Optimal estimation for an m/m/c queue with time varying parameters

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Abstract
We consider a parameter estimation problem in a time varying M/M/c queue where the arrival and service rates arc given by general time-dependent stochastic processes. First we derive minimum variance unbiased estimators of the arrival rate, the mean of the service requirement and the system intensity in a time homogeneous queue with a time constraint on the observation period. The results from the homogeneous case are then used to derive the minimal mean square error linear estimators of the parameters at any moment in a time varying queue. We also show that the optimal linear estimators can be computed by the Kalman-Bucy filter for a specific linear dynamic additive noise model. This computational procedure is efficient and can be easily implemented in real time environments such as communication networks.

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