Financial
Institutions
Center
Computing Performance Measures
in a Multi-Class Multi-Resource
Processor-Shared Loss System
by
O. Zeynep AkÕÕin Patrick T. Harker 96-02-C
THE WHARTON FINANCIAL INSTITUTIONS CENTER
The Wharton Financial Institutions Center provides a multi-disciplinary research approach to the problems and opportunities facing the financial services industry in its search for competitive excellence. The Center's research focuses on the issues related to managing risk at the firm level as well as ways to improve productivity and performance.
The Center fosters the development of a community of faculty, visiting scholars and Ph.D. candidates whose research interests complement and support the mission of the Center. The Center works closely with industry executives and practitioners to ensure that its research is informed by the operating realities and competitive demands facing industry participants as they pursue competitive excellence.
Copies of the working papers summarized here are available from the Center. If you would like to learn more about the Center or become a member of our research community, please let us know of your interest.
Anthony M. Santomero Director
The Working Paper Series is made possible by a generous grant from the Alfred P. Sloan Foundation
Zeynep AkÕin is at INSEAD, Technology Management Area, Boulevard de 1
Constance, 77305 Fontainebleau, France.
Patrick Harker is at the Department of Operations and Information Management, The Wharton School, University of Pennsylvania, Philadelphia, PA 19104-6366,
Computing Performance Measures in a Multi-Class Multi-Resource Processor-Shared Loss System 1
December 1996 Revised: October 1998
Abstract: This paper develops methods to compute performance measures in a specific type of loss system with multiple classes of customers sharing the same processor. Such systems arise in the modeling of a call center, where the performance measures of interest are blocking the probability of a call and the reneging probability of customers that are put on hold. Expressions for these performance measures have been derived in previous work by the authors. Given the difficulty of computing these performance measures for realistic systems, this paper proposes two different approaches to simplify this computation. The first method introduces the idea of multi-dimensional convolutions, and uses this approach to compute exact blocking and reneging probabilities. The second method establishes an adaptation of the Monte Carlo summation technique in order to obtain good estimates of blocking and reneging probabilities in large systems along with their associated confidence intervals. Keywords : Queuing; loss system; processor sharing; computational analysis; approximation
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