Estimation in M/Er /1 queueing systems

In this paper, the maximum likelihood estimates of the parameters for the M/Er /1 queueing model are derived when the queue size at each departure point is observed. A numerical example is generated by simulating a finite Markov chain to illustrate the methodology for estimating the parameters with variable Erlang service time distribution. The problem of hypothesis testing and simultaneous Confidence regions of the parameter is also investigated.0