Perturbation analysis has proven to be a fruitful technique in the analysis of several multidimensional Markov models. In order to successfully apply perturbation analysis, one must find an appropriate scaling parameter. This leaves the approach with a large degree of freedom. In this paper we explore the use of perturbation analysis to determine the stationary distribution of a specific polling model with random time-limited service. We discuss four candidate scaling approaches to analyze the polling model and describe the difficulties that must be overcome to construct a computationally feasible algorithm.

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Keywords Singular perturbation, Analytic expansion, Time-limited polling
Conference International conference on Queueing Theory and Network Applications
Saxena, M, Kapodistria, S, & Núñez Queija, R. (2020). Perturbation analysis of two queues with random time-limited polling. In Queueing Theory and Network Applications.