Semi-Markov Queues with Heavy Tails

Soren Asmussen
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Soren Asmussen: Lund University

Chapter Chapter 17 in Semi-Markov Models and Applications, 1999, pp 269-284 from Springer

Abstract: Abstract We consider queues with a sub-exponential heavy-tailed service time distribution B. Classical results stating that the tails of the steady-state waiting time, resp. the maximal waiting time within a regenerative cycle, are proportional to $$\int_x^\infty {\bar B(y)dy,{\text{resp}}{\text{. }}\bar B(y) = 1 - B(y),} $$ , are extended to various semi-Markov queues.

Keywords: Cycle maximum; M/G/l queue; Markov-modulation; rare event; regular variation; sub-exponential distribution. (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-1-4613-3288-6_17

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