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 r₁ 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 ri. 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 12 P12 Server I 2 P13 P2.out P23 Server 3 143 Plout P31 Figure 19.3: Network of queues with probabilistic routing.