Data-Driven Fitting of the G/G/1 Queue

The Maximum Likelihood Estimation (MLE) method is an established statistical method to estimate unknown parameters of a distribution. A disadvantage of the MLE method is that it requires an analytically tractable density, which is not available in many cases. This is the case, for example, with applications in service systems, since waiting models from queueing theory typically have no closed-form solution for the underlying density. This problem is addressed in this paper. MLE is used in combination with Stochastic Approximation (SA) to calibrate the arrival parameter θ of a G/G/1 queue via waiting time data. Three different numerical examples illustrate the application of the proposed estimator. Data sets of an M/G/1 queue, G/M/1 queue and model mismatch are considered. In a model mismatch, a mismatch is present between the used data and the postulated queuing model. The results indicate that the estimator is versatile and can be applied in many different scenarios.