Question: Consider a single-server queueing system that is initially empty. A customer arrives at time 0, and successive inter-arrival times are exactly x minutes. The

Consider a single-server queueing system that is initially empty. A customer arrives at time 0, and (Poisson Arrivals See Time Averages: PASTA). Suppose the arrival process is Poisson and {N(t+s), s 0} is

Consider a single-server queueing system that is initially empty. A customer arrives at time 0, and successive inter-arrival times are exactly x minutes. The suc- cessive service times are exactly y minutes. Verify Theorem 6.1. Do the limiting probabilities p; exist? Does PASTA (Theorem 6.2) hold? (Hint: Consider the cases y x and y > x separately.) (Poisson Arrivals See Time Averages: PASTA). Suppose the arrival process is Poisson and {N(t+s), s 0} is independent of {X(u), 0 u t}. If the limits in (6.1) or (6.4) exist, Pj = ftj, j0.

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