We consider a single-server cyclic polling system with three queues where the server follows an adaptive rule: if it finds one of queues empty in a given cycle, it decides not to visit that queue in the next cycle. In the case of limited service policies, we prove stability and instability results under some conditions which are sufficient but not necessary, in general. Then we discuss open problems with identifying the exact stability region for models with limited service disciplines: we conjecture that a necessary and sufficient condition for the stability may depend on the whole distributions of the primitive sequences, and illustrate that by examples. We conclude the paper with a section on the stability analysis of a polling system with either gated or exhaustive service disciplines.
- Fluid limits
- Limited, gated and exhaustive service disciplines
- Polling system
ASJC Scopus subject areas
- Management Science and Operations Research
- Decision Sciences(all)