Abstract
We discuss the problem of establishing an upper bound for the distribution tail of the stationary waiting time D in the GI/GI/1 FCFS queue.
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Abate, J., Choudhury, G.L., Whitt, W.: Waiting-time tail probabilities in queues with long-tail service-time distributions. Queueing Syst. 16, 311–338 (1994)
Asmussen, S.: Applied Probability and Queues, 2nd edn. Springer, New York (2003)
Baltrunas, A.: Second-order asymptotics for the ruin probability in the case of very large claims. Sib. Math. J. 40, 1034–1043 (1999)
Borovkov, A.A., Borovkov, K.A.: Asymptotic Analysis of Random Walks. Heavy-Tailed Distributions. Cambridge University Press, Cambridge (2008)
Embrechts, P., Veraverbeke, N.: Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insur. Math. Econ. 1, 55–72 (1982)
Foss, S., Korshunov, D., Zachary, S.: An Introduction to Heavy-Tailed and Subexponential Distributions. Springer, Berlin (2011)
Kalashnikov, V.: Geometric Sums: Bounds for Rare Events with Applications. Kluwer Academic, Dordrecht (1997)
Kalashnikov, V.: Bounds for ruin probabilities in the presence of large claims and their comparison. Insur. Math. Econ. 20, 146–147 (1997)
Kalashnikov, V., Tsitsiashvili, G.: Tails of waiting times and their bounds. Queueing Syst. 32, 257–283 (1999)
Kalashnikov, V., Tsitsiashvili, G.: Asymptotically correct bounds of geometric convolutions with subexponential components. J. Math. Sci. 106, 2806–2819 (2001)
Korolev, V.Yu., Bening, V.E., Shorgin, S.Ya.: Mathematical Foundations of Risk Theory. Fizmatlit, Moscow (2007) (in Russian)
Korshunov, D.A.: On distribution tail of the maximum of a random walk. Stoch. Process. Appl. 72, 97–103 (1997)
Lindley, D.V.: The theory of queues with a single server. Proc. Camb. Philos. Soc. 48, 277–289 (1952)
Meyn, S.P., Tweedie, R.L.: Markov Chains and Stochastic Stability. Springer, Berlin (1993)
Pakes, A.G.: On the tails of waiting-time distribution. J. Appl. Probab. 12, 555–564 (1975)
Richards, A.: On upper bounds for the tail distribution of geometric sums of subexponential random variables. Queueing Syst. 62, 229–242 (2009)
Veraverbeke, N.: Asymptotic behavior of Wiener-Hopf factors of a random walk. Stoch. Process. Appl. 5, 27–37 (1977)
Willekens, E., Teugels, J.L.: Asymptotic expansions for waiting time probabilities in an M/G/1 queue with long-tailed service time. Queueing Syst. 10, 295–313 (1992)
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Korshunov, D. How to measure the accuracy of the subexponential approximation for the stationary single server queue. Queueing Syst 68, 261–266 (2011). https://doi.org/10.1007/s11134-011-9243-0
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DOI: https://doi.org/10.1007/s11134-011-9243-0
Keywords
- FCFS single server queue
- Stationary waiting time
- Heavy tails
- Large deviations
- Long tailed distribution
- Subexponential distribution
- Integrated tail distribution
- Accuracy of approximation
- Lower and upper bounds