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Exercise 3. Consider the open network of two queues shown in Figure 2. Customers enter the network at Queue 1 H1 Queue 2 M2 - Figure 2: Open queueing network. rate immediately reaching queue 1. Customers leaving queue 1 will either choose queue 2 with probability (1 - p), or return to queue 1 with probability p. Customers leaving queue 2 will either depart from the system with probability (1), or return to queue 2 with probability q. 1 A) Compute the average number of times the same customer enters queue 1 (pt. 10). B) Assuming that each time a customer enters queue 1, it will stay in the queue for an average time of T/" (including both waiting and service time), compute the average number of jobs in queue 1, i.e., N. (note that the same customer may enters queue 1 multiple times, but in this question represents the average time spent in the queue during one single visit to the queue) [pt. 10). C) Assuming that the average number of jobs in queue 2 is Ng, compute the average time a customer spends in the entire network of queues, i.e., the time elapsed from the moment the customer enters queue 1 for the first time and the moment the customer leaves the second queue and decides not to return to queue 2 (pt. 10) Exercise 3. Consider the open network of two queues shown in Figure 2. Customers enter the network at Queue 1 H1 Queue 2 M2 - Figure 2: Open queueing network. rate immediately reaching queue 1. Customers leaving queue 1 will either choose queue 2 with probability (1 - p), or return to queue 1 with probability p. Customers leaving queue 2 will either depart from the system with probability (1), or return to queue 2 with probability q. 1 A) Compute the average number of times the same customer enters queue 1 (pt. 10). B) Assuming that each time a customer enters queue 1, it will stay in the queue for an average time of T/" (including both waiting and service time), compute the average number of jobs in queue 1, i.e., N. (note that the same customer may enters queue 1 multiple times, but in this question represents the average time spent in the queue during one single visit to the queue) [pt. 10). C) Assuming that the average number of jobs in queue 2 is Ng, compute the average time a customer spends in the entire network of queues, i.e., the time elapsed from the moment the customer enters queue 1 for the first time and the moment the customer leaves the second queue and decides not to return to queue 2 (pt. 10)