The number of overlapping customers

We consider the number of overlapping customers in several single- and multiserver queues, i.e., the number of customers whose visit to a service system at some point in time has an overlap with that of a tagged customer. Restricting ourself to the FCFS policy, we obtain the probability generating function and moments of the number of overlaps in the M / G / 1 , M / G / 1 / N , M / M / c and G / M / c queue and (as an approximation) the M / G / c queue.