Approximations for Short Service Times

Abstract

Chapter II dealt mostly with the behavior of systems for which the expected service time E{S} was comparable with the duration of the rush hour, but, in any case, E{S} was large compared with the time spent going through any transition period when it was uncertain as to whether there was a queue of customers or of servers. The analysis was fairly straightforward, though, at times, somewhat tedious, because we chose to consider a more or less arbitrary curve E{A_c(t)} for the expected number of arriving customers, which varied considerably on a time scale comparable with the service time. The complications were due mostly to a variety of possible shapes of the curves E{A_c(t)}, E{D(t)}, etc., in the deterministic approximations. Stochastic effects were relatively small but also easily handled because they did not accumulate.