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On the infinite server shortest queue problem: Non-symmetric case

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Abstract

We consider two parallel M/M/∞ queues. All servers in the first queue work at rate μ1 and all in the second work at rate μ2. A new arrival is routed to the system with the lesser number of customers. If both queues have equal occupancy, the arrival joins the first queue with probability ν1, and the second with probability ν2 = 1−ν1. We analyze this model asymptotically. We assume that the arrival rate λ is large compared to the two service rates. We give several different asymptotic formulas, that apply for different ranges of the state space. The numerical accuracy of the asymptotic results is tested.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Queensborough Community College, the City University of New York, 22-05 56th Ave., Bayside, NY, 11364

    Haishen Yao

  2. Department of Mathematics, Statistics and Computer Science (M/C 249), University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL, 60607-7045

    Charles Knessl

Authors
  1. Haishen Yao
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  2. Charles Knessl
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Correspondence to Charles Knessl.

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AMS subject classification 60K25 60K30 34E20

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Yao, H., Knessl, C. On the infinite server shortest queue problem: Non-symmetric case. Queueing Syst 52, 157–177 (2006). https://doi.org/10.1007/s11134-006-5500-z

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  • DOI: https://doi.org/10.1007/s11134-006-5500-z

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