A note on calculating steady state results for an M/M/k queuing system when the ratio of the arrival rate to the service rate is large

The formulas for calculating steady state results for the M/M/k queuing system are well known. Computational difficulties, however, can arise in using these formulas in situations in which the ratio of the arrival rate to the service rate is high. In this paper we consider a recursive approach for calculating steady state results which avoid such computational difficulties. As an additional benefit, such formulas are far easier to program into a spreadsheet package than the traditional formulas presented in most management science texts.