Rational Abandonment from Tele-Queues: Nonlinear Waiting Costs with Heterogeneous Preferences
Queueing Systems: Theory and Applications
Contact Centers with a Call-Back Option and Real-Time Delay Information
Operations Research
Pricing and Dimensioning Competing Large-Scale Service Providers
Manufacturing & Service Operations Management
Exploiting Market Size in Service Systems
Manufacturing & Service Operations Management
Exploiting network effects in the provisioning of large scale systems
ACM SIGMETRICS Performance Evaluation Review - Special Issue on IFIP PERFORMANCE 2011- 29th International Symposium on Computer Performance, Modeling, Measurement and Evaluation
Queueing Systems: Theory and Applications
Optimizing the profit of on-demand multimedia service via a server-dependent queuing system
WAIM '06 Proceedings of the 7th international conference on Advances in Web-Age Information Management
A Diffusion Regime with Nondegenerate Slowdown
Operations Research
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We investigate how performance scales in the standardM/M/n queue in the presence of growing congestion-dependent customer demand. We scale the queue by letting the potential (congestion-free) arrival rate be proportional to the number of servers,n, and lettingn increase. We let the actual arrival rate withn servers be of the form ? n =f(? n)n, wheref is a strictly-decreasing continuous function and ? n is a steady-state congestion measure. We consider several alternative congestion measures, such as the mean waiting time and the probability of delay. We show, under minor regularity conditions, that for eachn there is a unique equilibrium pair (?* n ?* n) such that ?* n is the steady-state congestion associated with arrival rate ?* n, ?* n. Moreover, we show that, asn increases, the queue with the equilibrium arrival rate ?* n is brought into heavy traffic, but the three different heavy-traffic regimes for multiserver queues identified by Halfin and Whitt (1981) each can arise depending on the congestion measure used. In considerable generality, there is asymptotic service efficiency: the server utilization approaches one asn increases. Under the assumption of growing congestion-dependent demand, the service efficiency can be achieved even if there is significant uncertainty about the potential demand, because the actual arrival rate adjusts to the congestion.