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Analysis of Three Server Queues with Stalling

  • Sivasamy, R
  • Thaga, K
  • Mokgatlhe, L. L.
This article analyses a Markovianqueueing system M/(M1,M2,M3)/3/(B1,B2) with stalling. It stalls customers ofqueue-1 into a finite buffer B1 of maximum size ‘Kμ2> μ3. Arrivals occur according to a Poisson process with mean arrival rateλ. Main focus is on the steady state queue length distribution which consists of two stages. Instage-1, ‘Queue Length’ process of the finite M/(M1,M2,M3)/3/(B1,3) system is formulated as a Quasi-Birth and Death process in a three dimensional finite state space. The stationary probability vector of the queue length is obtained using matrix analyticalmethods. In stage-2, using analytical methods, stage-1 results obtained on the finite queue length are linked to the infinite queue length process of the M/(M1,M2,M3)/3/(B1,B2) system subject to a condition ρ=(λ/μ)
Select Volume / Issue:
Year:
2017
Type of Publication:
Article
Keywords:
Generator Matrix; Heterogeneous Servers; Mean Queue Length; Stationary Probability Vector; Quasi-Birth-Death Process
Journal:
IJASM
Volume:
4
Number:
2
Pages:
25-30
Month:
March
ISSN:
2394-2894
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