Excessive backlog probabilities of two parallel queues

Kamil Demirberk Ünlü and Ali Devin Sezer ()
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Kamil Demirberk Ünlü: Ankara University
Ali Devin Sezer: Middle East Technical University

Annals of Operations Research, 2020, vol. 293, issue 1, No 8, 174 pages

Abstract: Abstract Let X be the constrained random walk on $${\mathbb Z}_+^2$$ Z + 2 with increments (1, 0), $$(-1,0)$$ ( - 1 , 0 ) , (0, 1) and $$(0,-1)$$ ( 0 , - 1 ) ; X represents, at arrivals and service completions, the lengths of two queues (or two stacks in computer science applications) working in parallel whose service and interarrival times are exponentially distributed with arrival rates $$\lambda _i$$ λ i and service rates $$\mu _i$$ μ i , $$i=1,2$$ i = 1 , 2 ; we assume $$\lambda _i 0$$ x ( 1 ) > 0 , $$P_{(n-x_n(1),x_n(2))}( \tau

Keywords: Approximation of probabilities of rare events; Exit probabilities; Constrained random walks; Queueing systems; Large deviations (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10479-019-03324-w

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