Analysis of a general service nonexhaustive polling system using a heuristic combination method and pseudoconservation law

This paper is devoted to the analysis of the mean waiting time for a polling system with general service order sequence and nonexhaustive service discipline. We obtain an expression for the mean waiting time in terms of a so-called residual cycle time and derive a pseudoconservation law (PCL) to help improve the accuracy of estimations of the mean waiting time. By multiplying the estimations of the residual cycle times for all stations by equal and unequal constants, we obtain two separate solutions for the mean waiting time. We furthermore propose a heuristic method that combines these separate mean waiting times into a final solution for the mean waiting time. Numerical examples show that our combination method generates accurate estimations for the mean waiting times in both cyclic and general cases over all traffic loads.