Abstract
We consider the M(t)/M(t)/m/m queue, where the arrival rate ?(t) and service rate ?(t) are arbitrary (smooth) functions of time. Letting pn(t) be the probability that n servers are occupied at time t (0? n? m, t > 0), we study this distribution asymptotically, for m?? with a comparably large arrival rate ?(t) = O(m) (with ?(t) = O(1)). We use singular perturbation techniques to solve the forward equation for pn(t) asymptotically. Particular attention is paid to computing the mean number of occupied servers and the blocking probability pm(t). The analysis involves several different space-time ranges, as well as different initial conditions (we assume that at t = 0 exactly n0 servers are occupied, 0? n0? m). Numerical studies back up the asymptotic analysis. [PUBLICATION ABSTRACT]