Nonparametric Estimation for Multi-server Queues Based on the Number of Clients in the System

In this article, we introduce a nonparametric (or distribution-free) estimator for traffic intensity in multi-server queues, which has not yet been discussed in the literature. Because this is a very useful model with many potential practical applications, it is the main focus of this study. We compare the performance of a new nonparametric estimator for situations in which the use of Markovian multi-server queues (M/M/s queues in Kendall notation) is adequate or in which it is necessary to consider multi-server queues with general arrival and general service times. We show that, when the parametric Markovian assumptions of M/M/s queues are satisfied, the new estimator is not superior to the maximum likelihood estimator based on the Markovian assumption with respect to M/M/s queues. However, for situations in which the interarrival time distribution and/or the service time distribution cannot be considered exponential (that is, non-Markovian), the new nonparametric estimator is superior. All evaluations are carried out using Monte Carlo simulations. A detailed numerical example is presented to show the usefulness of the technique for practical applications.