Analysis of polling systems
Variance effects in cyclic production systems
Management Science
Efficient visit frequencies for polling tables: minimization of waiting cost
Queueing Systems: Theory and Applications
Computing distributions and moments in polling models by numerical transform inversion
Performance Evaluation
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
A Practical Scheduling Method for Multiclass Production Systems with Setups
Management Science
Polling systems in heavy traffic: Exhaustiveness of service policies
Queueing Systems: Theory and Applications
Polling systems in heavy traffic: Higher moments of the delay
Queueing Systems: Theory and Applications
Decomposition results for general polling systems and their applications
Queueing Systems: Theory and Applications
Operations Research Letters
Multiproduct Systems with Both Setup Times and Costs: Fluid Bounds and Schedules
Operations Research
Probability in the Engineering and Informational Sciences
Branching-type polling systems with large setups
OR Spectrum
Closed-form waiting time approximations for polling systems
Performance Evaluation
On open problems in polling systems
Queueing Systems: Theory and Applications
On polling systems with large setups
Operations Research Letters
Manufacturing & Service Operations Management
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Multiclass single-server systems with significant setup times (polling models) are common in industry. This article considers asymptotics for polling models with increasing setup times. Two types of polling model are considered, namely (a) polling models with polling tables, exhaustive service, and deterministic setups, and (b) cyclic exhaustive service polling models with general setups under heavy traffic. It is shown that as the mean setup time increases to infinity, the scaled intervisit time for each queue (time between service of that queue) converges in probability to a constant. This, in turn, is shown to imply that scaled steady-state waiting time converges in distribution to either a uniform distribution or a simple discrete random variable multiplied by a uniform random variable as setups tend to infinity. These results lead to considerable insight into the behavior of systems with setups, and conclusions are drawn with respect to previous studies.