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I do not know how to solve these Problem 4: A queueing system has four queues in the configuration shown. Each queue is identical, with

I do not know how to solve these

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Problem 4: A queueing system has four queues in the configuration shown. Each queue is identical, with a single server with IID exponential service times, each with density he . The service times are IID both within each queue and between each queue. The left most queue (queue 1, say) is M/M/1 with an input which is a Poisson process of rate A 0. Use the Wald identity to find an upper bound to P. of the form P., c e-of where A is a constant that does not depend on a. Evaluate A. Hint: you may assume that the Wald identity applies to a single threshold at a > 0 without any lower threshold or assume another threshold at some f Be " where A is the same as in part b) and B > 0 is a constant that does not depend on a. Hint: Keep it simple - you are not being asked to find the tightest possible such bound. If you use 2 thresholds, find your lower bound in the limit 8 - -00

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