For the queue with deterministic, not necessarily equidistant arrival times and exponential service times and for the dual queue with Poisson arrivals and deterministic but unequal service times we derive some explicit formulas for the distribution of the number of customers served during a busy...

Let (Sn)n[greater-or-equal, slanted]0 be a renewal process with interarrival times X1,X2,... Several results on the behavior of the renewal process up to a given time t0 or up to a given Sn=s are proved. For example, X1 is stochastically dominated by XN(t)+1, and X0=0, X1,...,XN(t)+1 is a...