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Queuing theory 3

  • 1. elSSMAt Date 2-8.»a Page UE UIN THEORy RECAP memorless andem vaYiahloS expenental (2) poiess.n (At) geometri t h twoSucces.Sive airivals indepenolent At pLexaty one arrival i At AAt + oAt mare than one armival in At soCat) hen the proCassis a PotsSon process oith param2ter 2A._ n_arrarrivals in t tima units) e ( t nl a vindhya KCIS
  • 2. claMAt Dote 202202o Paga urd , 12,)t).nKarnivals cn t time units) e + O cn Second queu E K mhtrst qveve E k- in Lirst quevet n Second qveve E th trstqueve K n Second GUve pK packets in queweI& K-K packets en quwe2) K 0 tdepenclt (A (ate Ko K1! Ck-K)I e K poisson C2+2) poisson RV X(A) Ex 2L xpenentinl RvX(p) Ex V
  • 3. AsSMAteDate 20 822 Page 3 tTt ho packas ànt. ext pa.ckat arrival time -Tst) PT 1- exponeryHiat- A=5 packels Second O. 03 5 5 packok h se.conda) e 1o 0:175 packais in Lsa.cond e 5 51 lo pLCKak in econd ey O183 A/B/c/D/E_ r A/B/ AOrmivalprocess mean 2 servite rate () Servey max no o CUxfaners on packek he Sstem, pepulahien max. nc o Cusfomer toill ouer need fb Serv
  • 4. elasSMAte Dota20:8.2020/ Poge 4- M/M M-memcrylessCpotsson)2 M-Senuice process memoryleg Cu exponential -oneServer cobur copopulattonsize BIRTH-DEATH PRoCESS load bactor P A P(E probabikity onceluctomers ch th system at Ame t n t4At)At) : honew arrial9noneu) olepartre yo were in State n at time t._ OR one ne arrival, yoULwer in Mate. at ime t R M neu olepartora &OUwerr in_State nH at ime
  • 5. SSMAte Date 26.82020 Page AL) AAt )+uAt PTt kaking lim_At>o dp, (Atup,t) +Agt) 4uE) or Steady &iate dnct)o olt Calculatinq loP et
  • 7. elassMAteDate 20 2:0 Page M/Mtlizathon -P P- 1 .9999 0,93 75 b.9 3 5 p (o 3) -28 35p C2 Col2 tPtP+P+ P+R -6.999 12timeA (6 2 . 5 2 5 S O = S . . 2 2 b12 2 O-0 2