2.1 Maxinum Outsiide Arrival Rate

For the network-of-queues with robabilistic routing given in figure 2.3, suppose that each server serves at an average rate of 10 jobs/sec; that is, ?_i = 10, ?i. Suppose that r₂ = r₃ = 1. Suppose that p₁₂ = p_2,out = 0.8, p₂₃ = p₁₂ = 0.2, p_1,out = 0, and p₃₁ = 1. What is the maximum allowable value of r₁ to keep the system stable?

ckets have to follow the same routing Server 2 P2,out 2 P23 P12 Server 3 Server 1 P13 P31 Pi,out r3 Figure 2.3. Network of queues with probabilistic routing. n: In modeling packet flows in the Internet, for example, one f the packet (and hence its route) depend on its source and des In modeling delays, each wire might be replaced by a server tha del the wire latency. The goal might be to predict mean round-tr a particular route, given the presence of the other packets. W Chapter 18. ckets have to follow the same routing Server 2 P2,out 2 P23 P12 Server 3 Server 1 P13 P31 Pi,out r3 Figure 2.3. Network of queues with probabilistic routing. n: In modeling packet flows in the Internet, for example, one f the packet (and hence its route) depend on its source and des In modeling delays, each wire might be replaced by a server tha del the wire latency. The goal might be to predict mean round-tr a particular route, given the presence of the other packets. W Chapter 18