1) The document discusses queueing theory concepts like the Poisson process, birth-death processes, and the M/M/1 queue.
2) It provides the equations for the average time spent by each packet, average number of packets/customers in the system, and expected time in the queue.
3) Examples are given to calculate the average time customers spend in the queue and system for different arrival and service rates.
1. clasSMAate
Date 21: 8.2020
Page
UEUIN GTHEORY_
RECAP
poLsSon process
on pois&on PrOcessS
2 potssooProceseA
birthcleafh proces
Stare n ocostornars/ packeis in Hhe sstem
AlBlc/D/E
A- arrval pracess (A) mean
B Service processs Cmean uD
C senverS
D- t maxek Cusfonarspacketk (bohtersize
E*populafion &ize thct uorl need service
AlBl A/BleD
Eo
MM on Serven
afivalproes
smemes
he service proASA-
s mema le
paiscan arivo orth_ Cexpoantiad Oth Seviea
Yote
3. aAssMte
Data 2482020
Paga 3-
LpL (1p)p(tP+Ā¢2
L .9 L
0 - 5 4
P:5
S07
L
L
20Mbpt 99 Mbpss
SDMbps
L Lo t Ls tnivy 2 mn
A Lmin
09ost min
4. elasSmate
Date 2182020
Page .
QS LITTLE'SLALD
L_A avg. ma spent b each pacdet
Qvg.t pockek/Aime
Cvg. H packek|austamers
K=Vz
E EY. Ez X
not aluwauE Costemers Qrived
roein lo,t1):At
avg Rach costomRn sperds w unit of ma
total tme spent o ol the
E D0Stomors thosa uoha arcivedin to,t].
L
Fotal time Spnt by thae
Customers : lt
t Lt Atw
tmtn 2mA g0ee
temy mt 5m
L Au
t lau
5. alassmate
Data 24 8 2020/
Paga S-
0 . A: 9 customens/min
mins
A 9 Ccostomasmn MloCostornars min.
m i n : Wa twsoe
LL Lsar
L:0.9 9
Wser W
L-
3A=49 castonersmin ioCustorerimin
houo much time coil yo0 penchhe Quetx o averac22
C I min u - Wser min-0:1 0. mn 54Se.
- 1 CUstomermin 2o Customan mn_
Conct She xpectedfime to be Sp@nt in the Queue
P: 0.9
1-P
6.5min18
05-O.05 _o15min 21se2D