## Subexponential Loss Rates in a GI/GI/1 Queue with Applications (1999)

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Citations: | 17 - 4 self |

### BibTeX

@MISC{Jelenkovic99subexponentialloss,

author = {Predrag R. Jelenkovic},

title = {Subexponential Loss Rates in a GI/GI/1 Queue with Applications},

year = {1999}

}

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### Abstract

Consider a single server queue with i.i.d. arrival and service processes, fA; A n ; n 1g and fC; C n ; n 1g, respectively, and finite buffer B. The queue content process fQ B n ; n 0g is recursively defined as Q B n+1 = min((Q B n + A n+1 \Gamma C n+1 ) + ; B), q + = max(0; q). When E(A \Gamma C) ! 0, and A has a subexponential distribution, we show that the stationary expected loss rate for this queue E(Q B n + A n+1 \Gamma C n+1 \Gamma B) + has the following explicit asymptotic characterization E(Q B n +A n+1 \Gamma C n+1 \Gamma B) + ¸ E(A \Gamma B) + as B !1; independently of the server process C n . For a fluid queue with capacity c, M/G/1 arrival process a t , characterized by intermediately regularly varying On periods ø on , that arrive with Poisson rate , the average loss rate B loss satisfies B loss ¸ E(ø on j \Gamma B) + as B !1; where j = r + ae \Gamma c, ae = Ea t ! c, and r; r c, is the rate at which the fluid is arriving during an On per...