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STAFFING TO STABILIZE BLOCKING IN LOSS MODELS WITH TIME-VARYING ARRIVAL RATES

Published online by Cambridge University Press:  09 December 2015

Andrew Li ,
Ward Whitt  and
Jingtong Zhao
Andrew Li
Affiliation:
Operations Research Center, M.I.T. 77 Mass Ave, Bldg E40-130, Cambridge, MA 02139-4307, USA E-mail: aali@mit.edu
Ward Whitt
Affiliation:
Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA E-mail: ww2040@columbia.edu
Jingtong Zhao
Affiliation:
Department of Industrial Engineering and Operations Research Columbia University, New York, NY 10027, USA E-mail: jz2477@columbia.edu
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Abstract

The modified-offered-load approximation can be used to choose a staffing function (the time-varying number of servers) to stabilize delay probabilities at target levels in multi-server delay models with time-varying arrival rates, with or without customer abandonment. In contrast, as we confirm with simulations, it is not possible to stabilize blocking probabilities to the same extent in corresponding loss models, without extra waiting space, because these probabilities necessarily change dramatically after each staffing change. Nevertheless, blocking probabilities can be stabilized provided that we either randomize the times of staffing changes or average the blocking probabilities over a suitably small time interval. We develop systematic procedures and study how to choose the averaging parameters.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 30 , Issue 2 , April 2016 , pp. 185 - 211
Copyright
Copyright © Cambridge University Press 2015 

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