  The polling system with switch-over durations is a useful model with several
practical 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 modelling
the polling system of interest has been a Continuous-time Markov Decision
Process (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 numerical
integrals which naturally leads to the question of whether the SMDP policy
provides a worthwhile advantage. To further add to this scenario, it is shown
how sparsity can be exploited in the CTMDP to develop a computationally
efficient model. The discounted performance of the SMDP and CTMDP policies are
evaluated using a Semi-Markov Process simulator. The two policies are
accompanied by a heuristic policy specifically developed for this polling
system a well as an exhaustive service policy. Parametric and non-parametric
hypothesis tests are used to test whether differences in performance are
statistically significant.
