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Excessive backlog probabilities of two parallel queues

Author

Listed:
  • Kamil Demirberk Ünlü

    (Ankara University
    Middle East Technical University)

  • Ali Devin Sezer

    (Middle East Technical University)

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

Suggested Citation

  • Kamil Demirberk Ünlü & Ali Devin Sezer, 2020. "Excessive backlog probabilities of two parallel queues," Annals of Operations Research, Springer, vol. 293(1), pages 141-174, October.
    • Handle: RePEc:spr:annopr:v:293:y:2020:i:1:d:10.1007_s10479-019-03324-w
    DOI: 10.1007/s10479-019-03324-w
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    References listed on IDEAS

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