Dominance relations in polling systems
Queueing Systems: Theory and Applications
Workloads and waiting times in single-server systems with multiple customer classes
Proceedings of the workshop held at the Mathematical Sciences Institute Cornell University on Mathematical theory of queueing systems
Performance evaluation of polling systems by means of the power-series algorithm
Annals of Operations Research - Special issue on stochastic modeling of telecommunication systems
A decomposition result for a class of polling models
Queueing Systems: Theory and Applications - Polling models
IEEE/ACM Transactions on Networking (TON)
Computing distributions and moments in polling models by numerical transform inversion
Performance Evaluation
Polling Systems in Heavy Traffic: a Bessel Process Limit
Mathematics of Operations Research
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
LIMIT THEOREMS FOR POLLING MODELS WITH INCREASING SETUPS
Probability in the Engineering and Informational Sciences
Mean value analysis for polling systems in heavy traffic
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Multiproduct Systems with Both Setup Times and Costs: Fluid Bounds and Schedules
Operations Research
Heavy traffic analysis of polling models by mean value analysis
Performance Evaluation
Probability in the Engineering and Informational Sciences
On a unifying theory on polling models in heavy traffic
ITC20'07 Proceedings of the 20th international teletraffic conference on Managing traffic performance in converged networks
Polling systems with periodic server routing in heavy traffic: renewal arrivals
Operations Research Letters
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We study the expected delay in cyclic polling models with general ‘branching-type’ service disciplines. For this class of models, which contains models with exhaustive and gated service as special cases, we obtain closed-form expressions for the expected delay under standard heavy-traffic scalings. We identify a single parameter associated with the service discipline at each queue, which we call the ‘exhaustiveness’. We show that the scaled expected delay figures depend on the service policies at the queues only through the exhaustiveness of each of the service disciplines. This implies that the influence of different service disciplines, but with the same exhaustiveness, on the expected delays at the queues becomes the same when the system reaches saturation. This observation leads to a new classification of the service disciplines. In addition, we show monotonicity of the scaled expected delays with respect to the exhaustiveness of the service disciplines. This induces a complete ordering in terms of efficiency of the service disciplines. The results also lead to new rules for optimization of the system performance with respect to the service disciplines at the queues. Further, the exact asymptotic results suggest simple expected waiting-time approximations for polling models in heavy traffic. Numerical experiments show that the accuracy of the approximations is excellent for practical heavy-traffic scenarios.