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STABILIZING PERFORMANCE IN NETWORKS OF QUEUES WITH TIME-VARYING ARRIVAL RATES

Published online by Cambridge University Press:  09 July 2014

Yunan Liu  and
Ward Whitt
Yunan Liu
Affiliation:
Department of Industrial Engineering, North Carolina State University, Raleigh, NC 27695, USA E-mail: 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

This paper investigates extensions to feed-forward queueing networks of an algorithm to set staffing levels (the number of servers) to stabilize performance % at Quality of Service (QoS) targets in an Mt/GI/st+GI multi-server queue with a time-varying arrival rate. The model has a non-homogeneous Poisson process (NHPP), customer abandonment, and non-exponential service and patience distributions. For a single queue, simulation experiments showed that the algorithm successfully stabilizes abandonment probabilities and expected delays over a wide range of Quality-of-Service (QoS) targets. A limit theorem showed that stable performance at fixed QoS targets is achieved asymptotically as the scale increases (by letting the arrival rate grow while holding the service and patience distributions fixed). Here we extend that limit theorem to a feed-forward queueing network. However, these fixed QoS targets provide low QoS as the scale increases. Hence, these limits primarily support the algorithm with a low QoS target. For a high QoS target, effectiveness depends on the NHPP property, but the departure process never is exactly an NHPP. Thus, we investigate when a departure process can be regarded as approximately an NHPP. We show that index of dispersion for counts is effective for determining when a departure process is approximately an NHPP in this setting. In the important common case when all queues have high QoS targets, we show that both: (i) the departure process is approximately an NHPP from this perspective and (ii) the algorithm is effective.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 4 , October 2014 , pp. 419 - 449
Copyright
Copyright © Cambridge University Press 2014 

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