On open problems in polling systems

Marko Boon (1) , Onno J. Boxma (1) , Erik M. M. Winands (2)

1 EURANDOM - European Institute for Statistics, Probability, Stochastic Operations Research and its Applications
2 Department of Mathematics, Section Stochastics

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.

Mots clés: Polling; Gated; One-limited; Branching-class; Switch-over time asymptotics; 60K25; 90B22

Domaines: Réseaux et télécommunications [cs.NI]

Marko Boon, Onno J. Boxma, Erik M. M. Winands. On open problems in polling systems. Queueing Systems, 2011, 68 (3-4), pp.365-374. ⟨10.1007/s11134-011-9247-9⟩. ⟨hal-00842611⟩