222
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

Transient Analysis for State-Dependent Queues with Catastrophes

, &
Pages 1201-1217 | Received 18 Feb 2008, Accepted 21 Apr 2008, Published online: 29 Oct 2008

REFERENCES

  • Kelton , W.D. 1985 . Transient exponential-Erlang queues and steady-state simulation . Communications of the ACM 28 : 741 – 749 .
  • Parthasarathy , P.R. , and Sudhesh , R. 2005 . The overflow process from a state-dependent queue . International Journal of Computer Mathematics 82 : 1073 – 1093 .
  • Parthasarathy , P.R. , and Sudhesh , R. 2006 . Exact transient solution of a state-dependent birth-death process . Journal of Applied Mathematics and Stochastic Analysis 19 : 1 – 16 .
  • Boucherie , R.J. , Boxma , O.J. , and Sigman , K. 1997 . A note on negative customers, G1/G/1 workload and risk processes . Probability in Engineering and Informational Sciences 11 : 305 – 311 .
  • Artalejo , J.R. , and Gomez-Corral , A. 1997 . Steady-state solution of a single server queue with linear request repeated . Journal of Applied Probability 34 : 223 – 233 .
  • Jain , G. , and Sigman , K. 1996 . A Pollaczek–Khinchine formula for M/G/1 queues with disasters . Journal of Applied Probability 33 : 1191 – 1200 .
  • Di Crescenzo , A. , Giorno , V. , Nobile , A.G. , and Ricciardi , L.M. 2003 . On the M/M/1 queue with catastrophes and its continuous approximation . Queuing Systems 43 : 329 – 347 .
  • Chao , X. 1995 . A queueing network model with catastrophes and product form solution . Operations Research Letters 18 : 75 – 79 .
  • Chen , A. , and Renshaw , E. 1997 . The M/M/1 queue with mass exodeus and mass arrivals when empty . Journal of Applied Probability 34 : 192 – 207 .
  • Gelenbe , E. 1991 . Product form queueing networks with positive and negative customers . Journal of Applied Probability 28 : 656 – 663 .
  • Gelenbe , E. 1993 . G-Networks with signals and batch removal . Probability in Engineering and Informational Sciences 7 : 335 – 342 .
  • Krishna Kumar , B. , and Arivudainambi , D. 2000 . Transient solution of an M/M/1 queue with catastrophes . Computers and Mathematics with Applications 40 : 1233 – 1240 .
  • Artalejo , J.R. 2000. G-Networks: a versatile approach for work removal in queueing networks. European Journal of Operations Research 126:233–249.
  • Wall , H.S. 1948 . Analytical Theory of Continued Fraction . D.Van.Nostrand , Toronto .
  • Natvig , B. 1974 . On the transient state probabilities for a queueing model where potential customers are discouraged by queue length . Journal of Applied Probability 11 : 345 – 354 .
  • Ng , C.H. 1996 . Queueing Modelling Fundamentals . John Wiley , Chichester .
  • Swift , R.J. 2001 . Transient probabilities for a simple birth-death-immigration process under the influence of total catastrophe . Journal of Mathematical Scientist 25 : 689 – 692 .
  • Gross , D. , and Harris , C.M. 1985 . Fundamentals of Queueing Theory . Wiley , New York .
  • Newell , G.F. 1984 . The M/M/∞ Service System with Ranked Servers in Heavy Traffic . Springer-Verlag , New York .
  • Coffman , E.G. Jr. , Kadota , T.T. , and Shepp , L.A. 1985 . A stochastic model of fragmentation in dynamic storage allocation . SIAM Journal of Computation 14 : 416 – 425 .
  • Abramowitz , M. , and Stegun , I. 1965 . Handbook of Mathematical Functions . Dover , New York .
  • Lorentzen , L. , and Waadeland , H. 1992 . Continued Fractions with Applications . North-Holland , Amsterdam .
  • Andrews , L.C. 1992 . Special Functions of Mathematics for Engineers. , 2nd ed. McGraw-Hill , Singapore .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.