Analysis of an asymmetric polling system

Polling models are used extensively in the field of operations research to analyze the performance of a variety of systems that can be viewed as a distributed queuing system served by a single server and to evaluate their operational characteristics. In the context of computer communication, a Local Area Network (LAN) with controlled access on a single transmission media can be viewed as such a polling system in which queues are being served in cyclic order. In this article, a LAN with reverse round robin scheduling for channel arbitration, called M-net [1], is modeled as a discrete time Markov chain representing an asymmetric polling system. Expressions for its performance measures like average channel utilization, mean and variance of delay and blocking probability at a station are derived. For a system of M stations, the solution complexity is of the order of 22(M−1) The analysis approach is applicable to both round robin and reverse round robin systems. Finally, performance measures of such a system are compared with that of Expressnet, as a representative example of round robin system. It is found that at lower arrival rates, the performance of M-net is comparable to that of Expressnet. However, with increasing values of arrival rates, M-net outperforms Expressnet. The analysis presented is applicable to the class of systems in operations research that can be viewed as multiple single buffer queues served by a server in round robin or reverse round robin fashion.