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.)

Chapter 4 RENEWAL PROCESSES 4.1 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,

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