Discrete Stochastic Processes, Chapter 4: Renewal Processes

Chapter 4 Renewal Processes Introduction Recall that a Renewal process is an arrival process in which the interarrival intervals are positive,1 independent and identically distributed (IID) random variables (rv s). Renewal Processes (since they are arrival Processes ) can be specified in three standard ways, first, by the joint distributions of the arrival epochs S1, S2, .. , second, by the joint distributions of the interarrival times X1, X2, .. , and third, by the joint distributions of the counting rv s, N(t) for t > 0. Recall that N(t) represents the number of arrivals to the system in the interval (0, t]. The simplest characterization is through the interarrival times Xi, since they are IID. Each arrival epoch Sn is simply the sum X1 + X2 ++ Xn of n IID rv s.)

developing some basic properties of renewal processes. Example 4.1.2 (The G/G/m queue:). The customer arrivals to a G/G/m queue form a renewal counting process, {N(t); t > 0}. Each arriving customer waits in the queue until one of m identical servers is free to serve it. The service time required by each customer

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