NDLI: Stochastic grey-box modeling of queueing systems: fitting birth-and-death processes to data

Content Provider	Springer Nature Link
Author	Whitt, Ward Dong, James
Copyright Year	2014
Abstract	This paper explores grey-box modeling of queueing systems. A stationary birth-and-death (BD) process model is fitted to a segment of the sample path of the number in the system in the usual way. The birth (death) rates in each state are estimated by the observed number of arrivals (departures) in that state divided by the total time spent in that state. Under minor regularity conditions, if the queue length (number in the system) has a proper limiting steady-state distribution, then the fitted BD process has that same steady-state distribution asymptotically as the sample size increases, even if the actual queue-length process is not nearly a BD process. However, the transient behavior may be very different. We investigate what we can learn about the actual queueing system from the fitted BD process. Here we consider the standard $$GI/GI/s$$ queueing model with $$s$$ servers, unlimited waiting room and general independent, non-exponential, interarrival-time and service-time distributions. For heavily loaded $$s$$ -server models, we find that the long-term transient behavior of the original process, as partially characterized by mean first passage times, can be approximated by a deterministic time transformation of the fitted BD process, exploiting the heavy-traffic characterization of the variability.
Ending Page	426
Page Count	36
Starting Page	391
File Format	PDF
ISSN	02570130
e-ISSN	15729443
Journal	Queueing Systems
Issue Number	3-4
Volume Number	79
Language	English
Publisher	Springer US
Publisher Date	2014-12-02
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	First passage times Grey-box modeling Non-Markovian processes: estimation Reliability, availability, maintenance, inspection Transient behavior Systems Theory, Control Birth-and-death processes Fitting stochastic models to data Functional limit theorems; invariance principles Probability Theory and Stochastic Processes Heavy traffic Operations Research/Decision Theory Production/Logistics/Supply Chain Continuous-time Markov processes on general state spaces Queueing theory Computer Communication Networks
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Management Science and Operations Research Computational Theory and Mathematics Computer Science Applications

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