Polling with a General-Service Order Table

This paper derives exact results for a polling system such as a token bus or token ring with exhaustive service and priority polling. The results can also be used to analyze a terminal controller with a general-service order table. There are N stations in the system and the token is passed among them according to a polling table of length M (>N). Stations are given higher priority by being listed more frequently in the polling table. By a straightforward extension of results of Ferguson and Aminetzah 151 for systems with circular polling and exhaustive service, it is shown that in general, the N mean waiting times require the solution of a set of M-N simultaneous equations and a set of M(M-1) simultaneous equations. We show that partial symmetry in the polling table and the station characteristics can be used to significantly reduce the number of equations which must be solved. We present the reduced equation set for a two-priority class system and apply the results to a large token-passing bus network in which a few nodes account for a substantial portion of the network traffic. We show that in the latter case, the overall average message waiting time can be' significantly reduced by using priority polling: average waiting times at the high-priority nodes have large reductions in return for a smaller increase at low-priority nodes.