Queues, stores, and tableaux

Journal of Applied Probability

Volumn 42, Issue 4, 2005, Pages 1145-1167

  Draief, Moez ^a,c   Mairesse, Jean ^a,c   O'Connell, Neil ^b  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b UNIVERSITY OF WARWICK   (United Kingdom)

^c UNIVERSITÉ PARIS DIDEROT   (France)

Author keywords

Burke's theorem; Noncolliding random walk; Robinson Schensted Knuth algorithm; Single server queue; Storage model; Tandem of queues

Indexed keywords

EID: 33645356189     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1134587823     Document Type: Article

References (38)

1. ANANTHARAM, V. (1987). Probabilistic proof of the interchangeability of ·/M/1 queues in series. Queueing Systems Theory Appl. 2, 387-392.
2. BACCELLI, F., BOROVKOV, A. AND MAIRESSE, J. (2000). Asymptotic results on infinite tandem queueing networks. Prob. Theory Relat. Fields 118, 365-405.
3. BARYSHNIKOV, YU. (2001). GUEs and queues. Prob. Theory Relat. Fields 119, 256-274.
4. BEDEKAR, A. S. AND AZIZOG̃LU, M (1998). The information-theoretic capacity of discrete-time queues. IEEE Trans. Inf. Theory 44, 446-461.
5. BRÉMAUD, P. (1981). Point Processes and Queues. Martingale Dynamics. Springer, Berlin.
6. BRUNEEL, H. AND KIM, B. G. (1993). Discrete-Time Models for Communication Systems Including ATM. Kluwer, Boston, MA.
7. BURKE, P. (1956). The output of a queueing system. Operat. Res. 4, 699-704.
8. CHANG, C. S. (1994). On the input-output map of a G/G/1 queue. J. Appl. Prob. 31, 1128-1133.
9. DALEY, D. J. AND VERE-JONES, D. (1988). An Introduction to the Theory of Point Processes. Springer, New York.
10. DRAIEF, M., MAIRESSE, J. AND O'CONNELL, N. (2003). Joint Burke's theorem and RSK representation for a queue and a store. In Discrete Random Walks (Paris, 2003), eds C. Banderier and C. Krattenthaler, Association of Discrete Mathematics and Theoretical Computer Science, Nancy, pp. 69-82.
11. GLYNN, P. W. AND WHITT, W. (1991). Departures from many queues in series. Ann. Appl. Prob. 1, 546-572.
12. HAMBLY, B., MARTIN, J. AND O'CONNELL, N. (2001). Pitman's 2M-X theorem for skip-free random walks with Markovian increments. Electron. Commun. Prob. 6, 73-77.
13. HARRISON, J. AND WILLIAMS, R. (1990). On the quasireversibility of a multiclass Brownian service station. Ann. Prob. 18, 1249-1268.
14. HSU, J. AND BURKE, P. (1976). Behavior of tandem buffers with geometric input and Markovian output. IEEE Trans. Commun. 24, 358-361.
15. KELLY, F. (1979). Reversibility and Stochastic Networks. John Wiley, New York.
16. KIPNIS, C. AND LANDIM, C. (1999). Scaling Limits of Interacting Particle Systems. Springer, Berlin.
17. KNUTH, D. (1970). Permutations, matrices, and generalized Young tableaux. Pacific J. Math. 34, 709-727.
18. KÖNIG, W., O'CONNELL, N. AND ROCH, S. (2002). Non-colliding random walks, tandem queues, and discrete orthogonal polynomial ensembles. Electron. J. Prob. 7, 1-24.
19. LIGGETT, T. M. (1999). Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Springer, Berlin.
20. MAIRESSE, J. AND PRABHAKAR, B. (2003). The existence of fixed points for the ·/GI/1 queue. Ann. Prob. 31, 2216-2236.
21. MUTH, E. (1979). The reversibility property of production lines. Manag. Sci. 25, 152-158.
22. O'CONNELL, N. (2003). A path-transformation for random walks and the Robinson-Schensted correspondence. Trans. Amer. Math. Soc. 355, 3669-3697.
23. O'CONNELL, N. (2003). Conditioned random walks and the RSK correspondence. J. Phys. A 36, 3049-3066.
24. O'CONNELL, N. AND YOR, M. (2001). Brownian analogues of Burke's theorem. Stoch. Process. Appl. 96, 285-304.
25. O'CONNELL, N. AND YOR, M. (2002). A representation for non-colliding random walks. Electron. Commun. Prob. 7, 1-12.
26. PRABHAKAR, B. (2003). The attractiveness of the fixed points of a ·/GI/1 queue. Ann. Prob. 31, 2237-2269.
27. PRABHAKAR, B. AND GALLAGER, R. (2003). Entropy and the timing capacity of discrete queues. IEEE Trans. Inf. Theory 49, 357-370.
28. RAJEWSKY, N., SANTEN, L., SCHADSCHNEIDER, A. AND SCHRECKENBERG, M. (1998). The asymmetric exclusion process: comparison of update procedures. J. Statist. Phys. 92, 151-194.
29. RATNARAJAH, T., VAILLANCOURT, R. AND ALVO, M. (2005). Eigenvalues and condition numbers of complex random matrices. SIAM J. Matrix Anal. Appl. 26, 441-456.
30. REICH, E. (1957). Waiting times when queues are in tandem. Ann. Math. Statist. 28, 768-773.
31. ROBERT, P. (2003). Stochastic Networks and Queues (Appl. Math. 52). Springer, Berlin.
32. SAGAN, B. (2001). The Symmetric Group. Representations, Combinatorial Algorithms, and Symmetric Functions (Graduate Texts Math. 203), 2nd edn. Springer, Berlin.
33. SEPPÄLÄINEN, T. (2000). A variational coupling for a totally asymmetric exclusion process with long jumps but no passing. In Hydrodynamic Limits and Related Topics (Fields Inst. Commun. 27; Toronto, ON, 1998), American Mathematical Society, Providence, RI, pp. 117-130.
34. STANLEY, R. (1999). Enumerative Combinatorics (Camb. Studies Adv. Math. 62), Vol. 2. Cambridge University Press.
35. SZCZOTKA, W. AND KELLY, F. (1990). Asymptotic stationarity of queues in series and the heavy traffic approximation. Ann. Prob. 18, 1232-1248.
36. TAKAGI, H. (1993). Queueing Analysis: A Foundation of Performance Evaluation, Vol. 3, Discrete-Time Systems. North-Holland, Amsterdam.
37. TEMBE, S. AND WOLFF, R. (1974). The optimal order of service in tandem queues. Operat. Res. 24, 824-832.
38. WEBER, R. (1979). The interchangeability of ·/M/1 queues in series. J. Appl. Prob. 16, 690-695.