Example 7.19 (A Queueing System with Renewal Arrivals) Consider a waiting time system in which customers arrive in accordance with an arbitrary renewal process and are served one at time by a single server having an arbitrary service distribution. If we suppose that at time 0 the initial customer has just arrived, then {X(t), t  0} is a regenerative process, where X(t) denotes the number of customers in the system at time t. The process regenerates each time a customer arrives and finds the server free.