Approximations of the Mean Waiting Time in an M/G/s Queueing System

This paper considers the problem of obtaining approximate expressions for the first moment W_Gs of the stationary waiting time distribution in an M/G/s queueing system. Special attention is paid to the case G ≡ D, i.e., constant service times. Most known approximations are in fact heavy traffic approximations which have rather large relative errors in the light traffic case. In the present study both the light traffic and heavy traffic behavior of W_Gs (W_Ds) are taken into account. In order to obtain mean waiting time approximations it appears to be useful to introduce a quantity (the “normed cooperation coefficient”) which is inversely proportional to W_Gs and which is in some sense a measure for the “cooperation” between the servers of the service facility. A part of the paper is devoted to the analysis of this normed cooperation coefficient.