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Loss rates in the single-server queue with complete rejection

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  • Bert Zwart

Abstract

Consider the single-server queue in which customers are rejected if their total sojourn time would exceed a certain level $$K$$ K . A basic performance measure of this system is the probability $$P_K$$ P K that a customer gets rejected in steady state. This paper presents asymptotic expansions for $$P_K$$ P K as $$K\rightarrow \infty $$ K → ∞ . If the service time $$B$$ B is light-tailed and inter-arrival times are exponential, it is shown that the loss probability has an exponential tail. The proof of this result heavily relies on results on the two-sided exit problem for Lévy processes with no positive jumps. For heavy-tailed (subexponential) service times and generally distributed inter-arrival times, the loss probability is shown to be asymptotically equivalent to the trivial lower bound $$P(B>K)$$ P ( B > K ) . Copyright The Author(s) 2015

Suggested Citation

  • Bert Zwart, 2015. "Loss rates in the single-server queue with complete rejection," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 299-315, June.
    • Handle: RePEc:spr:mathme:v:81:y:2015:i:3:p:299-315
    DOI: 10.1007/s00186-015-0497-x
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