ON THE RELATIVE WAITING TIMES IN THE GI/M/s AND THE GI/M/1 QUEUEING SYSTEMS.

The average waiting time in a GI/M/s queue was compared with the average waiting time in an ″equivalent″ system comprised of s separate GI/M/1 queues. The results may be used to find the optimal partition of servers into several groups when designing a service system where certain restrictions eliminate the possibility of assigning all the servers in a single parallel group. The results may be qualitatively summarized as follows. If the inter-arrival times for both systems is of the ″same type″ then one would wait, on the average, at least s times as long in the separate system than in the combined one, when rho goes to 1. When rho becomes small the ratio of waiting times goes to infinity.