Queueing analysis of polling models: progress in 1990-1994
Frontiers in queueing
Polling Systems in Heavy Traffic: a Bessel Process Limit
Mathematics of Operations Research
Distribution of the delay in polling systems in heavy traffic
Performance Evaluation
Polling Systems with Switch-over Times under Heavy Load: Moments of the Delay
Queueing Systems: Theory and Applications
Polling systems in heavy traffic: Higher moments of the delay
Queueing Systems: Theory and Applications
Performance Analysis and Optimization with the Power-Series Algorithm
Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
Mean value analysis for polling systems
Queueing Systems: Theory and Applications
Mean value analysis for polling systems in heavy traffic
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Iterative approximation of k-limited polling systems
Queueing Systems: Theory and Applications
Polling systems with periodic server routing in heavy traffic: renewal arrivals
Operations Research Letters
Cyclic-service systems with probabilistically-limited service
IEEE Journal on Selected Areas in Communications
Probability in the Engineering and Informational Sciences
A note on polling models with renewal arrivals and nonzero switch-over times
Operations Research Letters
On ergodicity conditions in a polling model with Markov modulated input and state-dependent routing
Queueing Systems: Theory and Applications
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We consider asymmetric cyclic polling systems with an arbitrary number of queues, general service-time distributions, zero switch-over times, gated service at each queue, and with general renewal arrival processes at each of the queues. For this classical model, we propose a new method to derive closed-form expressions for the expected delay at each of the queues when the load tends to 1, under proper heavy-traffic (HT) scalings. In the literature on polling models, rigorous proofs of HT limits have only been obtained for polling models with Poisson-type arrival processes, whereas for renewal arrivals HT limits are based on conjectures [E.G. Coffman, A.A. Puhalskii, M.I. Reiman, Polling systems with zero switch-over times: A heavy-traffic principle, Ann. Appl. Probab. 5 (1995) 681-719; E.G. Coffman, A.A. Puhalskii, M.I. Reiman, Polling systems in heavy-traffic: A Bessel process limit, Math. Oper. Res. 23 (1998) 257-304; T.L. Olsen, R.D. van der Mei, Periodic polling systems in heavy-traffic: Renewal arrivals, OR Lett. 33 (2005) 17-25]. Therefore, the main contribution of this paper lies in the fact that we propose a new method to rigorously prove HT limits for a class of non-Poisson-type arrivals. The results are remarkably simple and provide new fundamental insight and reveal explicitly how the expected delay at each of the queues depends on the system parameters, and in particular on the interarrival-time distributions at each of the queues. The results also suggest simple approximations for the expected delay in stable polling systems. Numerical results show that the approximations are highly accurate when the system load is roughly 90% or more.