Analysis of a Two Server Polling System with Overlapping Skills and 1-Limited Service

Abstract

The main aim of the thesis is to find the optimal division of load in the three queues, i.e. the optimal degree of overlap of skills between the two servers with waiting time in queue as the performance measure. The model under consideration is a polling system with two servers and three queues - two specialized queues, 1 and 2, and a common queue, queue 3. One of the servers cycles between queues 1 and 3 and the other between 2 and 3. The imbedded Markov chain state equations and the functional equations for queue length probability generating functions are formulated. It was not possible to obtain a closed for expression for the exact mean waiting time in the queues by solving the functional equations. So, an attempt has been made to get an approximate closed form expression that could be used to find the optimal division of load in the three queues. Since the results are available only for the symmetric system we first assume the two specialized queues to be identical. But later we relax this assumption and give approximation method for the asymmetric system. The recommended method to approximate the mean waiting time in a queue can be used to determine the optimal allocation of load to the three queues.