Paper Info
Title
Subexponential loss rates in a GI/GI/1 queue with applications
Abstract
Consider a single server queue with i.i.d. arrival and service processes, \{A,\ A_n,n\geq 0\} and \{C,\ C_n,n\geq 0\}, respectively, and a finite buffer B. The queue content process \{Q^B_n,\ n\geq 0\} is recursively defined as Q^B_{n+1}=\min((Q^B_n+A_{n+1}-C_{n+1})^+,B), q^+=\max(0,q). When \mathbb{E}(A-C), and A has a subexponential distribution, we show that the stationary expected loss rate for this queue \mathbb{E}(Q^B_n+A_{n+1}-C_{n+1}-B)^+ has the following explicit asymptotic characterization: \mathbb{E}(Q^B_n+A_{n+1}-C_{n+1}-B)^+\sim \mathbb{E}(A-B)^+ \quad \hbox{as} \ B\rightarrow \infty, independently of the server process C_n. For a fluid queue with capacity c, M/G/\infty arrival process A_t, characterized by intermediately regularly varying on periods \tau^{\mathrm{on}}, which arrive with Poisson rate \Lambda, the average loss rate \lambda_{\mathrm{loss}}^B satisfies {\lambda_{\mathrm{loss}}^B}\sim \Lambda \mathbb{E}(\tau^{\mathrm{on}}\eta-B)^+ \quad \hbox{as}\ B\rightarrow \infty, where \eta=r+\rho-c, \rho=\mathbb{E}A_t; r (c\leq r) is the rate at which the fluid is arriving during an on period. Accuracy of the above asymptotic relations is verified with extensive numerical and simulation experiments. These explicit formulas have potential application in designing communication networks that will carry traffic with long-tailed characteristics, e.g., Internet data services.
Year
DOI
Venue
1999
10.1023/A:1019167927407
Queueing Syst.
Keywords
Field
DocType
long-tailed traffic models,subexponential distributions,long-range dependency,network multiplexer,finite buffer queue,fluid flow queue,M/G/∞ process
Combinatorics,Mathematical optimization,Arrival process,Queue,Single server queue,Queueing system,Long-range dependency,Calculus,Mathematics,Lambda
Journal
Volume
Issue
ISSN
33
1/3
1572-9443
Citations 
PageRank 
References 
14
1.48
12
Authors
1
Name
Order
Citations
PageRank
Predrag R. Jelenkovic121929.99