On open problems in polling systems

TL;DR

This paper investigates two unresolved issues in polling systems involving multiple queues and a single server, focusing on specific service disciplines and the impact of large deterministic switch-over times.

Contribution

It addresses two open problems in polling systems: one with mixed service disciplines and another with general arrivals and large switch-over times, discussing known results and challenges.

Findings

Analysis of the first open problem with gated and 1-limited services.

Discussion of the second problem with renewal arrivals and large deterministic switch-over times.

Identification of difficulties in solving these open problems.

Abstract

In the present paper we address two open problems concerning polling systems, viz., queueing systems consisting of multiple queues attended by a single server that visits the queues one at a time. The first open problem deals with a system consisting of two queues, one of which has gated service, while the other receives 1-limited service. The second open problem concerns polling systems with general (renewal) arrivals and deterministic switch-over times that become infinitely large. We discuss related, known results for both problems, and the difficulties encountered when trying to solve them.