An ODE for an Overloaded X Model Involving a Stochastic Averaging Principle
Year: 2011
Type: article
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).
Source: Stochastic Systems
DOI: 10.1287/10-ssy009
Authors: Ohad Perry, Ward Whitt
Institutions: Centrum Wiskunde & Informatica, Columbia University
Language: English
Subfield: Management Information Systems
Domain: Social Sciences
Open Access status: diamond
OpenAlex ID: W2000228116