Approximations for the delay probability in the M/G/s queue

This paper develops approximations for the delay probability in an M/G/s queue. For M/G/s queues, it has been well known that the delay probability in the M/M/s queue, i.e. the Erlang delay formula, is usually a good approximation for other service-time distributions. By using an excellent approximation for the mean waiting time in the M/G/s queue, the paper provides more accurate approximations of the delay probability for small values of s. To test the quality of the present approximations, the paper compares them with the exact value and the Erlang delay formula for some particular cases.