For a single-server multi-station polling system, we focus on the generating function and LaplaceStieltjes transform of the time-stationary joint queue length and workload distributions, respectively, under no further assumptions on the service discipline. We express these quantities as expressions involving the generating functions of the joint queue length distribution at visit beginnings and visit completions at the various stations. The latter is known for a broad variety of cases. Finally, we identify a workload decomposition result.
Bibliographical noteFunding Information:
The second author is supported by grant No. 434/09 from the Israel Science Foundation and the Vigevani Chair in Statistics . The third author is supported by NWO grant 613.000.701 . The authors would also like to thank Marko Boon for reading the first draft of this paper, which led to the nice simplification of Formula (9) into (10) .
- Polling system
- Queue length
- Steady-state distribution