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Original Articles

A General Class of Closed Fork and Join Queues with Subexponential Service Times

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Pages 523-535 | Received 01 May 2005, Accepted 01 Jul 2007, Published online: 02 Nov 2007

REFERENCES

  • Arlitt , M.F. ; Williamson , C.L. Web server workload characterization: The search for invariants . Proceedings of the 1996 SIGMETRICS Conference on Measurement and Modeling Computer Systems , 1996 ; 126 – 137 .
  • Asmussen , S. ; Klüppelberg , C. ; Sigman , K. Sampling at subexponential times, with queueing applications . Stochastic Process. Appl. 1999 , 79 , 265 – 286 .
  • Asmussen , S. ; M⊘ller , J.R. Tail asymptotics for M/G/1 type queueing processes with subexponential increments . Queueing Systems 1999 , 33 , 153 – 176 .
  • Asmussen , S. ; Schmidli , H. ; Schmidt , V. Tail probabilities for non-standard risk and queueing processes with subexponential jumps . Adv. in Appl. Probab. 1996 , 31 , 422 – 447 .
  • Ayhan , H. ; Palmowski , Z. ; Schlegel , S. Cyclic queueing networks with subexponential service times . Journal of Applied Probability 2004 , 41 , 791 – 801 .
  • Baccelli , F. ; Brémaud , P. Elements of Queueing Theory: Palm-Martingale Calculus and Stochastic Recurrences ; Springer-Verlag : New York , 1994 .
  • Baccelli , F. ; Cohen , G. ; Olsder , G.J. ; Quadrat , J.-P. Synchronization and Linearity: An Algebra for Discrete Event Systems ; John Wiley and Sons : Chichester , 1992 .
  • Baccelli , F. ; Foss , S. Moments and tails in monotone-separable stochastic networks . Annals of Applied Probability 2004 , 14 , 612 – 650 .
  • Baccelli , F. ; Foss , S. ; Lelarge , M. Asymptotics of subexponential max plus networks: The stochastic event graph case . Queueing Systems 2004 , 46 , 75 – 96 .
  • Baccelli , F. ; Foss , S. ; Lelarge , M. Tails in generalized jackson networks with subexponential service distributions . Journal of Applied Probability 2005 , 42 , 513 – 530 .
  • Baccelli F. ; Schlegel S. ; Schmidt V. Asymptotics of stochastic networks with subexponential service times . Queueing Systems 1999 , 33 , 205 – 232 .
  • Crovella , M.E. ; Bestavros , A. Self-Similarity in World Wide Web Traffic: Evidence and Possible Causes . Proceedings of the 1996 SIGMETRICS Conference on Measurement and Modeling Computer Systems , 1996 ; 160 – 169 .
  • Crovella , M.E. ; Lipsky , L. Long-lasting transient conditions in simulations with heavy tailed workloads. Proceedings of the 1997 Winter Simulation Conference, 1997; 1005–1012.
  • Embrechts , P. ; Veraverbeke , N. Estimates for the probability of ruin with special emphasis on the possibility of large claims . Insurance Math. Econom. 1982 , 1 , 55 – 72 .
  • Feldmann , A. ; Gilbert , A.C. ; Willinger , W. ; Kurtz , T.G. The changing nature of the network traffic: Scaling phenomena . ACM SIGCOMM Computer Communication Review 1998 , 28 , 42 – 55 .
  • Fowler , T.B. A short tutorial on fractals and internet traffic . The Telecommunications Review 1999 ; Mitretek Systems : McLean, VA , 1999 .
  • Huang , T. ; Sigman , K. Steady state asymptotics for tandem, split-match and other feedforward queues with heavy tailed service . Queueing Systems 1999 , 33 , 233 – 259 .
  • Jelenkovic , P. ; Lazar , A.A. Subexponential asymptotics of a markov-modulated random walk with queueing applications . J. Appl. Probab. 1998 , 35 , 325 – 347 .
  • Ko , S.-K. ; Serfozo , R.F. Response times in M/M/s fork-join networks . Adv. in Appl. Probab. 2004 , 34 , 854 – 871 .
  • Lelarge , M. ; Dieker , A.B. Tails for (max, +) recursions under subexponentiality . Queueing Systems 2006 , 53 , 213 – 230 .
  • Pakes , A.G. On the tails of the waiting time distributions . J. Appl. Probab. 1975 , 12 , 555 – 564 .
  • Paxson , V. ; Floyd , S. Wide area traffic: The failure of poisson modeling . IEEE/ACM Transactions on Networking 1995 , 3 , 226 – 244 .
  • Rolski , T. ; Schmidli , H. ; Schmidt , V. ; Teugels , J.L. Stochastic Processes for Insurance and Finance ; Wiley : Chichester , 1999 .
  • Sigman , K. Appendix: A primer on heavy-tailed distributions . Queueing Systems 1999 , 33 , 261 – 275 .
  • Willekens , E. ; Teugels , J. Asymptotic expansions for waiting time probabilities in an M/G/1 queue with long-tailed service time . Queueing Systems 1992 , 10 , 295 – 312 .
  • Xia , C.H. ; Liu , Z. Queueing sytems with long-range dependent input process and subexponential service times . Proceedings of ACM Sigmetrics 2003 , 25 – 36 .

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