PARAMETER-ESTIMATION FOR PARTIALLY OBSERVED QUEUES

In this paper, we consider parameter estimation for a FIFO queue with deterministic service times and two independent arrival streams of ''o bserved'' and ''unobserved'' packets. The arrivals of unobserved packe ts are Poisson with an unknown rate lambda while the arrivals of obser ved packets are arbitrary. Maximum likelihood estimation of lambda is formulated based on the arrival times and waiting times of k observed packets. The likelihood function is derived in terms of the transition probabilities of the unfinished work process which are calculated rec ursively. Sufficient conditions for consistency, asymptotic normality, and asymptotic efficiency are given. The mean and variance of the MLE are measured in simulation experiments. Numerical results indicate th at the MLE is consistent and asymptotically normal.