The paper is a sequel to a previous paper by the present author in which the limiting behavior of various stochastic processes arising from a generalized single server queueing system was studied. In this generalized system the first N customers of each busy period (N random) experience service times drawn from distributions u1(1),...,uN(1), respectively, while all remaining customers of the busy period, if any, are serviced according to the distribution u0(1). Furthermore, the first N arrivals to the system, if any, after the initiation of the busy period occur at intervals drawn from distributions u1(2),...,uN(2), respectively, while other arrivals, if any, during the busy period occur at intervals distributed as u0(2). This model is quite general.
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