Heavy-traffic fluid limits for periodic infinite-server queues

Ward Whitt ()
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Ward Whitt: Columbia University

Queueing Systems: Theory and Applications, 2016, vol. 84, issue 1, No 5, 143 pages

Abstract: 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 $$M_t/GI/\infty $$ M t / G I / ∞ 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 $$M_t/GI/\infty $$ M t / G I / ∞ model that should be seen with data if the $$M_t/GI/\infty $$ M t / G I / ∞ 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 $$M_t/GI/\infty $$ M t / G I / ∞ model is appropriate. We also establish many-server heavy-traffic fluid limits for the steady-state distribution in the periodic $$M_t/GI/\infty $$ M t / G I / ∞ model. For the special case of sinusoidal arrival rates, the limiting steady-state distribution has an arcsine law.

Keywords: Stochastic grey-box queueing models; Periodic queues; Periodic arrival rates; Periodic steady state; Birth-and-death processes; Fitting birth-and-death processes to data; Many-server heavy-traffic limits; 60F17; 60J25; 60K25; 62M09; 90B22 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11134-016-9494-x

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