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The polling system with switch-over durations is a useful model with severalpractical applications. It is classified as a Discrete Event Dynamic System(DEDS) for which no one agreed upon modelling approach exists. Furthermore,DEDS are quite complex. To date, the most sophisticated approach to modellingthe polling system of interest has been a Continuous-time Markov DecisionProcess (CTMDP). This paper presents a Semi-Markov Decision Process (SMDP)formulation of the polling system as to introduce additional modelling power.Such power comes at the expense of truncation errors and expensive numericalintegrals which naturally leads to the question of whether the SMDP policyprovides a worthwhile advantage. To further add to this scenario, it is shownhow sparsity can be exploited in the CTMDP to develop a computationallyefficient model. The discounted performance of the SMDP and CTMDP policies areevaluated using a Semi-Markov Process simulator. The two policies areaccompanied by a heuristic policy specifically developed for this pollingsystem a well as an exhaustive service policy. Parametric and non-parametrichypothesis tests are used to test whether differences in performance arestatistically significant.

Solving the non-preemptive two queue polling model with generally  distributed service and switch-over durations and Poisson arrivals as a  Semi-Markov Decision Process