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STAFFING A SERVICE SYSTEM WITH NON-POISSON NON-STATIONARY ARRIVALS

Published online by Cambridge University Press:  13 June 2016

Beixiang He ,
Yunan Liu  and
Ward Whitt
Beixiang He
Affiliation:
Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27695, USA E-mail: bhe@ncsu.edu; yliu48@ncsu.edu
Yunan Liu
Affiliation:
Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27695, USA E-mail: bhe@ncsu.edu; yliu48@ncsu.edu
Ward Whitt
Affiliation:
Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA E-mail: ww2040@columbia.edu
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Abstract

Motivated by non-Poisson stochastic variability found in service system arrival data, we extend established service system staffing algorithms using the square-root staffing formula to allow for non-Poisson arrival processes. We develop a general model of the non-Poisson non-stationary arrival process that includes as a special case the non-stationary Cox process (a modification of a Poisson process in which the rate itself is a non-stationary stochastic process), which has been advocated in the literature. We characterize the impact of the non-Poisson stochastic variability upon the staffing through the heavy-traffic limit of the peakedness (ratio of the variance to the mean in an associated stationary infinite-server queueing model), which depends on the arrival process through its central limit theorem behavior. We provide simple formulas to quantify the performance impact of the non-Poisson arrivals upon the staffing decisions, in order to achieve the desired service level. We conduct simulation experiments with non-stationary Markov-modulated Poisson arrival processes with sinusoidal arrival rate functions to demonstrate that the staffing algorithm is effective in stabilizing the time-varying probability of delay at designated targets.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 30 , Issue 4 , October 2016 , pp. 593 - 621
Copyright
Copyright © Cambridge University Press 2016 

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