Pseudoconservation Law for Service Systems with a Polling Table

摘要

The paper is devoted to the analysis of waiting times in polling systems in which the stations are polled according to a general service order table. Such systems may, e.g., be used to represent token-bus local area networks in which the 'routing' of the token is fixed. Stations are given higher priority by being listed more frequently in the table, or by receiving service according to the exhaustive service discipline. The polling system is modelled by a single-server multi-queue system in discrete time. Non-zero switch-over times between the queues are assumed. An extension of the principle of work conservation to systems with non-zero switch-over times leads to the main result of the paper, an exact expression for a weighted sum of the mean waiting times at the various queues. Via limiting procedure, the discrete-time results are translated to continuous-times at the various queues. Via a limiting procedure, the discrete-time results are translated to continuous-time results. Finally, the special case of polling in a star network is discussed and compared with polling in a corresponding network with strictly cyclic service order.