Consider a queueing model in which all customers have service times equal to 1, and where the times between successive customers are always greater than 1 (for instance, the interarrival times could be uniformly distributed over (1, 2)). Hence, as every arrival finds the system empty and every departure leaves it empty, we have a0 = d0 = 1 However, P0 = 1 as the system is not always empty of customers. 

It was, however, no accident that an equaled dn in the previous example. That arrivals and departures always see the same number of customers is always true as is shown in the next proposition.