Waiting Times in Polling Systems with Markovian Server Routing
This study is devoted to a queueing analysis of polling systems with a probabilistic server routing mechanism. A single server serves a number of queues, switching between the queues according to a discrete time parameter Markov chain. The switchover times between queues are nonneghgible. It is observed that the total amount of work in this Markovian polling system can be decomposed into two independent parts, viz., (i) the total amount of work in the corresponding system without switchover times and (ii) the amount of work in the system at some epoch covered by a switching interval. This work decomposition leads to a pseudoconservation law for mean waiting times, i.e., an exact expression for a weighted sum of the mean waiting times at all queues. The results generalize known results for polling systems with strictly cyclic service.
Unable to display preview. Download preview PDF.
- 1.Boxma, O.J. (1989). Workloads and waiting times in single-server systems with multiple customer classes. To appear in Queueing Systems.Google Scholar
- 3.Boxma, O.J., Groenendijk, W.P., Weststrate, J.A. (1988). A pseudoconservation law for service systems with a polling table. Report Centre for Mathematics and Computer Science, Amsterdam; to appear in IEEE Trans. Commun.Google Scholar
- 8.Groenendijk, W.P. (1988). Waiting-time approximations for cyclic-service systems with mixed service strategies, in: M. Bonatti (ed.), Proceedings ITC-12 (North-Holland, Amsterdam).Google Scholar
- 12.Levy, H. (1984). Non-Uniform Structures and Synchronization Patterns in Shared-Channel Communication Networks. CSD-840049, Computer Science Department, University of California, Los Angeles, Ph.D. Dissertation.Google Scholar
- 13.Levy, H., Sidi, M. (1988). Correlated arrivals in polling systems. Report Department of Computer Science, Tel Aviv University.Google Scholar
- 14.Mitrani, L, Adams, J.L., Falconer, R.M. (1986). A modelling study of the Orwell ring protocol. In: Teletraffic Analysis and Computer Performance Evaluation, eds. O.J. Boxma, J.W. Cohen and H.C. Tijms (North-Holland, Amsterdam), pp. 429–438.Google Scholar
- 16.Takagi, H. (1986). Analysis of Polling Systems (The MIT Press, Cambridge, MA).Google Scholar
- 18.Tedijanto (1988). Exact results for the cyclic-service queue with a Bernoulli schedule. Report Electrical Engineering Department and Systems Research Center, University of Maryland.Google Scholar