An Interpretation and Extensions of Duality Relations among Queueing Systems

대기행렬시스템의 쌍대관계에 대한 해석 및 확장

  • Published : 2003.03.01

Abstract

Using the concept of closed queueing network, we present a consistent way of interpreting existing duality relations among queueing systems. Also, using embedded Markov chains, we present a few new duality relations for the queueing systems with negative customers.

Keywords

References

  1. 대기행렬이론(개정판) 이호우
  2. Stochastic Models v.6 no.4 Probabilistic Interpretations of Some Duality Results for the Matrix Paradingms in Queueing Theory Asmussen, S.;V. Ramaswani https://doi.org/10.1080/15326349908807170
  3. An Introduction to Probability Theory and its Applications (second edition) v.2 Feller, W.
  4. Operations Research Letters v.21 A Note on an M/G/1/N Queue with Vacation Time and Exhaustive Service Discipline Frey, A.;Y. Takahashi https://doi.org/10.1016/S0167-6377(97)00027-8
  5. Operations Research Letters v.21 The Loss Probability in an Overloaded Queue Using the Dual Queue Gouweleeuw, F.N. https://doi.org/10.1016/S0167-6377(97)00020-5
  6. Operations Research Letters v.14 Comments on Duality of Queues with Finite Buffer Size Hlynka, M.;T. Wang https://doi.org/10.1016/0167-6377(93)90016-A
  7. J. of the Operational Research Society v.47 The Finite Capacity GI/M/1 Queue with Server Vacations Karaesmen, F.;S.M. Gupta https://doi.org/10.1057/jors.1996.101
  8. Computers and Operations Research v.24 no.6 Duality Relations for Queues with Arrival and Service Control Karaesmen, F.;S.M. Gupta https://doi.org/10.1016/S0305-0548(96)00072-X
  9. European J. of Operational Research v.142 A Recursive Method for the N Policy G/M/1 Queueing System with Finite Capacity Ke, J.C.;K.H. Wang https://doi.org/10.1016/S0377-2217(01)00317-4
  10. Operations Research Letters v.13 Duality between the Erlang Loss System and a Finite Source Queue Kimura, T. https://doi.org/10.1016/0167-6377(93)90007-4
  11. Queueing Systems, Theory v.1 Kleinrock, L.
  12. Mathematics of Operations Research v.14 no.2 Duality and Other Results for M/G/1 and GI/M/1 Queues, via a New Ballot Theorem Niu, S.C.;R.B. Cooper https://doi.org/10.1287/moor.14.2.281
  13. Queueing Systems v.8 A Duality Relation for Busy Cycles in GI/G/1 Queues Niu, S.C.;R.B. Cooper https://doi.org/10.1007/BF02412250
  14. Queues and Inventories: A Study of Their Basic Stochastic Processes Prabhu, N.U.
  15. Introduction to the Theory of Queues Takacs, L.
  16. J. of Applied Probability v.38 no.4 A Note on the GI/M/1 Queue with Poisson Negative Arrivals Yang, W.S.;K.C.Chae https://doi.org/10.1239/jap/1011994196