Maximum Likelihood Estimates and Confidence Intervals of an M/M/R Queue with Heterogeneous Servers

This paper studies maximum likelihood estimates as well as confidence intervals of an M/M/R queue with heterogeneous servers under steady-state conditions. We derive the maximum likelihood estimates of the mean arrival rate and the three unequal mean service rates for an M/M/3 queue with heterogeneous servers, and then extend the results to an M/M/R queue with heterogeneous servers. We also develop the confidence interval formula for the parameter ρ, the probability of empty system P 0 , and the expected number of customers in the system E[N], of an M/M/R queue with heterogeneous servers Copyright Springer-Verlag 2006