Journal of the Korean Statistical Society

  • 제29권4호
  • /
  • Pages.473-488
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  • 2000
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  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

Stochastic Comparisons of Markovian Retrial Queues

  • 발행 : 2000.12.01
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초록

We consider a Markovian retrial queue with waiting space in which the service rates and retrial rates depend on the number of customers in the service facility and in the orbit, respectively. Each arriving customer from outside or orbit decide either to enter the facility or to join the orbit in Bernoulli manner whose entering probability depend on the number of customers in the service facility. In this paper, a stochastic order relation between two bivariate processes(C(t), N(t)) representing the number of customers C(t) in the service facility and one N(t) in the orbit is deduced in terms of corresponding parameters by constructing the equivalent processes on a common probability space. some applications of the results to the stochastic bounds of the multi-server retrial model are presented.

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참고문헌

  1. Operations Research Letters v.17 A queueing systme with returning customers and waiting line Artalejo, J. R.
  2. Top v.7 no.2 A classified bibliography of research on retrial queues: Progress in 1990-1999 Artalejo, J. R.
  3. Queueing Systmes v.1 Almost sure comparison of birth and death processes with appliccation to M/M/s queneing systems Bhaskaran, B. G.
  4. Theory of Probability and Its Applications v.33 no.2 Comparability of migration processes Falin, G. I.
  5. Retrial queues Falin, G. I.;Templetion, J. G. C.
  6. Journal of Applied Probability v.24 An upper bound on the performance of queues with returning customers Greenberg, B. S.;Wolf, R. W.
  7. Journal of Applied Probability v.24 Explicit fomulas for the characteristics of the M/M/2/2 quenue with repeated attempts Hanschke, T.
  8. The Annals of Probability v.5 no.6 Stochastic inequalities on partially ordered spaces Kamae, T.;Krengel, U.;O'Brien, G. L.
  9. Frontiers in Queueing, ed. J. H. Dshalalow Retrial queues revisited Kulkarni, V. G.;Liang, H. M.
  10. Stochastic Models v.9 no.3 Monotonicity properties of singleserver retrial queues Liang, H. M.;Kulkarni, V. G.
  11. Mathematics of Operations Research v.4 Almost sure comparisons of renewal processes and Poisson processes with application to reliability theory Miller, D. R.
  12. Queueing Systems v.7 no.2 Numerical investigation of multi-server retrial model Neuts, M. F.;Rao, B. M.
  13. Advances in Applied Probability v.21 Extended continued fractions, recurrence relations and two dimensional Markov processes Pearce, C. E. M.
  14. Stochastic Orders and Their Applications Shaked, M.;Shanthikumar, J. G.
  15. Advances in Applied Probability v.11 Comparing multi-server queues with finite waiting rooms, I: Same number of servers Sonderman, D.
  16. Advances in Applied Probability v.11 Comparing multi-server queues with finite waiting rooms, II: Different number of servers Sonderman, D.
  17. Comparison Methods for Queues and Other Stochastic Models Stoyan, D.