EURO 2025 Leeds
Abstract Submission

976. Stability of Polling Systems: A Linear Class of Two-Phase Switching Policies Near Fluid Limit

Invited abstract in session TC-54: Methods & stochastic modelling , stream Stochastic modelling.

Tuesday, 12:30-14:00
Room: Liberty 1.08

Authors (first author is the speaker)

1. Kousik Das
Industrial Engineering & Operations Research, Indian Institute of Technology Bombay
2. Vartika Singh
3. Konstantin Avrachenkov
INRIA
4. Veeraruna Kavitha
IEOR, Indian Institute of Technology Bombay

Abstract

Among queueing systems, polling systems represent a special class where a single server cyclically visits multiple queues, potentially incurring non-zero switching times between queues. These switching times introduce vacation, making polling systems non-work-conserving. Polling systems are useful for traffic signals, manufacturing systems, logistics, railway crossings, etc. The analytical complexity of polling systems heavily depends on the service discipline adopted (e.g., exhaustive or gated). We anticipate that servers periodically switch between queues depending upon switching policies. This opens up an exciting new development in the analysis of polling systems under a fluid limit. We investigate a two-queue polling system embracing a fairly general and comprehensive class of two-phase switching policies near fluid regimes via the uniform acceleration technique. This class also contains one-phase switching policies. Here, the arrival and departure epochs form the potential switching epochs. Our switching policies include: (a) a class covering the Pareto frontier related to performance measures like stationary waiting times or mean number of waiting customers in each queue and (b) a class covering robust policies having performance measures like fraction of times the individual queue have reached specified danger levels. We formulate precise mathematical conditions under which the proposed two-phase switching policies ensure queue stability within fluid limit framework.

Keywords

Status: accepted

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