Estimation for queues from queue length data

We consider the estimation of arrival and service rates for queues based on queue length data collected at successive, not necessarily equally spaced, time points. In particular, we consider the M/M/c queue, for c large, but application of the method to the repairman problem is almost identical, and the general approach presented should extend to other queue types. The estimation procedure makes use of an OrnsteinUhlenbeck diffusion approximation to the Markov process description of the queue. We demonstrate the approach through simulation studies and discuss situations in which the approximation works best.