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- W4299550147 abstract "We study an ordinary differential equation (ODE) arising as the many-server heavy-traffic fluid limit of a sequence of overloaded Markovian queueing models with two customer classes and two service pools. The system, known as the X model in the call-center literature, operates under the fixed-queue-ratio-with-thresholds (FQR-T) control, which we proposed in a recent paper as a way for one service system to help another in face of an unanticipated overload. Each pool serves only its own class until a threshold is exceeded; then one-way sharing is activated with all customer-server assignments then driving the two queues toward a fixed ratio. For large systems, that fixed ratio is achieved approximately. The ODE describes system performance during an overload. The control is driven by a queue-difference stochastic process, which operates in a faster time scale than the queueing processes themselves, thus achieving a time-dependent steady state instantaneously in the limit. As a result, for the ODE, the driving process is replaced by its long-run average behavior at each instant of time; i.e., the ODE involves a heavy-traffic averaging principle (AP)." @default.
- W4299550147 created "2022-10-02" @default.
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- W4299550147 date "2010-08-06" @default.
- W4299550147 modified "2023-09-27" @default.
- W4299550147 title "An ODE for an Overloaded X Model Involving a Stochastic Averaging Principle" @default.
- W4299550147 doi "https://doi.org/10.48550/arxiv.1008.1289" @default.
- W4299550147 hasPublicationYear "2010" @default.
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