lec9 (1) - Queueing Systems Lecture 5 Amedeo R Odoni...

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Queueing Systems: Lecture 5 Amedeo R. Odoni October 30, 2006 Lecture Outline A fundamental result for queueing networks State transition diagrams for Markovian queueing systems and networks: examples Examples Dynamic queueing systems and viable approaches Qualitative discussion of behavior Reference: Sections 4.10, 4.11 + material in handout
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A result which is important in analyses of queueing networks Let the arrival process at a M/M/m queueing system with infinite queue capacity have parameter λ . Then, under steady state conditions ( λ< m μ ) the departure process from the queueing system is also Poisson with parameter λ. Implication: greatly facilitates analysis of open acyclic networks consisting of M/M/m queues with infinite queue capacities. The bad news: result holds only under exact set of conditions described above. Open acyclic network of M/M/. systems #1: μ =3 (per server) M/M/2 λ =4 #2: μ =2 1 negative exponential server #3: μ =6 1 negative exponential server P=1/3 Q=2/3 λ =4/3 λ =4/3 λ =8/3 λ =4 +
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State transition diagrams for queuing systems and networks When external arrivals are Poisson and service times are negative exponential, many complex queueing systems and open acyclic queueing networks can be analyzed, even
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