This paper deals with refining Cosmetatos’s approximation for the mean waiting time in an M/D/s queue. Although his approximation performs quite well in heavy traffic, it overestimates the true value when the number of servers is large or the traffic is light. The paper first focuses on a normalized quantity that is a ratio of the mean waiting times for the M/D/s and M/M/s queues. Using some asymptotic properties of the quantity, Cosmetatos’s approximation is modified to obtain better accuracy both for large s and in light traffic. To see the quality of the present approximation, it is compared with the exact value and some previous approximations. Extensive numerical tests indicate that the relative percentage error is less than 1% for almost all cases with s•20 and at most 5% for other cases.
