Stationary distributions and convergence for M/M/1 queues in interactive random environment

Guodong Pang (), Andrey Sarantsev (), Yana Belopolskaya () and Yuri Suhov ()
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Guodong Pang: The Pennsylvania State University
Andrey Sarantsev: University of Nevada in Reno
Yana Belopolskaya: Saint Petersburg State University of Architecture and Civil Engineering
Yuri Suhov: University of Cambridge

Queueing Systems: Theory and Applications, 2020, vol. 94, issue 3, No 7, 357-392

Abstract: Abstract A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depend on the queue length. We consider in detail two types of Markov random environments: a pure jump process and a reflected jump diffusion. In both cases, the joint dynamics are constructed so that the stationary distribution can be explicitly found in a simple form (weighted geometric). We also derive an explicit estimate for the exponential rate of convergence to the stationary distribution via coupling.

Keywords: Queues in interactive random environment; Stationary distribution; Rate of convergence to stationarity; Coupling; 60K25; 60K30; 60K35; 60K37; 90B22; 60J60; 60J65; 37A25 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11134-019-09644-9

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