STATIONARY-PROCESS APPROXIMATIONS FOR THE NONSTATIONARY ERLANG LOSS MODEL

In this paper we consider the M(t)/G/s/0 model, which has s servers in parallel, no extra waiting space, and i.i.d. service times that are i ndependent of a nonhomogeneous Poisson arrival process. Arrivals findi ng all servers busy are blocked (lost). We consider approximations for the average blocking probabilities over subintervals (e.g., an hour w hen the expected service time is five minutes) obtained by replacing t he nonstationary arrival process over that subinterval by a stationary arrival process. The stationary-Poisson approximation, using a Poisso n (M) process with the average rate, tends to significantly underestim ate the blocking probability. We obtain much better approximations by using a non-Poisson stationary (G) arrival process with higher stochas tic variability to capture the effect of the time-varying deterministi c arrival rate. In particular, we propose a specific approximation bas ed on the heavy-traffic peakedness formula, which is easy to apply wit h either known arrival-rate functions or data from system measurements . We compare these approximations to exact numerical results for the M (t)/M/s/0 model with linear arrival rate.