@article{d939650bb44741ef864c5a2a5da9af5d,

title = "Stationary distributions and convergence for M/M/1 queues in interactive random environment",

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.",

author = "Guodong Pang and Andrey Sarantsev and Yana Belopolskaya and Yuri Suhov",

note = "Funding Information: G. Pang was supported in part by NSF grants CMMI-1635410, and DMS/CMMI-1715875 and in part by an Army Research Office Grant W911NF-17-1-0019. Y. Belopolskaya was supported in part by RSF 17-11-01136. Y. Suhov thanks Department of Mathematics at Pennsylvania State University for hospitality and support. Funding Information: G. Pang was supported in part by NSF grants CMMI-1635410, and DMS/CMMI-1715875 and in part by an Army Research Office Grant W911NF-17-1-0019. Y. Belopolskaya was supported in part by RSF 17-11-01136. Y. Suhov thanks Department of Mathematics at Pennsylvania State University for hospitality and support. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2020",

month = apr,

day = "1",

doi = "10.1007/s11134-019-09644-9",

language = "English (US)",

volume = "94",

pages = "357--392",

journal = "Queueing Systems",

issn = "0257-0130",

publisher = "Springer Netherlands",

number = "3-4",

}