NDLI: Heavy-traffic fluid limits for periodic infinite-server queues

Content Provider	Springer Nature Link
Author	Whitt, Ward
Copyright Year	2016
Abstract	To better understand what stochastic model might be appropriate in applications with system data, we study the consequences of fitting a stationary birth-and-death (BD) process to the sample path of a periodic $$M_t/GI/\infty $$ model. The fitted BD process will necessarily have the correct steady-state distribution (appropriately defined), but will not have the correct transient behavior. Nevertheless, the fitted birth-rate and death-rate functions have structure determined by the $$M_t/GI/\infty $$ model that should be seen with data if the $$M_t/GI/\infty $$ model is appropriate. In this paper, we establish heavy-traffic fluid limits that yield explicit approximation formulas for the fitted birth-rate and death-rate functions that can help evaluate whether a periodic $$M_t/GI/\infty $$ model is appropriate. We also establish many-server heavy-traffic fluid limits for the steady-state distribution in the periodic $$M_t/GI/\infty $$ model. For the special case of sinusoidal arrival rates, the limiting steady-state distribution has an arcsine law.
Ending Page	143
Page Count	33
Starting Page	111
File Format	PDF
ISSN	02570130
e-ISSN	15729443
Journal	Queueing Systems
Issue Number	1-2
Volume Number	84
Language	English
Publisher	Springer US
Publisher Date	2016-07-20
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Non-Markovian processes: estimation Periodic queues Many-server heavy-traffic limits Queues and service Systems Theory, Control Birth-and-death processes Functional limit theorems; invariance principles Probability Theory and Stochastic Processes Stochastic grey-box queueing models Periodic steady state Fitting birth-and-death processes to data Periodic arrival rates Operation Research/Decision Theory Supply Chain Management 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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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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