .en roF ex ,elpma revres s may krow retsaf aht n
lausu nehw eht gnitiaw enil si ,gnol suht ef evitcef ly icuder ng eht ecivres t mi se .
 A gnieueuq s metsy stsisnoc fo a rebmun fo ecivres sretnec dna gnitcennocretni .seueuq
hcaE ecivres nec t re noc s stsi fo emos rebmun fo ,srevres ,c wo ikr ng ni ;lellarap taht ,si
nopu gnitteg ot eht daeh fo eht ,enil a remotsuc sekat eht tsrif elbaliava es .revr lellaraP

ecivres smsinahcem era rehtie elgnis res v re c( = ,)1 elpitlum revres (1 < c < ,)∞ or
detimilnu srevres =c( ∞ .) A( es lf- ecivres ytilicaf si lausu ly char deziretca sa ivah ng an
detimilnu rebmun fo res v .sre )
:1elpmaxE -
redisnoC a tnuocsid esuoheraw erehw sremotsuc yam rehtie evres ;sevlesmeht ro iaw t
fo eerht ,skrelc dna yllanif evael retfa gniyap a elgnis reihsac . The s metsy is
detneserper by eht wolf d margai ni erugif 1 :woleb
erugiF 1: tnuocsiD esuoheraw htiw eerht ecivres retnec s
ehT bus s ,metsy gnitsisnoc fo euq ue 2 dna vres i ec nec t re ,2 si nwohs ni m ero ed ta li ni
erugif 2 .woleb rehtO snoitairav fo ecivres smsinahcem edulcni hctab ecivres a( revres ivres ng
lareves sremotsuc suoenatlumis l )y ro a remotsuc gniriuqer s eve r la srevres s suoenatlumi ly.
erugiF 2: ecivreS nec t re ,2 w hti c arap3= ll el srevres .

• Ex elpma :2 -A nac dy utcafunam r re sah a cudorp t noi enil hcihw stsisnoc fo eerht enihcam s
arapes t de yb otnevni ry- ni - ssecorp sreffub . ehT fi tsr enihcam sekam dna sparw eht vidni i aud l
seceip of nac d ,y the ces o dn kcap s 05 seceip in a ob x, dna eht driht s slae a dn parw s t eh ob x.
ehT owt yrotnevni effub rs evah seiticapac fo 0001 ob x se hcae . sA detartsulli by Fi erug ,3 eht
s metsy si om d dele sa h gniva eerht ecivres nec t ,sre cae h retnec ivah ng c = 1 res ver (a
,)enihcam htiw euq ue- icapac ty stniartsnoc neewteb ihcam n se . tI is ussa m de taht a suffici ne t
ppus ly of war am t laire is wla ays elbaliava at ht e first euq u .e esuaceB fo eht eueuq - icapac ty
,stniartsnoc enihcam 1 stuhs nwod revenehw eht yrotnevni reffub sllif ot icapac t ,y elihw
enihcam 2 stuhs nwod revenehw eht reffub em eitp s. nI rb i ,fe eht s metsy stsisnoc fo erht e
elgnis - revres euq u se ni s seire htiw qu eue - ac p ica ty stniartsnoc na d a itnoc n suou avirra l aerts m
ta eueuqtsrifeht .
erugiF 3: ydnaC tcudorp io niln e
gnieueuQ :noitatoN -
 gnizingoceR eht id ytisrev fo ieueuq ng s ,smetsy lladneK ]3591[ desoporp a lanoitaton
s metsy rof lellarap res v re s sy t sme hcihw sah b nee ediw ly .detpoda nA degdirba oisrev n
fo siht noitnevnoc si bas de no ht e rof mat A /B / c / N / .K Th ese l rette s tneserper t eh
gniwollof s sy met :scitsiretcarahc
 A stneserper eht rraretni i lav t emi rtsid i noitub .
 B er p stneser eht s ecivre -t emi tubirtsid i no .
 nommoC[ s slobmy rof A dna B edulcni M e( x laitnenop ro ,)vokraM D
tnatsnoc( ro ,)citsinimreted kE alrE( ng of redro ,)k HP esahp( -t ,)epy H
aitnenopxerepyh( ,)l G artibra( ry ro ,)lareneg dna IG eG( n lare edni p .)tnedne ]
 c stneserper eht rebmun fo lellarap srevres .
 N stneserper eht s metsy icapac ty.
 K stneserper eht ezis fo eht illac ng upop la it no
 roF ex ,elpma M / M / 1 / ∞ / ∞ setacidni a elgnis - evres r s metsy taht sah detimilnu eueuq
yticapac dna na etinifni noitalupop fo laitnetop slavirra . ehT lavirraretni ti sem dna civres e

semit era laitnenopxe ly .detubirtsid nehW N dna K are ni ,etinif ht ey m ya eb pord ped
morf oneht ta it no . roF ex ,elpma M / 1/M / ∞ / ∞ is fo t ne rohs t dene ot /M/M l.
 lanoitiddA noitaton esu d rof par lella res v re s etsy sm is detsil ni lbaT e 1 gi nev woleb . hT e
sgninaem may av ry thgils ly morf s metsy ot s tsy em. llA s smetsy lliw eb a demuss ot vah e
a OFIF qu eue picsid l eni .
elbaT 1. uQ gnieue noitatoN rof lellaraP revreS smetsyS
ώ gnoL - nur egareva it me tneps ni s metsy rep uc s remot
ώQ oL ng- nur sucrepeueuqnitnepsemitegareva tom re
noitalumiS fo Qu ue ni g tsys ems
 A ieueuq ng s metsy si debircsed by sti gnillac pop ,noitalu eht erutan fo t eh irra val ,s t eh
ecivres ,msinahcem eht metsys icapac t ,y dna eht gnieueuq .enilpicsid A elgnis - ennahc l
gnieueuq metsys si deyartrop ni 1erugif .
erugiF :1 gnieueuQ S metsy

DNAGNILLEDOMMETSYS OITALUMIS N 01 28SC
 nI the is n elg -ch lenna qu ,eue eht gnillac noitalupop si ;etinifni t ah t ,si if a tinu evael s ht e
gnillac noitalupop dna j snio eht gnitiaw enil ro sretne vres i ,ec ereht si on ahc n eg ni ht e
lavirra etar fo rehto stinu taht yam n dee es ecivr .
 slavirrA rof vres i ec cco ur eno ta a emit ni a modnar ;noihsaf ecno yeht jo ni eht gnitiaw
,enil yeht era lautneve ly .devres nI ,noitidda es r eciv semit era of emos modnar el n htg
idrocca ng ot a p ytilibabor noitubirtsid hcihw eod s ton ahc n eg revo ti em .
 ehT s metsy ac icap t ;y has on ,timil gninaem taht any rebmun fo inu ts nac wa ti ni il en .
 laniF l ,y stinu era devres in eht redro fo th rie lavirra by a is n elg revres or ch lenna .
 slavirrA dna s secivre era denifed by eht tubirtsid i sno fo eht emit neewteb slavirra dna the
noitubirtsid fo ecivres ,semit evitcepser ly.
 roF any elpmis is n elg or itlum - lennahc qu ,eue the evo r lla evitceffe a rr ival etar tsum be
ssel naht eht latot ecivres ,etar ro the itiaw ng li en w li l worg uohtiw t dnuob . nehW eueuq s
worg tuohtiw ,dnuob yeht a er demret e“ x ”evisolp ro elbatsnu .
 ehT etats fo eht s sy t me si eht rebmun fo stinu ni eht s metsy and eht ats tus fo eht res v ,re
ysub ro eldi .
 nA tneve si a tes fo secnatsmucric taht esuac na suoenatnatsni ahc n eg ni eht etats fo t eh
etsys m. nI a elgnis – lennahc ieueuq ng s metsy th ere era no ly owt elbissop stneve taht nac
tceffa eht ehtfoetats s sy t me .
 yehT era eht tne ry o af u tin ehtotni s metsy .
 ehT noitelpmoc fo vres i ec no a nu it.
 ehT ieueuq ng s metsy sedulcni eht ,revres eht tinu eb gni ,decivres dna stinu ni eht eueuq .
eH noitalumis colc k si u des to rt a kc umis l eta d t emi . fI a tinu h sa tsuj co detelpm ivres c ,e
eht noitalumis sdeecorp ni eht rennam nwohs ni eht wolf margaid fo figu .2.er etoN taht
eht revres h sa no ly owt p elbisso tats :se ti si rehtie ub sy ro eldi .
erugiF :2 ecivreS - tsuj - detelpmoc olf w margaid

 ehT lavirra tneve srucco nehw a tinu sretne eht s metsy . ehT wolf margaid rof eht lavirra
tneve si nwohs ni rugif e .3 ehT tinu yam dnif eht revres rehtie eldi ro bus ;y rofereht e,
rehtie eht tinu snigeb s ecivre etaidemmi l ,y ro ti sretne eht euq ue for eht s revre . ehT inu t
swollof eht esruoc of tca i no nwohs ni gif 4.
erugiF 3: tinU - niretnE g metsys olf w id marga
 fI eht revres si ub s ,y eht tinu sretne eht eueuq . fI eht revres si eldi dna eht eueuq si pme t ,y
eht tinu snigeb s .ecivre It si ton elbissop for eht evres r to eb eldi dna the ueuq e ot eb
ytpmenon .

 retfA eht noitelpmoc fo a ecivres eht ecivres yam emoceb eldi ro iamer n ub sy htiw eht
en xt tinu . ehT pihsnoitaler fo eseht owt semoctuo ot eht sutats fo eht eueuq si nwohs ni
gif .5 fI eht qu eue si on t pme t ,y rehtona tinu lliw retne eht s revre dna ti liw l eb ub s .y If
eht eueuq si pme ty, eht revres lliw eb eldi fa t re a vres ice is oc mplet de . esehT t ow
seitilibissop era nwohs sa eht dedahs snoitrop fo fig .5 tI si elbissopmi rof eht revres ot
emoceb ub sy if eht qu eue si pme ty ehw n a ecivres si detelpmoc . ralimiS l ,y ti is
elbissopmi rof eht res v re ot eb eldi retfa a s vre i ec si oc m etelp d ehw n eht ueuq e is on t
tpme y.
noitalumiS kcolc semit rof slavirra dna ed par serut era detupmoc ni a noitalumis elbat
imotsuc z de rof hcae rp oblem. In ,noitalumis stneve lausu ly rucco ta nar d mo tim .se nI seht e
,sesac a lacitsitats edom l fo eht atad si ed v epole d morf rehtie ad ta celloc t de dna ana lyz ,de ro
evitcejbus setamitse dna as us mpt snoi .
 modnaR srebmun era detubirtsid mrofinu ly dna tnednepedni ly no eht lavretni ,0( .)1
modnaR stigid era mrofinu ly detubirtsid no eht tes ,0{ ,1 …2 .}9 modnaR stigid nac eb
desu ot fo mr odnar m nu srebm by s itcele ng eht p repor mun b re of di stig f ro e hca odnar m
rebmun dna icalp ng a lamiced tniop ot eht tfel fo eht av l eu sele .detc ehT reporp ebmun r
fo stigid si detatcid by the arucca cy fo eht d ata gnieb desu for tupni oprup s se . fI eht tupni
noitubirtsid sah seulav htiw owt lamiced ,secalp owt stigid era nekat fr mo a odnar m-
stigid elbat dna eht d ce i lam tniop si decalp ot eht tfel to mrof a r odna m rebmun .
 nehW srebmun era etareneg d gnisu a rp o ,erudec ht ey are etfo n derrefer ot as
modnaroduesp srebmun . ecniS eht dohtem si kn ,nwo ti is wla ays ssop ible ot wonk ht e
ecneuqes of srebmun aht t lliw eb eg n are t de roirp to eht s mi noitalu .
 nI a elgnis - lennahc q gnieueu s ,metsy avirraretni l semit dna ecivres semit era etareneg d
morf eht snoitubirtsid fo eseht modnar selbairav . ehT selpmaxe taht wollof wohs woh
hcus semit era tareneg e .d roF icilpmis t ,y emussa taht eht semit neewteb slavirra rew e
detareneg by lor gnil a die evif semit dna cer o gnidr eht pu ecaf . baT le 1 co niatn s a es t of

evif lavirraretni semit era desu ot etupmoc eht lavirra semit fo is x sremotsuc at t eh
gniueuq s metsy .
elbaT :1 lavirraretnI dna kcolC T emi s
 ehT tsrif remotsuc si demussa ot evirra ta cl kco ti em 0. sihT strats t eh cl kco in noitarepo .
ehT dnoces remotsuc rra i sev owt emit stinu ,retal ta a kcilc it em fo 2. ehT driht emotsuc r
sevirra of ur mit e stinu ,retal ta a kcolc t emi fo 6 a; dn so no .
 ehT noces d emit fo tseretni is t eh vres i ec t .emi T eh no ly elbissop ecivres semit era one,
,owt ,eerht dna ruof it me nu its. gnimussA taht lla ruof seulav era yllauqe ekil ly ot rucco ,
eseht lav u se luoc d h eva neeb detareneg by icalp ng the srebmun no e orht u hg uof r no pihc s
dna gniward eht spihc morf a tah htiw ,tnemecalper gnieb erus ot cer o dr eht srebmun
eles cted.
 ,woN eht lavirraretni t semi dna ecivres semit tsum eb m ehse d ot umis late t eh
nahcelgnis len gnieueuq metsys . sA nwohs ni elbat ,2 eht tsrif remotsuc sevirra ta cl kco
emit 0 na d etaidemmi ly nigeb s ,ecivres hw i hc er qui ser t ow mi setun . ecivreS si pmoc let de
ta kcolc emit .2 ehT dnoces remotsuc sevirra ta kcolc emit 2 dna si a dehsinif ta kcolc
ti em 3. etoN taht eht htruof remotsuc irra v de ta cl kco emit ,7 tub ecivres c dluo ton nigeb
litnu kcolc t emi .9 sihT derrucco esuaceb tsuc o rem 3 did ton nif si h es rvi ec itnu l colc k
ti em 9.
 elbaT 2 saw dengised lacificeps ly rof a is n elg -ch lenna eueuq hcihw res v se sremotsuc no
a tsrif - ,ni tsrif - tuo )OFIF( .sisab tI speek kcart fo eht kcolc emit ta hcihw hcae neve t
o cc urs. The dnoces loc u nm fo elbat 2 r sdroce eht kcolc emit fo hcae irra v la ,tneve lihw e
eht tsal nmuloc sdrocer t eh kcolc emit fo hcae d erutrape tneve .

elbaT :2 noitalumiS elbaT gnizisahpme kcolC Tim se
ELPMAXE :1 elgniS -C lennah euQ ue
 A llams ecorg ry erots sah no ly eno uokcehc t .retnuoc sremotsuC evirra ta siht
tuokcehc retnuoc ta modnar morf 1 ot 8 setunim .trapa hcaE elbissop eulav of
lavirraretni emit sah eht emas ilibaborp ty of cco u nerr ce. ehT ecivres semit yrav morf
1 ot 6 im n setu` htiw ht e ibaborp il eit s nwohs in table 5. hT e melborp si ot ana l ezy ht e
s metsy by gnitalumis eht lavirra dna s ecivre 02fo sremotsuc .
elbaT :5 ecivreS emiT noitubirtsiD

 A noitalumis fo a yrecorg erots taht strats htiw an pme ty s metsy si ton reali ts ci nu l sse
eht noitnetni si ot om d le eht s etsy m morf rats t pu ro to edom l tnu il aets dy st ta e
noitarepo si dehcaer .
 A tes fo nu i mrof ly detubirtsid modnar srebmun is edeen d ot etareneg the avirra ls at
eht tuokcehc retnuoc . modnaR srebmun evah eht gniwollof porp e :seitr
1. ehT tes fo modnar srebmun si mrofinu ly rtsid i detub neewteb 0 dna 1.
2. evisseccuS modnar srebmun era tnednepedni .
 ehT emit - neewteb - irra v la animreted noit si hs o nw in t ba le .6 etoN taht eht fi sr t
modnar di stig era .319 To niatbo eht gnidnopserroc emit b neewte a rr i av ls, etne r ht e
htruof nmuloc fo bat le 4 dna daer 8 setunim f mor t eh tsrif oc l nmu of eht elbat .
evitanretlA l ,y ew ees taht 319.0 si neewteb eht evitalumuc ibaborp li eit s 678.0 na d
,000.1 niaga itluser ng ni 8 setunim sa eht eneg ra et d it me
elbaT :6 emiT neewteb slavirrA oitanimreteD n
 ecivreS semit rof lla 20 sremotsuc era nwohs in bat le .7 esehT vres i ec t semi rew e
areneg t de desab no eht olodohtem gy debircsed ab ,evo rehtegot htiw eht dia fo elbat 5.
ehT tsrif s’remotsuc res v eci emit si 4 setunim esuaceb eht modnar stigid 84 llaf ni eht
tekcarb 16 - ,58 ro evitanretla ly esuaceb eht d evire d modnar rebmun 48.0 laf ls eewteb n
eht evitalumuc seitilibaborp 16.0 dna 58.0 .

elbaT :7 ecivreS semiT etareneG d
 ehT esse n ec fo a launam noitalumis si eht noitalumis t ba le. esehT selbat era sed i eng d
rof eht melborp ta nah d, htiw snmuloc dedda ot rewsna eht snoitseuq .desop hT e
noitalumis elbat rof eht elgnis - lennahc euq u ,e hs o ,nw ni elbat 8 taht si na ex noisnet of
elbat 2. ehT tsrif pets si to ezilaitini eht elbat by fi gnill ni sllec rof eht tsrif otsuc m re .
 ehT tsrif remotsuc si demussa ot evirra at t emi .0 ecivreS snigeb yletaidemmi dna
sehsinif ta emit .4 ehT remotsuc saw ni eht s metsy rof 4 .setunim retfA eht srif t
,remotsuc neuqesbus t swor ni eht elbat era b desa no eht modnar n rebmu s of r
lavirraretni emit dna es r eciv emit na d eht pmoc l noite it me fo t eh p ver ious otsuc m .re
roF ex ,elpma eht noces d remotsuc sevirra ta emit .8 ,suhT eht revres saw eldi rof 4
unim t se . gnippikS nwod ot eht htruof ,remotsuc ti si nees taht siht remotsuc devirra at
emit 51 tub dluoc ton eb s devre nu t li t emi 81 . sihT remotsuc dah ot tiaw in eht eueuq
m3rof i setun . sihT ssecorp seunitnoc rof lla 02 cu ts remo s.
elbaT :8 talumiS noi elbaT rof eht qu gniue p bor el m

1. ehT egareva gnitiaw emit rof a motsuc er si unim8.2 t se . siht si denimreted in t eh
gniwollof rennam :
latoT emit tsuc sremo aw it ni eueuq nim( )
revA a eg gnitiaW emiT =
latoT on . fo remotsuc s
= 56 = 8.2 mi un et s
02
2. ehT ilibaborp ty th ta a uc s remot sah ot tiaw ni eht q eueu si 56.0 . sihT is ted erm deni
ni eht gniwollof m nna er:
ytilibaborP )tiaw( = rebmun fo sremotsuc who tiaw
latoT rebmun fo motsuc e sr
31
= = 56.0
02

3. ehT noitcarf fo eldi emit fo eht s vre er is 12.0 . sihT si denimreted in t eh
gniwollof :rennam
latoT eldi emit fo revres m( )setuni
ilibaborP ty fo revreseldi =
latoT nur emit fo is talum i no unim( t )se
81
= = 12.0
68
ehT ilibaborp ty of eht revres ieb ng ub sy si eht co tnemelpm fo ,12.0 ro .0 79.
4. ehT egareva s ecivre emit si 4.3 m ,setuni ed t re m deni sa of l wol :s
latoT res eciv time
egarevA ecivres emit m( i un t )se =
latoT rebmun fo motsuc ers
86
= = 4.3 m etuni s
02
sihT tluser nac eb derapmoc htiw eht ex detcep s ecivre emit by idnif ng the aem n
fo eht ecivres - emit noitubirtsid gnisu t eh auqe t oi n
)s(E (psΣ= )s
ppA l iy ng eht ex detcep - eulav qe u noita ot eht di noitubirts ni elbat 7.2 gi sev na
ex detcep ecivres emit :fo
= )01.0(1 + 2 )02.0( + 3(0 )03. )52.0(4+ + )01.0(5 + 05.0(6 )
2.3= m etuni s

hT e detcepxe ecivres t emi si thgils ly rewol t nah eht egareva emit ni eht
oitalumis n. ehT regnol si ,noitalum eht resolc eht egareva lliw eb ot E (S).
5. ehT egareva emit eb t neew slavirra si 3.4 mi un t se . sihT retedsi im den in eht of ll wo i gn
:rennam
muS fo a ll ebsemit t eew n rra i av ls (m uni t se )
egarevA emit neewteb slavirra )setunim( =
rebmuN fo slavirra - 1
28
= = unim3.4 t se
91
enO si detcartbus morf eht rotanimoned b esuace eht tsrif lavirra si sa s demu to
rucco ta emit .0 sihT tluser nac be apmoc r de to eht ex detcep emit teb w nee a rr i av ls by
gnidnif eht naem of eht d etercsi finu o mr dist ubir it no ohw se ne d op in st ra ae = 1 dna b = 8.
sinaemehT nevig by
a + b 1 + 8
E )A( = = 5.4= m etuni s
2 2
ehT ex etcep d emit teb w nee slavirra si ls i thg ly hi ehg r aht n eht eva ar eg . ,revewoH
sa eht noitalumis semoceb ,regnol eht egareva v eula fo eht emit teb w nee slavirra will
hcaorppa eht laciteroeht ,naem E )A( .
6. ehT av egare itiaw ng t emi fo esoht ohw w ia t is 3.4 mi .setun sihT si denimreted ni ht e
gniwollof :rennam
egarevA itiaw ng emit fo latot emit sremotsuc tiaw in ueuq e
esohT ohw tiaw etunim( s) =
latoT rebmun fo sremotsuc ohw aw it

65
= = unim3.4 t se
31
7. ehT egareva emit a remotsuc sdneps ni eht s metsy si 2.6 .setunim sihT nac eb
denimreted ni owt wa .sy ,tsriF eht itatupmoc on nac be hca i deve by eht gniwollof
hsnoitaler i :p
egarevA emit remotsuc latot emit sremotsuc dneps ni eht etsys m
ehtnisdnepS s sy te =m
latoT mun reb fo otsuc m re s
421
= = unim2.6 t se
02
ehT dnoces way fo moc p gnitu siht emas tluser si ot ezilaer taht eht gniwollof er l pihsnoita
sum t :dloh
egarevA emit remotsuc egareva emit remotsuc egareva emit suc tomer
sdnepS ehtni s sy tem = sdneps nitiaw g ni eht qu eue + sdneps ni vres ice
morF idnif n sg dna1 4 this stluser ni :
egarevA emit remotsuc s sdnep ni eht s metsy = .2 8+ 4.3 = 2.6 mi un t se .
ELPMAXE :2 - ehT elbA rekaB raC hop orP elb m
 sihT ex elpma setartsulli eht noitalumis erudecorp nehw ht ere si erom naht eno s vre ice
hc a nn el. redisnoC a evird - ni uatser r tna erehw ac r spoh ekat sredro dna gnirb doof ot ht e

ac r. sraC evirra ni eht m renna nwohs in t ba le .1 erehT era owt hrac spo - elbA dna aB k re .
elbA si retteb elba to do eht boj dna krow s a bit saf ter t ah n B ka e .r The noitubirtsid fo
rieht ecivres semit era sh nwo batni l se 2 dna 3.
 ehT noitalumis eecorp ds ni a rennam ralimis ot ex elpma ,1 ex tpec taht ti sti m ero
elpmoc x esuaceb fo eht t ow srevres . A iyfilpmis ng elur si taht bA le steg eht suc t remo if
htob spohrac era eldi . ,spahreP elbA sah iroines ty. ehT( noitulos dluow eb reffid tne fi ht e
noisiced erew edam ta modnar ro yb any rehto ur l ).e

 ereH ereht era erom ev :stne a remotsuc ,sevirra a remotsuc snigeb ecivres morf ,elba a
suc remot setelpmoc s ecivre morf bA l ,e a tsuc o rem snigeb vres i ec rf om ,rekaB dna a
remotsuc setelpmoc ecivres morf rekaB . ehT mis u noital elbat si nwohs ni elbat 4.
 retfA eht tsrif remotsuc , eht sllec rof eht rehto sremotsuc tsum eb ab sed no cigol dna
rof salum . roF ex ,elpma eht kcolc“ emit fo ar avir l” ni eht wor rof eht ces o dn uc st remo si
detupmoc sa :swollof
C+1D=2D 2
 ehT cigol ot etupmoc ohw steg a nevig ,remotsuc dna nehw taht ecivres ,snigeb si rom e
elpmoc x. ehT cigol goes sa swollof wh ne a uc remots :sevirra fi eht tsuc o rem sdnif lba e
,eldi eht remotsuc igeb ns ecivres etaidemmi ly wi ht .elba fI elba si ton eldi tub rekab ,si
neht eht remotsuc nigeb s ecivres etaidemmi ly htiw rekab . fI htob era ub s ,y eht otsuc m re
snigeb ecivres htiw eht tsrif s revre ot b emoce eerf .
ehT sisylana fo elbat 4 stluser ni the f lo lowin :g
1. revO eht 26 - etunim p doire elba saw ub sy %09 fo eht emit .
2. rekaB saw ub sy no ly 6 %9 emotehtfo . ehT ytiroines elur speek rekab ssel ub sy.
3. eniN fo lavirra62eht s dah to wa ti . ehT av egare gnitiaw emit rof lla sremotsuc saw
ylno tuoba 24.0 ,etunim hcihw si ev ry llams .
4. esohT enin ohw did evah ot tiaw no ly detiaw an reva a eg fo 22.1 im setun , hcihw is
etiuq wol .
5. nI ammus r ,y siht s metsy smees llew decnalab . enO revres c tonna dnah le lla eht srenid ,
dna eerht revres s luow d baborp ly be oot am ny. gniddA an lanoitidda s evre r dluow
ylerus der u ec eht gnitiaw emit ot raen ly orez . Ho revew , eht tsoc fo gnitiaw dluow ah ve
ot eb etiuq hgih ot yfitsuj na lanoitidda vres er.
lbaT e :4 noitalumiS elbaT f ro eht raC hop E max ple

4.2 noitalumiS fo yrotnevnI S tsy ems
nA tnatropmi ssalc fo noitalumis smelborp sevlovni otnevni ry s sy t sme .
 A elpmis yrotnevni s sy t me si nwohs ni gif 1. sihT yrotnevni s sy t me sah a p cidoire revi we
fo el n htg ,N ta hcihw emit eht otnevni ry el vel si cehc k .de nA ro d re si m eda ot rb ing ht e
yrotnevni pu ot eht el vel M. tA eht dne fo eht weiver ,doirep na o redr q nau it t ,y ,1Q is
ecalp d. nI siht yrotnevni metsys eht dael emit si orez . dnameD si nwohs as gnieb rofinu m
revo eht emit doirep in gif .1 nI ilautca t ,y sdnamed era ton lausu ly mrofinu dna od
etautculf ov re t .emi One ilibissop ty si taht d sdname lla rucco ta eht be nnig ing of ht e
cy elc . rehtonA si taht eht dael emit si modnar fo some sop ti evi l gne th.
 ecitoN taht ni eht s oce nd c ,elcy the tnuoma ni i yrotnevn spord b wole ez ,or acidni t gni a
trohs age. nI fig ,1 th ese u stin era b rokca d dere . nehW eht ro d re irra v ,se eht d dname rof ht e
deredrokcab smeti si s deifsita tsrif . oT diova ohs r ,segat a bu ,reff ro safet ,y kcots luow d
deen ot eb deirrac .
 raC r gniy kcots ni nevni t yro sah na detaicossa co ts detubirtta ot eht tseretni diap no eht
sdnuf deworrob ot buy t eh item .s ehtO r stsoc can eb lp a dec in the c ra ryi gn or gnidloh
tsoc :nmuloc gnitner fo st egaro ,ecaps irih ng raug ds, dna os no .

 nA evitanretla ot rac r gniy hgih otnevni ry si ot ekam erom f neuqer t ,sweiver na d
tneuqesnoc l ,y erom tneuqerf sesahcrup ro .stnemhsinelper sihT sah na detaicossa :tsoc
eht gniredro .tsoc ,oslA ereht si a tsoc in eb ing .trohs regraL seirotnevni aerced se ht e
seitilibissop fo egatrohs s. esehT stsoc tsum eb dedart fo f ni redro ot eziminim eht t lato
tsoc fo na otnevni ry s metsy .
 ehT latot tsoc fo na yrotnevni s metsy si eht erusaem fo rofrep m ecna . sihT nac eb detceffa
yb eht ilop cy itanretla v .se roF ex ,elpma ni gif ,1 eht noisiced rekam nac lortnoc t eh
am x mumi yrotnevni ,level ,M dna eht c ,elcy N.
 nI na ,M( )N otnevni ry sys ,met eht ev stne taht yam oc ruc :era eht dnamed f ro items ni t eh
,yrotnevni eht weiver fo eht yrotnevni ,noitisop dna eht tpiecer fo na ro ed r at t eh dne of
hcae weiver .doirep nehW eht dael emit si ,orez sa ni gif ,1 eht tsal owt neve ts rucco
uoenatlumis ls y.
• ehT repapsweN s’relleS melborP
 A lacissalc otnevni ry melborp snrecnoc eht esahcrup dna elas of
repapswen s. ehT repap s relle bu sy eht srepap rof 33 stnec hcae dna slles
meht rof 05 stnec hcae . apsweN p sre ton dlos ta eht dne of t eh day a er os ld
sa parcs for 5 stnec cae h. srepapsweN c na eb p ru desahc ni seldnub fo 01 .
,suhT eht repap s relle nac buy ,05 ,06 dna os no .
 erehT era eerht t sepy fo dsweN a ,s’y doog“ ,” ”,riaf“ dna roop“ ,” htiw
seitilibaborp fo ,53.0 ,54.0 dna ,52.0 evitcepser l .y ehT noitubirtsid fo
srepap dednamed no hcae fo eseht da sy si nevig ni elbat .51.2 ehT
melborp si ot enimreted t eh lamitpo rebmun of pa srep t eh n apswe p re s elle r
dluohs esahcrup . sihT wi ll eb dehsilpmocca by si gnitalum sdnamed rof 20
syad dna gnidrocer rp o stif morf selas hcae day.
ehT stiforp era nevig yb eht ollof w gni er l oita ns pih :

 mroF eht melborp ats t ,tneme eht never ue morf selas si 05 stnec rof each
repap .dlos ehT tsoC 9 fo srepapswen si 33 tnec s rof ea hc pap er
hcrup ased. The tsol tiforp morf ex ssec dnamed si 71 stnec rof hcae p epa r
dednamed taht dluoc ton eb .dedivorp cuS h a sh egatro tsoc si mos e ahw t
laisrevortnoc ub t sekam eht melborp cum h erom seretni t gni . ehT s gavla e
eulav fo parcs ap p sre si 5 nec ts ea hc .
 selbaT 6 dna 7 ivorp de eht modnar -di tig stnemngissa rof eht t sepy of
s’yadsweN dna eht sdnamed rof esoht dsweN a s’y .
elbaT :6 modnaR tigiD tnemngissA rof Type fo N dswe ay

 nO eht tfif h day the dnamed si retaerg th na ht e s ppu l .y ehT never eu
morf selas si .53$ ,00 ecnis no ly 07 srepap era elbaliava rednu th si
cilop y. An lanoitidda 20 repap s dluoc ah ve be ne s .dlo ,suhT a sol t
tiforp fo 04.3$ *02( 17 )stnec si .dessessa ehT iad ly rp o tif si
denimreted sa :swollof
tiforP = 00.53$ - 01.32$ - 04.3$ + 0 = 5.8$ 0
 ehT rp o tif rof eht 20-d ya doirep si eht sum fo eht da li y forp ti ,s
9.471$ 0. ti nac osla be detupmoc morf eht slatot rof t eh 02 da sy of ht e
noitalumis sa of l wol :s
latoT tiforp = 546$ - 4$ 62 - 31$ 06. + 05.5$ = 1$ 7 09.4
 nI ,lareneg ecnis eht er s stlu fo eno day are tnednepedni fo esoht fo
suoiverp da ,sy tnevni ory p smelbor fo siht t epy era ae is er t nah
gnieueuq smelborp .
noitalumiS fo na ,M( )N nI ev n yrot S tsy em
 esoppuS taht eht mumixam yrotnevni ,level ,M si 11 stinu dna eht ver i we ,doirep
,N si 5 da sy . ehT melborp si ot ,etamitse by is m ,noitalu eht av re a eg dne i gn tinu s
ni otnevni ry na d eht nu rebm of da sy ehw n a s roh t ega dnoc ti noi cco urs. hT e
noitubirtsid fo eht rebmun fo stinu dednamed p re yad si nwohs ni t ba le 9. nI iht s
ex ,elpma dael - emit si a modnar ,elbairav sa nwohs ni elbat 01 . emussA taht sredro
era pl eca d ta eht esolc of ssenisub dna era deviecer rof otnevni ry ta eht innigeb ng
sa denimreted yb eht dael - emit .
elbaT :9 modnaR stigid emngissa nts f ro da li y de am dn
.tpeD ESIfo , TIBJS 24

etoN : R refe cy elc 4,3,2 ,5 morf txeT koob p ega no 74 .
 oT ekam na etamitse fo eht aem n stinu ni idne ng otnevni r ,y am ny c cy l se dluow
evah ot eb .detalumis roF sesoprup fo siht ,elpmaxe no ly if ve c selcy lliw eb
nwohs . ehT redaer si deksa ot eunitnoc eht ex elpma sa na ex esicre ta eht dne fo
tpahceht re .
 ehT modnar -di tig stnemngissa rof iad ly dnamed dna dael emit era wohs n ni eht
tsomthgir snmuloc fo selbat 9 dna .01 hT e gnitluser noitalumis elbat si nwohs ni
elbat ehT.11 noitalumis sah eeb n detrats htiw eht otnevni ry level ta 3 inu ts dna na
redro fo 8 stinu cs h lude ed ot evirra ni 2 da sy it em .
 gniwolloF eht noitalumis elbat rof lareves celes t de syad acidni t se woh t eh secorp s
repo ates. The ro d re for 8 stinu si elbaliava no eht gninrom fo the ht i dr day of t eh
tsrif cyc l ,e gnisiar eht in yrotnev el v le morf 1 tinu ot 9 ;stinu sdnamed gnirud ht e
redniamer fo eht tsrif c elcy decuder eht gnidne i yrotnevn el v le ot 2 stinu no eht
htfif day. suhT , na o edr r rof 9 inu ts w sa p al dec . T eh ael d emit rof siht dro er aw s 1
ad y. ehT redro fo 9 stinu saw da d de ot otnevni ry on eht inrom ng of day 2 of c cy le
2.

 ecitoN taht eht gninnigeb yrotnevni no eht dnoces yad of eht driht c elcy w sa z ore .
nA redro for 2 stinu no taht day l de ot a rohs t ega dnoc ti .noi ehT inu ts ew re
deredrokcab on taht day dna eht en xt da ;;y osla on eht inrom n fog da o4y f c cy le 3
ereht was a b gninnige yrotnevni fo 9 stinu taht erew kcab o deredr dna the 1 nu it
dednamed taht day decuder eht idne ng otnevni ry to 4 stinu .
 desaB no evif c selcy of ,noitalumis eht egareva en gnid otnevni ry si pa p or x etami ly
5.3 )52/88( inu ts. nO 2 fo 52 syad a egatrohs dnoc i noit ex si t de .

eW/srH e :k 40 xE am sruoH : 30
TRAP – A
TINU – 2 6 oH sru
lareneG ,selpicnirP oitalumiS n Softw :era
- stpecnoC ni etercsiD -E tnev Simulat noi
- ehT tnevE - gniludehcS / emiT - ecnavdA mhtiroglA
- dlroW sweiV
- launaM noitalumis gnisU tnevE gniludehcS
- tsiL gnissecorp
- miS noitalu ni J ;ava noitalumiS in G SP S

UN TI 2
SELPICNIRPLARENEG
oitcudortnI n
• sihT retpahc ed v spole a nommoc wemarf o kr rof eht gniledom fo elpmoc x s sy met s
gnisu csid r ete -ev tne talumis i no .
• It srevoc eht cisab gnidliub kcolb s fo lla di cs rete- neve t is mulat noi dom e :sl ne t ti i se
dna ,setubirtta seitivitca dna stneve .
• In ercsid te-ev tne ,noitalumis a s metsy si om d dele ni smret fo sti state at ea hc p nio t in
;emit eht seititne taht ssap hguorht eht s metsy na d eht seititne taht per -j er s tne s metsy
;secruoser dna eht seitivitca dna stneve taht esuac s metsy etats ot chan eg .
• sihT retpahc slaed ex lc u evis ly htiw d ,cimany ts o citsahc s metsy .e.i( vni o vl gni t mi e
dna gniniatnoc modnar )stnemele hcihw segnahc ni a etercsid rennam .
1.2 stpecnoC ni etercsiD - tnevE oitalumiS n
• ehT tpecnoc fo a s sy t me dna a ledom fo a s metsy erew id s dessuc feirb ly in eilrae r
tpahc re s.
• sihT noitces ex sdnap no eseht c stpecno dna spoleved a krowemarf rof eht
tnempoleved fo a etercsid - tneve ledom of a s metsy .
• ehT rojam oc n stpec era b feir ly denifed dna neht detartsulli htiw ex :selpma
• etsyS :m A noitcelloc fo seititne e( . ,.g poep le na d senihcam ) t ah t ii t ego th re over
emit ot hsilpmocca eno ro erom slaog .

• ledoM : nA tcartsba rep noitatneser fo a s metsy , lausu ly noc t gninia rts u ,larutc
lacigol , ro tam h lacitame spihsnoitaler hcihw d ebircse a s sy tem in te mr s of st eta ,
seititne dna rieht ,setubirtta ,stes secorp s ,se tneve s, ,seitivitca dna led a sy .
• metsyS etats : A noitcelloc fo v selbaira th ta noc t nia lla eht noitamrofni n ssece ary
ot ebircsed eht s tametsy an emity .
• :ytitnE Any tcejbo or tnenopmoc ni eht s metsy hcihw seriuqer ex lp icit
erper s noitatne ni eht ledom ,.g.e( a s ,revre a tsuc o ,rem a ihcam n )e .
• :setubirttA The seitreporp fo a nevig itne ty e( . .g , eht iroirp ty of a v ,remotsuc ht e
gnituor fo hguorhtboja boja s )poh .
• iL st: A noitcelloc fo tnenamrep( ly ro iraropmet ly) detaicossa seititne ro d dere ni
emos igol c la noihsaf s( u hc sa lla sremotsuc cu tnerr ly ni a gnitiaw ,enil ro d dere by
tsrif ,emoc tsrif ,devres ro yb p iroir t )y .
• tnevE : nA oenatnatsni us rucco r ecne th ta ahc n seg eht etats fo a s etsy m sa na
lavirra fo a wen )remotsuc .
• tnevE :eciton A cer o dr fo na ev tne ot rucco ta t eh tnerruc ro emos erutuf it ,em
gnola htiw any cossa i deta atad secen sary ot ex etuce eht ;tneve ta a ,muminim eht
drocer in sedulc eht ev tne t epy dna eeht v tne t emi .
• tnevE :tsil A tsil fo tneve seciton rof tuf u er ,stneve o deredr by time fo
;ecnerrucco osla nwonk sa eht erutuf ev tne tsil F( E )L .
• ivitcA t :y A noitarud fo emit fo deificeps tgnel h ,.g.e( a ecivres emit ro avirra l
,)emit ihw hc si wonk n nehw ti snigeb guohtla( h ti may eb d fe i en d in ter sm fo a
lacitsitats dist tubir i )no .
• yaleD : A noitarud fo ti em fo deificepsnu etinifedni gnel t ,h hw i hc is on t nwonk
litnu ti sdne e( . .g , a uc s 'remot s led ay ni a tsal -i ,n tsrif - uo t wai gnit li en hw i ,hc
nehw ti ,snigeb sdneped no aerutuf rri av l )s .
• kcolC : A elbairav erper s gnitne detalumis emit . · ehT erutuf tneve tsil si deknar by
eht tneve emit dedrocer in eht tneve ton i ec .

OITALUMISDNAGNILLEDOMMETSYS N 01 SC 28
 nA ivitca ty t lacipy ly stneserper a ecivres emit , na lavirraretni ,emit ro any rehto
gnissecorp emit esohw noitarud sah neeb deziretcarahc dna denifed by eht reledom .
 nA s’ytivitca noitarud yam eb ceps i deif ni a un m reb fo wa :sy
1. citsinimreteD - rof ,elpmaxe syawla tcaxe ly 5 m setuni .
2. lacitsitatS - rof ex ,elpma sa a modnar d war morf gnoma 7,5,2 htiw qe u la p eitilibabor s.
3. A noitcnuf gnidneped no s metsy selbairav dna / ro itne ty setubirtta .
 ehT noitarud fo na ytivitca si elbatupmoc morf sti iceps noitacif ta eht atsni nt ti snigeb .
 A led a s'y noitarud si ton deificeps by eht mo reled daeha fo ,emit tub rehtar si
denimreted by s metsy snoitidnoc .
 A led ay si semitemos dellac a lanoitidnoc w ,tia elihw na ivitca ty si dellac dnocnu ti anoi l
tiaw .
 ehT noitelpmoc fo na ca t ivi ty si na ,tneve fo t ne dellac amirp r tnevey .
 ehT noitelpmoc fo a d yale si semitemos dellac a lanoitidnoc ro adnoces ry e tnev .
ELPMAXE 1.3 elbA( dna ,rekaB veR isi et d)
redisnoC eht elbA - rekaB pohrac s metsy fo Ex elpma .2.2 A etercsid - tneve ledom sah t eh
gniwollof tnenopmoc s:
metsyS S tat e
LQ ,)t( eht rebmun of srac gnitiaw to eb se devr ta t emi t
LA ,)t( 0 ro etacidniot1 iebelbA ng ubroeldi s ittay me t
BL ,)t( 0 or etacidniot1 iebrekaB n ubroeldig sy at it me t
tnE i eit s

rehtieN eht sremotsuc ,.e.i( )srac ron eht srevres deen ot eb ex ticilp ly er p ,detneser ex tpec
ni smret fo eht etats v ra i ,selba sselnu niatrec suc t remo segareva era derised c( om ap re Exam elp s
dna4.3 5.3 )
stnevE
tnevelavirrA
ecivreS noitelpmoc by elbA
ecivreS noitelpmoc by rekaB
seitivitcA
lavirraretnI ,emit enifed d ni elbaT 11.2
ecivreS emit by ,elbA denifed ni elbaT 1.2 2
ecivreS emit by ,rekaB denifed ni lbaT e 1.2 3
De yal
A emotsuc r s' tiaw ni eueuq litnu elbA ro rekaB b semoce rf ee.
2.2 ehT tnevE - emiT/gniludehcS - ecnavdA glA o tir hm
 ehT msinahcem rof gnicnavda noitalumis emit dna gnieetnaraug th ta lla stneve rucco in
tcerroc lacigolonorhc ro d re si desab no eht erutuf tneve tsil F( E )L .
 sihT tsil sniatnoc lla tneve seciton rof stneve taht evah neeb cs h delude ot rucco at a uf ture
time.
 tA yna nevig emit ,t eht LEF sniatnoc lla iverp o su ly s deludehc utuf re stneve dna rieht
detaicossa tneve semit

OITALUMISDNAGNILLEDOMMETSYS N 01 CS82
 ehT LEF si ro d dere by tneve ,emit gninaem taht t eh stneve a er arra n deg igolonorhc c la l ;y
taht tneveeht,si ti sem as ti fs y
t =<1t< 3t=<2t =< .… , =< tn
t si eht eulav fo C COL K, eht tnerruc v eula fo sim alu t de t emi . ehT tneve detad htiw emit
1t si dellac eht tnenimmi ;tneve taht i ,s it si t eh en xt tneve w li l .rucco retfA eht s metsy
tohspans ta si noitalum time
C KCOL == t sah neeb u ,detadp eht C KCOL si ad decnav ot noitalumis ti em
C KCOL =_ 1t dna eht tnenimmi tneve eciton si devomer orf m eht FEL
dna eht tneve detucexe .. sihT ssecorp er p stae litnu eht is noitalum is revo .
 ehT euqes n ec fo snoitca hcihw a rotalumis tsum mrofrep ot da v ecna the cl kco s sy tem
tohspans si dellac eht tneve - emit/gniludehcs - avda n ec al htirog m
dlO s metsy tohspans tta ime t
tnevE - emit/gniludehcs - ecnavda rogla ithm
petS 1. evomeR eht eve nt eciton rof eht tnenimmi neve t
tneve( ,3 emit t morf) EP L
petS 2. ecnavdA OLC CK ot tnenimmi tneve emit

,.e.i( avda n ec C KCOL fr mo r ot )1t .
petS 3. Ex etuce tnenimmi :tneve etadpu s etsy m state,
egnahc ytitne ,setubirtta dna tes pihsrebmem sa n dedee .
petS 4. etareneG erutuf stneve fi( assecen r )y na d
ecalp rieht tneve seciton no LEP deknar by ev tne emit .
E( x :elpma tnevE 4 ot rucco ta emit ,*t erehw 2t < *t < .3t )
petS 5. etadpU evitalumuc scitsitats dna sretnuoc .
weN s metsy tohspans ta ti em 1t
erugiF 2.3 gnicnavdA noitalumis ti em dna gnitadpu s tsy em i gam e
 ehT eganam m tne fo a tsil si dellac tsil ssecorp i gn
 ehT rojam tsil issecorp ng po snoitare ep r demrof no a LEF era lavomer of eht mmi i tnen
,tneve noitidda fo a wen tneve ot eht ,tsil dna lanoisacco ly r lavome fo emos tneve (c ella d
noitallecnac fo na ev )tne .
 sA eht tnenimmi tneve si lausu ly ta eht pot of eht ,tsil sti avomer l is sa fe fici tne as
lbissop e. noitiddA fo a wen tneve dna( tallecnac i no fo na dlo )tneve seriuqer a hcraes fo
eht tsil . ehT lavomer dna noitidda fo stneve morf t eh PEL si detartsulli ni erugiF 2.3 .
• nehW tneve 4 ,yas( na lavirra )tneve htiw tneve emit *t si g detarene ta pets ,4 eno
elbissop yaw ot enimreted sti tcerroc noitisop no eht FEL si ot tcudnoc a t po -
:hcraesnwod
fI 4tneveecalp,2t<*t a tt eh t po fo eht FEL.
fI 2t < *t < eecalp,3t vent 4 dnoces no eht l tsi .
alp,4t<*t<,3tfI ce eve tn 4 t rih d no t eh tsil .

fI nt < ,*t tneve 4 tsal no t eh li ts .
• rehtonA way si ot dnoc u tc a mottob - pu s ae r hc .
 ehT metsys tohspans ta emit 0 si denifed by the laitini snoitidnoc dna eht eg ne noitar of
eht os - dellac suonegoxe stneve .
 ehT dohtem fo itareneg ng na ex lanret irra v la erts a ,m dellac ippartstoob ng.
 evE ry noitalumis tsum evah a gnippots ,tneve h ere ellac d ,E hw ich fed i en s woh l gno ht e
noitalumis iw ll nur . erehT era lareneg ly t ow wa sy ot :noitalumisapots
1. tA emit ,0 eludehcs a ts op is m noitalu neve t at a s ficep i de uf t eru it em T .E
,suhT erofeb gnitalumis , ti si nwonk taht eht talumis i no liw l nur revo t eh
emit avretni l [ ,0 ET ]. :elpmaxE etalumiS a boj pohs rof ET = 04 oh u sr .
2. nuR htgnel ET si denimreted by eht noitalumis i est lf. eneG r la l ,y ET si ht e
emit fo errucco n ec fo so em deificeps ev tne E. :selpmaxE ET si eht it em fo
eht ht001 ecivres noitelpmoc ta a rec t nia ivres ce retnec . TE is eht it em fo
nwodkaerb of a elpmoc x s etsy m.
VdlroW3.2 i swe
• nehW gnisu a noitalumis egakcap or neve wh ne gnisu a aunam l si ,noitalum a
reledom stpoda a wo dlr weiv ro noitatneiro for ed v gnipole a om d le .
• esohT tsom tnelaverp era eht tneve iludehcs ng wo dlr ,weiv eht secorp s- tni e tcar noi
,weivdlrow dna eht ytivitca - gninnacs dlrow weiv .
• nehW nisu g a gakcap e taht troppus s ht e ssecorp - oitcaretni n ,hcaorppa a
noitalumis ana l tsy skniht ni smret fo secorp s se .
• nehW gnisu eht ev tne - gniludehcs ,hcaorppa a si noitalum ana l tsy oc n nec t etar s on
stneve dna rieht tceffe no metsys etats .
• ehT ssecorp - noitcaretni hcaorppa si ralupop esuaceb fo sti evitiutni ,laeppa dna
esuaceb eht noitalumis kcap a seg taht tnemelpmi ti wolla na ana l tsy ot rcsed i eb eht
ssecorp wolf ni smret fo hgih - el v le colb k ro ten w kro stcurtsnoc .
• htoB eht tneve - iludehcs ng dna eht secorp s- noitcaretni sehcaorppa esu a / elbairav
ecnavdaemit .
• ehT ivitca ty-sc inna ng caorppa h sesu a if x de ti em tnemercni na d a ur le- desab
hcaorppa ot ediced wh rehte any seitivitca nac b nige ta hcae tniop ni umis lat de
emit .
• ehT erup ivitca ty nacs n gni rppa o hca h sa neeb deifidom by wh ta si ac l del eht
eerht - esahp hcaorppa .

• nI the eerht - ahp se rppa o ,hca ev stne era isnoc dered ot eb ivitca ty ud r noita - rez o
emit stinu . htiW siht ,noitinifed seitivitca era dedivid otni owt getac o seir c della B
Cdna .
 B :seitivitca seitivitcA dnuob ot ;rucco lla amirp ry
 C :seitivitca seitivitcA ro stneve taht era lanoitidnoc nopu rec t nia
snoitidnoc gnieb eurt .
• htiW t .eh eerht - esahp hcaorppa eht noitalumis sdeecorp htiw detaeper ex noituce
fo eht eerht ph sesa litnu ti is pmoc l :dete
 esahP :A evomeR eht tnenimmi tneve morf eht FEL dna avda n ec eht kcolc
ot sti tneve it m .e evomeR yna rehto stneve morf eht FEL taht evah eht
ittneve me.
 esahP :B etucexE lla B-type stneve taht erew er m devo morf eht FEL.
 esahP :C nacS eht idnoc t snoi taht reggirt hcae C-ty ep ac it iv ty na d ac it av te
yna esohw snoitidnoc ra e tem . nacseR litnu on ad lanoitid C-type seitivitca
nac nigeb ro stneve ucco r.
• ehT eerht - esahp hcaorppa sevorpmi eht ex noituce neiciffe cy fo eht ivitca ty
gninnacs dohtem .
ELPMAXE 2.3 elbA( dna aB k ,re B ca k iagA n)
gnisU eht eerht - esahp ,hcaorppa eht snoitidnoc rof gninnigeb hcae ivitca ty ni esahP C era :
tivitcA y noitidnoC
ecivreS emit by bA le A remotsuc si ni eueuq dna elbA si ,eldi
emitecivreS b rekaBy A remotsuc si ni ,eueuq rekaB si ,eldi
ysubsielbAdna .
5.2 launaM noitalumiS gnisU tnevE ehcS ud gnil

• nI na tneve -s iludehc ng ,noitalumis a noitalumis elbat si desu ot er droc t eh
evisseccus metsys stohspans sa emit secnavda .
• steL redisnoc eht ex elpma fo a ecorg ry pohs hcihw sah no ly eno ch uokce t
etnuoc r.
elpmaxE 3.3 elgniS( - lennahC euQ u )e
• ehT s metsy stsisnoc fo t esoh remotsuc s ni eht gnitiaw enil ulp s eht no e (if any)
gnikcehc tuo .
• ehT ledom sah eht ollof w gni stnenopmoc :
 metsyS etats ,)t(QL( L ,))t(S ehw re )t(QL si eht rebmun fo otsuc m sre in t eh
gnitiaw ,enil dna (SL t) si eht rebmun ieb ng res v de )1ro0( at it me t.
 tnE i eit s ehT revres dna sremotsuc era ton ticilpxe ly edom l ,de ex tpec ni mret s
fo eht etats selbairav ba o ev .
 stnevE
lavirrA A( )
erutrapeD )D(
gnippotS tneve (£ ,)" s deludehc ot rucco ta ti em 06 .
 tnevE seciton
( i,A ). R erpe s gnitne na lavirra tneve ot cco ur ta uf t eru it em t
,D( t ,) er p itneser ng a remotsuc erutraped ta erutuf ti em t
,£( ,)06 er p itneser ng eht s noitalumi - pots tneve at erutuf it em 06
 eitivitcA s
retnI lavirra ,emit enned d ni elbaT 6.2
ecivreS ,emit ifed n de ni elbaT .2 7
 eD l ya
remotsuC emit tneps ni tiaw i gn il en .
• nI siht ,ledom eht FEL w lli syawla noc t nia rehtie t ow ro eerht tneve eciton s.

• tceffeehT fo eht lavirra dna erutraped stneve saw tsrif nwohs ni Fi ug r se eb l wo
giF (1 A :) noitucexE fo eht lavirra tneve .

giF )B(1 : noitucexE fo eht traped u er event.

• laitinI snoitidnoc are aht t eht tsrif remotsuc evirra s ta emit 0 dna be snig s re v eci .
• sihT si detcelfer ni T elba woleb by the s sy t me tohspans ta t mi e z ore
(C KCOL = htiw,)0 )0(QL ,0= SL ,1=)0( dna b ahto eerutraped v tne
dna lavirra tneve no eht LEF .
• ehT noitalumis si udehcs l de to st po at it me 06 .
• owT ,scitsitats revres noitazilitu dna am x mumi eueuq el n ,htg lliw eb oc ll e tc de .
• revreS noitazilitu si denifed by latot revres ub sy ti em )B(. dedivid by latot t emi eT( ).
• latoT ub sy ,emit ,B na d am x mumi eueuq gnel th ,QM lliw eb alumucca t de as ht e
noitalumis sessergorp .
• sA noos sa eht s metsy tohspans ta emit C KCOL = 0 si ,etelpmoc ht e si noitalum
beg sni .
• eht,0emittA mi nevetnenim sit ,D( )4 .
• T eh C KCOL si ecnavda d ot emit ,4 dna ,D( )4 orfdevomersi tm eh FEL.
• ecniS (SL t) = 1 rof 0 =< t =< 4 ,.e.i( eht revres saw ub sy rof 4 m uni t ,)se ht e
evitalumuc ub sy emit si aercnI s morfde 0=B to B = 4.
• By eht tneve cigol ni Fi erug ,)B(1 tes SL )4( = (0 t ocebrevreseh m )eldise .
• ehT FEL si tfel htiw no ly owt erutuf ev ,stne 8,A( ) dna ,E( )0 .
• ehT noitalumis C KCOL si en xt decnavda ot emit 8 dna na lavirra ev tne si ex detuce .
• ehT noitalumis elbat srevoc lavretni [ 9,0 ].
noitalumiS elbat rof cehc kout oc nu ret .
elpmaxE 4.3 ehT( tuokcehC - retnuoC italumiS o ,n eunitnoC d)

• esoppuS eht s metsy anal tsy serised ot amitse te eht aem n nopser se emit dna m ae n
roporp noit fo sremotsuc ohw dneps 4 or erom setunim ni eht sy ts em eht a evob m tne i deno
ledom sah ot eb m do i eif d.
 tnE i eit s ,iC( ,)t neserper t gni remotsuc iC ohw rra i dev ta t mi e t.
 tnevE seciton ,A( t, iC ,) eht folavirra remotsuc C tai uf t eru it em t
,D( ,f ,)jC eht ed p erutra of remotsuc jC ta erutuf ti em t.
 teS TUOKCEHC" IL EN ", eht tes of lla sremotsuc tnerruc ly ta the ch ce k uo t
retnuoC gnieb( devres ro gnitiaw ot eb ,)devres deredro by emit fo avirra l
• eerhT n we scitsitats era :detcelloc ,S eht us m fo sremotsuc esnopser tim se rof all
sremotsuc ohw evah ed p detra by eht tnerruc ;emit ,F eht latot rebmun fo sremotsuc hw o
dneps 4 ro erom etunim s ta eht kcehc tuo nuoc t ;re DN eht total rebmun of raped t seru pu
ot eht tnerruc si noitalum t emi .
• hT ese eerht evitalumuc s scitsitat era detadpu wh revene eht d utrape re ev tne rucco s.
• ehT noitalumis elbat si gi nev woleb
noitalumiS elbaT rof maxE p el .3 4
etatsmetsyS evitalumuC ts a citsit s

GNILLEDOMMETSYS OITALUMISDNA N 01 28SC
elpmaxE 5.3 ehT( Du pm kcurT lborP em)
• iS x pmud skcurt era desu ot luah laoc morf eht ecnartne fo a llams enim ot eht .daorliar
hcaE kcurt si dedaol yb eno fo owt sredaol . retfA ,gnidaol a kcurt etaidemmi ly sevom to
acs ,el ot be wei dethg sa noos sa elbissop . toB h eht aol d sre dna eht s elac evah a srif t
,emoc srif t res ve gnitiaw ro(enil )eueuq for rt u kc s ehT. emit at k ne ot t evar l orf m l dao er to
elacs si deredisnoc retfA.elbigilgen gnieb ew i hg t ,de a kcurt snigeb a levart t emi dna neht
drawretfa snruter ot eht redaol eueuq .
noitubirtsiD fo gnidaoL rof the Dum Tp ruck

• ehT ledom sah eht wollof i gn stnenopmoc :
 metsyS etats
,)t(QL[ ,)r(QW,)t(L )r(W ], erehw
LQ )t( = rebmun fo kcurt s ni redaol eueuq
)t(L = rebmun fo skcurt ,1,0( ro gnieb)2 aoL ded
(QW t)= n rebmu fo rt ucks ni hgiew qu ue e
)t(W = rebmun fo skcurt 0( ro )1 ieb ng wei ,dehg lla ta is talum i no t emi t
 tnevE seciton
,QLA( ,)iTD,t pmud kcurt sevirra ta aol d re qu eue (A )QL ta it em t
,LE( ,t ,)iTD pmud kcurt i sdne gnidaol )LE( ta t emi t
,WE( ,t ,)iTD pmud curt k ewsdnei i gnihg )WE( ta ti em t
 tnE i eit s isehT x ud mp t skcur (DTI, ,... DT6)
 tsiL s
redaoL ,eueuq lla skcurt gnitiaw ot nigeb idaol ng, deredro no a tsrif - ,emoc
tsrif - devres b sisa
hgieW ,eueuq lla skcurt gnitiaw ot eb ew i ,dehg deredro no a tsrif - ,emoc
tsrif - evres b sisa .
 seitivitcA idaoL ng ,emit ihgiew ng ,emit dna evart l emit .
 Del ya s leD ay ta redaol ,eueuq dna led ay ta elacs .
• ehT ivitca ty semit era at k ne morf eht iwollof ng il ts

• noitalumiS elbat rof pmuD rT uck p or blem
etatsmetsyS stsiL
c evitalumu ts at

egarevA redaoL zilitU ation = 44 / 2 = 29.0
42
egarevA elacS itazilitU on 42= / 42 = 00.1
fo.tpeD ESI , TIBJS 26

eW/srH e :k 40 xE am sruoH : 30
TRAP – A
TINU – 3 6 oH sru
tS a ledoMlacitsit s Sni i italum o :n
- eR weiv fo ygolonimret dna stpecnoc
- lufesU lacitsitats ;sledom
- etercsiD tubirtsid i no s
- suounitnoC id ts ubir it sno
- nossioP ssecorp
- laciripmE tubirtsid i sno

TINU -3 TATS I TALUMISNISLEDOMLACITS I NO
esopruP & Ov re iv we
 T eh dlrow eht dom el- ub li ed r s ee s si prob ba citsili rat eh r
naht ted ermin citsi .
 oS me itats s lacit m ledo m thgi we ll ebircsed t eh rav i ta oi ns.
 nA etairporppa ledom ac n be ed vel epo d by sa pm il ng the
onehp me non fo i etn ser t:
 Se el ct a kno nw dis irt b noitu hguorht ude cat de g eu ss se
 aM ke itse m eta of eht arap m )s(rete
 T tse f ro endoog ss of f ti
 nI siht chapte :r
 weiveR se larev im tnatrop p ilibabor ty distrib tu i sno
 erP s tne some typ laci a ilpp c ita on of eht se m sledo
1.3 weiveR fo Te olonimr gy dna oC n tpec s
 nI siht ,noitces ew lliw weiver eht wollof i gn noc ec tp s:
 etercsiD r modna rav i lba es
 suounitnoC modnar irav a selb
 evitalumuC noitubirtsid noitcnuf
 noitatcepxE
peD ESIfo.t , TIBJS 46

etercsiD modnaR selbairaV P[ r abo bility Revi we ]
 X si a d rcsi ete random va ir ba le if ht e num eb r of po iss ble
val eu s of X si finit ,e or c nuo at b yl infinit .e
 Ex pma le: C no is ed r jo sb a ivirr ng ta a j bo s oh .p
 eL t X be ht e n mu reb of j bo s a virr gni e ca h w kee at a j bo hs .po
 Rx = possi lb e v ula es fo X r( gna e sp ca e of X) = ,0{ 1, ,2 }…
 (p xi) = proba ib til y ht e ar nd mo vari ba le si xi = X(P = xi)
 p x( i), i = 1, ,2 … must s sita f :y
1. p(xi ) ≥ ,0 rof lla i
2. p(xi ) =1
 T eh c lo lec it on of iap sr [xi, p(xi) ,] i = ,…,2,1 is ca ll de eht pr abo b li ity
id strib tu i no of X, a dn p x( i) is c la l de the probability mass f nu c noit
(p fm ) of X.
suounitnoC modnaR selbairaV ilibaborP[ ty ]weiveR
 X si a unitnoc ous odnar m airav ble if ti s r egna space Rx si na etni rval
ro a c noitcello of ni tervals.
 T eh ilibaborp ty taht X eil s ni eht i etn rval a[ , ]b si nevig :yb
b
P(a ≤ X ≤ b) = f (x) xd
a
 f x( ), detoned as eht p fd of X, s ita fs ei s:
1. f (x) ≥ ,0 llarof x ni RX
2. f (x) xd =1
RX
3. f (x) = ,0 if x is ton ni RX
 reporP t sei
x0
1. P(X = x0) = ,0 esuaceb f (x) xd = 0
x0
2. P(a ≤ X ≤ b) = P(a X ≤ b) = P(a ≤ X b) = P(a X b)
i=1∑
∞
∫
∫
∫

uounitnoC s modnaR selbairaV P[ or b ba ility veR i ]we
 nevigsiecivednoitcepsninafoefiL:elpmaxE yb X, a
suounitnoc modnar elbairav htiw :fdp
x ≥ 0
esiwrehto
 X h sa an xe pon tne ial di rts i tub ion wi ht naem 2 yea sr
 rP o bab ility t tah eht ved ic ’e s il ef is teb wee 2n na d 3 y srae i :s
e- x / 2
xd = 41.0
alumuC ti ev iD ts ubir t noi cnuF t noi P[ r abo bility Revie ]w
 uC m talu i ev Dist ir ub t noi Func noit c( df) is toned ed by F )x( , ehw re (F x)
= P(X =< x)
 fI X is discre et , then F(x) = p(xi )
la l
 fI X is con it un uo ,s then x
 Pr epo rt sei
1. F is aercednon s gni noitcnuf . If a b, neht F(a) ≤ F(b)
2. il mx→∞ F(x) =1
3. il mx→-∞ F(x) = 0
 All pr bo ab li ity euq st noi ba o tu X c na be na s ew r de ni et r sm of eht c ,fd
:.g.e
P(a X ≤ b) = F(b) - F(a ,) llarof a b
SIfo.tpeD E, TIBJS 66
f (x) =
2
P 2( ≤ x ≤ 3) =
1
2 ∫
3
�0,
�2
�
e- x
,�1
/ 2
�
∫F(x) = f (t) td
-∞
∑
xi ≤x

alumuC ti ev iD ts ubir t noi cnuF t noi aborP[ b ili ty eR vi we ]
 Ex pma l :e An in ps e oitc n ed civ e ah s dc f:
e-t / 2
td =1- e- x / 2
 T eh ilibaborp ty taht t eh dev eci al s st f ro ssel naht 2 year :s
P 0( ≤ X ≤ )2 = F )2( - F( )0 = F( )2 =1- e-1
= 236.0
 T eh ilibaborp ty taht ti stsal neewteb 2 dna 3 ye ra s:
P(2 ≤ X ≤ 3) = F(3) - F( )2 = (1- e-(3/ 2)
) - (1- e-1
) = 541.0
pxE ec tat ion [ aborP b ili ty Re iv e ]w
 T eh detcepxe val eu of X si oned t de by X(E )
E(x) = xi p(xi )
all i
∞
E(x) = fx (x) xd
-∞
 a.k.a eht em ,na m, or the 1 ts
m emo nt fo X
 A erusaem fo eht ce rtn la te edn cn y
 T eh irav ance of X si d one et d by )X(V or va (r )X or σ2
 tinifeD i no : )X(V = X([E – X[E ]2
]
 A ,osl )X(V = X(E 2
) – [ (E x ]) 2
 A erusaem fo t eh s daerp ro noitairav fo ht e poss bi le v la u se fo X ar nuo d
ht e me na
 T eh dradnats de aiv t noi of X si ed n deto by σ
 :noitinifeD uqs are or to fo )X(V
 E desserpx ni eht emas tinu s as eht mean
0
F(x) =
1
2 ∫
x
∫
∑ fI X si etercsid
 fI X si c suounitno

epxE c tat i no s [ ilibaborP ty R weive ]
 :elpmaxE ehT naem fo efil of eht suoiverp noitcepsni ecived
∞
∞ ∞
E( X ) = xe- x / 2
xd = + e- x / 2
xd = 2
 oT etupmoc ecnairav of X, ew f tsri etupmoc E X( 2
):
∞
+ e- x / 2
xd = 8
0
 cneH ,e eht ecnairav dna dradnats noitaived fo eht s’ecived il fe
:era
V ( X ) = 8 - 22
= 4
σ = V ( X ) = 2
2.3 lufesU tatS itsi lac sledoM
 nI siht ,noitces lacitsitats sledom etairporppa ot so em noitacilppa ar sae a er neserp t de .
ehT saera :edulcni
 Q gnieueu smetsys
 yrotnevnI dna ylppus - niahc smetsys
 ytilibaileR dna ilibaniatniam ty
 detimiL ad at
gnieueuQ smetsyS lufesU[ edoM sl ]
 nI a gnieueuq s ,metsy lavirraretni dna ivres ce- emit
nrettap s nac eb ilbaborp ts ci rof( erom ueuq eing
xe ma ,selp es e C ah pt re 2 .)
 elpmaS lacitsitats sledom rof lavirraretni ro s ivre ce
t emi ubirtsid t :noi
 laitnenopxE :noitubirtsid if ecivres semit a er c pmo lete yl
ar odn m
 lamroN :noitubirtsid ylriaf tnatsnoc tub htiw os em ar dn om
ilibairav ty rehtie( evitisop ro agen t vi e)
 T detacnur lamron :noitubirtsid ralimis ot no mr al
noitubirtsid tub htiw detcirtser val eu .
 ammaG dna W llubie :noitubirtsid mo er g ene ral t ah n
laitnenopxe ovni( l iv ng l itaco no of ht e edom s fo pdf s’ a dn
eht sepahs of ta ).sli
∞
0
2x 2
e- x / 2
xd =∫ ∫
2
E( X ) =
0 0
∞
-x e-x / 2
0
1
2
2 ∫
1
-xe-x / 2
∫
0
:si

YS OITALUMISDNAGNILLEDOMMETS N 01 CS82
yrotnevnI dna ylppus niahc lufesU[ doM sle ]
 nI citsilaer yrotnevni dna s ylppu - niahc ,smetsys
ereht era ta tsael eerht modnar airav lb :se
 T eh rebmun fo stinu dednamed ep r or ed r or ep r mit e
irep od
 T eh emit eb twe ne dem dna s
 T eh dael t emi
 elpmaS lacitsitats sledom rof dael emit sid t ubir t :noi
 Gamma
 elpmaS lacitsitats sledom rof dnamed :noitubirtsid
 :nossioP elpmis dna visnetxe e yl t uba lat de .
 tageN i ev laimonib noitubirtsid : ol nger at li ht na oP ssi on
erom( gral e med dna .)s
 :cirtemoeG laiceps esac fo evitagen ib nomial giv ne at
tsael eno dem na d ah s o cc u rr de .
ytilibaileR dna ytilibaniatniam lufesU[ ]sledoM
 emiT ot eruliaf )FTT(
 :laitnenopxE seruliaf era modnar
 :ammaG rof dnats by er d nadnu cy hw e er hcae c tnenopmo sah na ex laitnenop FTT
 :llubieW eruliaf si eud ot eht tsom suoires fo a egral mun b re fo d fe ec ist n a s metsy
fo stnenopmoc
 :lamroN seruliaf era due ot raew
 roF sesac htiw detimil ,atad emos lufesu dist tubir i sno era :
 ,mrofinU ralugnairt dna ateb
 rehtO :noitubirtsid ,illuonreB laimonib dna yh p re ex laitnenop .
3.3 ercsiD te itubirtsiD o sn
 etercsiD modnar rav i selba era desu ot d ebircse ar n mod anemonehp ni hcihw no ly tni e reg
rucconacseulav .
 nI siht ,noitces ew lliw l nrae uoba t:
 illuonreB slairt dna reB n illuo dist ubir it no
 laimoniB noitubirtsid
 cirtemoeG dna n evitage laimonib id ts ubir it no
 nossioP tubirtsid i no

B uonre ll i rT ia sl
and B uonre l il Di rts ib tu i no rcsiD[ ete ’tsiD n]
 eB r uon ill T ir a sl :
 noC s redi na ex ep rim tne c no sis it ng of n trials, ae ch ac n eb a
succe ss or a f ulia r .e
 teL Xj = 1 if eht j ht ex ep r mi ent si sa uc ssec
 na d Xj = 0 fi eht j ht exp re im ne t si a fail eru
 T eh onreB llu i distr ubi tion o( en irt al):
xj = 1, j =1 ..,2, .,n
xj = 0 j, =1,2, .. . n,
esiwrehto
 ehw re X(E j) = p dna V(Xj) = p(1-p) = pq
 eB r uon ill proce :ss
 T eh n eB rnou ll i trials ehw re tr lia s are in ed p ne d :tne
x(p 1 x, 2 x,…, n p=) 1 x( 1 p) 2 x( 2) … pn x( n)
laimoniB D noitubirtsi etercsiD[ Dis ]n’t
 The rebmun fo su cc e ss es in n Be onr u ill lairt s, X, sah a
laimonib d irtsi ub oit n.
p(x) =
�
ehT rebmun of
semoctuo gnivah eht
deriuqer rebmun fo
sesseccus dna
seruliaf
 T eh m ,nae )x(E = p + p + … + p = p*n
 T eh irav anc ,e V( )X = qp + qp + … + qp = *n pq
�0,
�
�jpj (x ) = p(xj ) = p = q,
�
�1-
p,
esiwrehto
borP a ytilib th ta
ereht era
x s sesseccu dna
n( - )x seruliaf
�0,
� �
� �
� n
�� px
qn- x
, x = 0,1,2, ... , n
��
x �

irtemoeG c & eN g ta vi e
laimoniB Dis rt i tub oi n etercsiD[ Dis ]n’t
 cirtemoeG d si t ir tub noi
 T eh un m reb of illuonreB lairt s, X, ot ihca e ev eht 1 ts
s cu cess:
qx-1
p, x = 0 1, ,2, .. ., n
�0, esiwrehto
 )x(E = ,p/1 dna )X(V = p/q 2
 tageN i ev onib m lai d si t ir ub it on
 T eh un m reb of illuonreB ,slairt ,X nu t li the kth
su cc e ss
 If Y si a evitagen binom lai dis ubirt tion htiw param ete rs p dna k,
�� q pk
, y = k, k +1, k +2, ...
�0, wrehto i es
 )Y(E = ,p/k and V(X) = k /q p2
oP i noss D si rt i tub i no
 nossioP noitubirtsid ircsed eb s nam y r na dom proce ss es
etiuq llew dna si ehtam m cita a yll qu ti e is pm le.
 erehw α > ,0 fdp dna c fd :era
i
, x = 0 1, , .. .
hto re esiw
 )X(E = α = )X(V
y-k
� y -1
� �
�
� �
��
k -1�
:neht
p(x) =
�p(x) =
�
x!
��0,
p(x) = �
F (x) =
x
∑
i=0
-α x
�e e-α
α
i!
� α

nossioP D si rt i tub i no
 maxE p :el A retupmoc er pa ri ep sr on si “ eeb ep d” ea hc
emit ereht si a ca ll for se civr e. The bmun er fo be pe s per
ho ru ~ Po ssi (no α = 2 per uoh .)r
 T eh ilibaborp ty of eerht b ee ps ni the en xt hour:
3(p ) = e
-2
2
3
!3/ = 81.0
,osla )3(p = )3(F – )2(F = 758.0 -0. 76 7 81.0=
 T eh ilibaborp ty of owt ro more eb eps ni a 1-hour ep rio :d
2(p or om re) = 1 – p(0) – p(1)
= 1 – (F 1)
= 495.0
4.3 suounitnoC snoitubirtsiD
 suounitnoC modnar selbairav nac eb us de ot rcsed i eb modnar emonehp na in hcihw eht
elbairav nac ekat no any eulav ni emos lavretni .
 nI siht ,noitces eht dist ubir it no s duts i de :era
 mrofinU
 aitnenopxE l
 oN rmal
 llubieW
 lamrongoL

mrofinU iD s rt i noitub suounitnoC[ ]n’tsiD
 A modnar irav ba le X si inu f ylmro tubirtsid de on ht e
lavretni (a,b ,) U(a,b ,) fi sti fdp dna fdc a :er
0, x a
, a ≤ x ≤ b
esiwrehto
 (P x1 < X < x2) is roporp t oi n la ot eht el n htg of eht i etn vr la [ x(F 2) –
x(F 1) = (x2-x1)/(b-a)]
 )X(E = (a+b) 2/ )X(V = b( -a)
2
21/
 )1,0(U sedivorp eht m ae ns to g ne erate random num eb ,sr
f mor ihw hc modnar setairav nac be g ene ra .det
tnenopxE ial D si rt i ub oit n suounitnoC[ ]n’tsiD
 A modnar irav ba le X si yllaitnenopxe irtsid detub tiw h
p ara me et r λ > 0 if sti fdp dna fdc ra e:
λe-λx
,
λe-λt
td =1 - e-λx
, x ≥ 0
 )X(E = /1 λ )X(V = /1 λ
2
 desU ot m ledo raretni ir val it mes
nehw slavirra era com yletelp
odnar m, dna ot m ledo s ivre ce
it mes taht are hgih ly irav able
 roF reves al di ff tnere ex op n laitne
dp f s’ ees( f ,)erugi eht value of
retni c tpe no eht rev tic la ixa s is λ,
dna a ll dp f s’ ev utne a yll tni e .tcesr
 sselyromeM ytreporp
 roF lla s dna t gr roretae otlauqe 0:
X(P > t+s | X > s) = P X( > t)
 Ex :elpma A pmal ~ ex l(p = 3/1 rep uoh r ,) ,ecneh on reva a ,eg 1 fai erul per 3 sruoh .
 ehT ilibaborp ty th ta eht pmal stsal regnol th na i st naem il ef i :s X(P >
1=)3 - 1( -e- /3 3) = e-1 = 863.0
f ( x) =
x ≥ b�1,�0,
 rP epo rties
�
x
F ( x) = , a ≤ x bb� - a
�
� - a
�b - a
1�
�
�
x
�� 0�0,
f (x) = �
�0, x
0F(x) = �
∫
x ≥ 0
sle e erehw
��

 ehT ilibaborp ty th ta eht stsalpmal neewteb 2 to 3 sruoh is:
2(P =< X (F=)3=< 3) – (F 2 41.0=) 5
 ehT ilibaborp ty th ta ti al sts rof rehtona oh ur nevig arepositi it gn for 5.2
:sruoh
X(P > 5.3 | )5.2>X X(P= > 1) e= - 3/1 17.0= 7
amroN l D tsi rib noitu suounitnoC[ ]n’tsiD
 A ar n mod irav able X si yllamron detubirtsid sah eht dp f:
2
� � �,
- ∞
 :naeM
 raV i na c :e
 oneD t de as X ~ N(µ,σ2
)
 laicepS pr epo itr e :s
 .
 f(µ-x) f= (µ x+ ); eht fdp si sy mm cirte tuoba µ.
 T eh maximum eulav fo eht fdp o cc ru s ta x = µ; eht m nae and
m edo are uqe a .l
 gnitaulavE eht irtsid ub tion:
 esU laciremun sdohtem on( olc des mrof )
 nI d tnednepe of m dna ,s gnisu eht dnats a dr ron am l rtsid i :noitub
Z ~ ,0(N 1)
 noitamrofsnarT fo v aira b :sel =Ztel X( - m) / s,
F(x) = P(X ≤ x) = P�
Z ≤
( x-µ ) / σ
-∞
= φ(z) zd = Φ( )
-∞
:elpmaxE ehT emit iuqer der ot daol na aeco n iog ng sev s ,le X, si ubirtsid t de sa ,21(N )4
 ehT ilibaborp ty th ta eht lessev si dedaol ni ssel than 01 :sruoh
σ
il mx→-∞ f (x) = 0, na d mil x→∞ f (x) = 0
0
- ∞ µ
2
σ
x ∞
��
∞
f (x) =
σ
� - µ
�
1
2
x �1
2π
��
xe p�-
�
x - µ
σ
�
�
�
erehw, Φ(z) =
�
�
1
2π
2
e-t /
2
td
∫
z
∫
∫
= 1
2π
2
e-z /
2
zd -∞
x-µ
( x-µ ) / σ
σ

 gnisU eht s temmy ry orp p re t ,y (F 1) si eht elpmoc me Ffotn (-1)
llubieW noitubirtsiD ]n’tsiDsuounitnoC[
 A modnar elbairav X sah llubieWa finoitubirtsid sti fdp sah eht :mrof
 3 :sretemarap
 noitacoL :retemarap υ,
 elacS :retemarap β , (β > )0
 epahS retemarap . ,α (> )0
 :elpmaxE υ = 0 dna α = 1:
nehW β = 1,
X ~ e px (λ = 1/α)

L rongo m la D si tubirt i no [ noC t suouni siD t ]n’
 A r dna mo va ir ba le X has a log on mr al d si irt b itu on if its
p fd ah s ht e of rm:
µ 1= ,
σ
2
0= .5,1, .2
esiwrehto
 naeM e=)X(E µ+σ2 2/
 ecnairaV =)X(V e µ2 +σ2 2/ (
eσ2
- )1
 Rel ta i no ship iw ht no mr al d irtsi ub it on
 W neh Y ~ (N µ, σ2
), ht en X = eY
~ rongol m la (µ, σ2
)
 araP m srete µ and σ2
ehttonera ehtfoecnairavdnanaem
rongol m la
tsiDnossioP r bi ut noi
 Definitio :n )t(N si a cou tn ing f nu cti no t ah t r pe res tne s
t eh nu ebm r fo ev tne s cco u rr de in [0,t].
 A cou tn ing proce ss { ,)t(N =>t 0} si a Po ssi on rp oce ss
tiw h em an rate λ if:
 rA riv la s occur one ta a time
 {N(t), 0=>t } ah s s oitat nary increm stne
 {N(t), 0=>t } ah s ni d pe endent ni rc em stne
, rof t ≥ 0 na d n = 0 1, ,2 ...,
 qE au l m nae dna varianc :e N[E (t)] = N[V (t)] = λt
 atS t oi nary ni c er m :tne T eh un m eb r of a rr lavi s in it me s ot t is
la so Poi ss no -distr ubi t de iw th m nae λ(t-s)
�
� �
�0,
2σ� �
�, x
0
2f (x) = �
�
� 1
2π xσ
�
xe p�-
( nl x - μ)2 �
e-λt
(λt)n
n!
 rP epo itr es
P[N(t) = n] =

rraretnI vi la T mi se [ nossioP siD t ]n’
 noC s redi eht ni t irrare v la it m se of a oP ss noi orp cess (A1, A2, …),
erehw Ai is eht e pal es d it me eb t neew irra v la i a dn rra vi la 1+i
 T eh 1 ts
a rr i av l oc uc rs a tf er t emi t i ff eht re are no a rr ivals in the ni t re v la
0[ ,t], eh nce:
A{P 1 > }t = (N{P t) = }0 = e-λt
A{P 1 <= t} = 1 – e-λt
dc[ f fo exp(λ ])
 nI tera rr ival times, A1, A2, …, are e px tneno i lla y d tsi r bi tu ed na d
dni e ep n ned t with me na 1/λ
A avirr l c nuo ts Int lavirrare time
~ oP i(λ) ~ Ex /1(p λ)
atS it onary & I dn e ep nd tne Mem ro yle ss
pS li tt ing dna P oo il gn [ nossioP siD t ]n’
 Sp til tin :g
 uS p esop e hca e tnev of a nossioP orp c se s nac be c al ssif dei as
T epy ,I htiw ilibaborp ty p dna T epy ,II htiw orp bab ili ty 1- .p
 )t(N = 1N (t) t(2N+ ), erehw )t(1N dna N2( )t era htob Po si s no
secorp ses htiw r eta s λp na d λ 1( - )p
ioP~)t(1N [λp]
)t(N ~ (ioP λ)
ioP~)t(2N [λ 1( -p)]
 Poo il n :g
 uS p esop t ow nossioP secorp es s are op o del t ego t reh
 )t(1N 2N+ (t) = t(N ), erehw N( )t si a Po nossi processes htiw rates
λ1 + λ2 )t(1N ~ [ioP λ1] λ1
λ1 + λ2
)t(N ~ (ioP λ1 + λ2)
)t(2N ~ [ioP λ2]
ESIfo.tpeD , TIBJS
λ2
77
λp
λ
λ 1( - )p

5.3 nossioP corp ;sse
noN s tat i yrano Po si s no
orP cess SN( PP ) [ nossioP siD t ]n’
 nossioP ssecorP tuohtiw eht s itat o an ry ni c er m ,stne arahc c et ir dez by
λ(t), arlavirraeht t ittae me t.
 T eh detcepxe un m reb fo virra a sl by it me ,t Λ )t( :
t
)t(Λ = sd)s(λ
0
 Re gnital s at t oi nary Po si son ssecorp t(n ) htiw r eta =λ 1 dna N PS P N( )t
htiw rate λ(t):
 teL lavirra it mes of a oitats nary ssecorp iw th r eta λ 1= eb t1, t2, ,…
dna lavirra tim se of a SN PP w hti rate λ )t( eb T1, T2 ew,…, k :won
ti = Λ(Ti)
Ti = Λ-1
(ti)
noN s tat i yrano Poiss no
P or cess N( PPS ) [ nossioP siD t ]n’
 Exam :elp Su opp se a rr iv la s ot a Post Office evah r eta s 2 ep r m etuni
from 8 am litnu 12 pm, dna neht 0.5 ep r m etuni nu it l 4 pm.
 teL t = 0 co rr es op nd ot 8 am, SN PP (N )t ah s r eta f nu c :noit
� ,5.0 4 ≤ t 8
Ex ep c det un m eb r of ra r vi la s by it me :t
0 ≤ t 4
+ ,6 4 ≤ t 8
 neH c ,e the probability dist ir tub i no of eht un m eb r of ra r vi als eb t neew
11 am dna 2 pm.
)6(N[P – )3(N = k] = (N[P Λ 6( )) – (N Λ(3 )) = k]
= (N[P 9) – )6(N = k]
e= (9-6)
9( - )6 k
/ !k = e3
(3)k
/k!
∫
�
� 0 4� 2
�2t,
t4
2 sd + .0 5 sd =
Λ(t) =
∫ ∫
t
�
�
�
λ(t) =
2, 0 ≤ t 4

6.3 laciripmE Di rts ubi tions
A noitubirtsid esohw sretemarap era eht bo s devre seulav ni a elpmas fo d ata .
 yaM be desu wh ne ti si elbissopmi ro assecennu ry ot hsilbatse taht a
ar modn elbairav sah any ralucitrap p rtemara ic noitubirtsid .
 :egatnavdA on itpmussa on dnoyeb the resbo v de seulav in eht s pma le.
 :egatnavdasiD elpmas mi thg ton revoc eht eritne egnar fo ssop ible seulav .
.tpeD ESIfo , TIBJS 97

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