State space collapse with application to heavy traffic limits for multiclass queueing networks
Queueing Systems: Theory and Applications
Designing a Call Center with Impatient Customers
Manufacturing & Service Operations Management
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects
Manufacturing & Service Operations Management
Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems
Manufacturing & Service Operations Management
Queue-and-Idleness-Ratio Controls in Many-Server Service Systems
Mathematics of Operations Research
Responding to Unexpected Overloads in Large-Scale Service Systems
Management Science
State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems
Mathematics of Operations Research
Shadow-Routing Based Control of Flexible Multiserver Pools in Overload
Operations Research
Overflow Networks: Approximations and Implications to Call Center Outsourcing
Operations Research
A Fluid Limit for an Overloaded X Model via a Stochastic Averaging Principle
Mathematics of Operations Research
Diffusion approximation for an overloaded X model via a stochastic averaging principle
Queueing Systems: Theory and Applications
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In a recent paper we considered two networked service systems, each having its own customers and designated service pool with many agents, where all agents are able to serve the other customers, although they may do so inefficiently. Usually the agents should serve only their own customers, but we want an automatic control that activates serving some of the other customers when an unexpected overload occurs. Assuming that the identity of the class that will experience the overload or the timing and extent of the overload are unknown, we proposed a queue-ratio control with thresholds: When a weighted difference of the queue lengths crosses a prespecified threshold, with the weight and the threshold depending on the class to be helped, serving the other customers is activated so that a certain queue ratio is maintained. We then developed a simple deterministic steady-state fluid approximation, based on flow balance, under which this control was shown to be optimal, and we showed how to calculate the control parameters. In this sequel we focus on the fluid approximation itself and describe its transient behavior, which depends on a heavy-traffic averaging principle. The new fluid model developed here is an ordinary differential equation driven by the instantaneous steady-state probabilities of a fast-time-scale stochastic process. The averaging principle also provides the basis for an effective Gaussian approximation for the steady-state queue lengths. Effectiveness of the approximations is confirmed by simulation experiments.