Loss rates in the single-server queue with complete rejection

Bert Zwart ()

Mathematical Methods of Operations Research, 2015, vol. 81, issue 3, 299-315

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

Keywords: Queues; Complete rejection; Loss probability; Lévy processes; Two-sided exit problem; Asymptotic expansions; 60K25 (primary); 60J30; 68M20; 90B22 (secondary) (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s00186-015-0497-x

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