For the network-of-queues with probabilistic routing given in Figure 19.3, sup- pose that that each server...

    

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For the network-of-queues with probabilistic routing given in Figure 19.3, sup- pose that that each server serves at an average rate of 10 jobs/sec; that is, p= 10, Vi. Suppose that r2 = r3= 1. Suppose that p12 = P2,out = 0.8, P23 = P13 = 0.2, P1,out= 0, and p31 = 1. What is the maximum allowable value of ry to keep this system stable? Example: Network of Queues with Probabilistic Routing This is shown in Figure 19.3. Here server i receives external arrivals ("outside arrivals") with rate r₁. Server i also receives internal arrivals from some of the other servers. A packet that finishes service at server i is next routed to server j with probability pij. Server 2 72 P12 Server I #1 Plout P13 PM 142 P2.out P23 Server 3 IC Figure 19.3: Network of queues with probabilistic routing. For the network-of-queues with probabilistic routing given in Figure 19.3, sup- pose that that each server serves at an average rate of 10 jobs/sec; that is, p= 10, Vi. Suppose that r2 = r3= 1. Suppose that p12 = P2,out = 0.8, P23 = P13 = 0.2, P1,out= 0, and p31 = 1. What is the maximum allowable value of ry to keep this system stable? Example: Network of Queues with Probabilistic Routing This is shown in Figure 19.3. Here server i receives external arrivals ("outside arrivals") with rate r₁. Server i also receives internal arrivals from some of the other servers. A packet that finishes service at server i is next routed to server j with probability pij. Server 2 72 P12 Server I #1 Plout P13 PM 142 P2.out P23 Server 3 IC Figure 19.3: Network of queues with probabilistic routing.