Series Jackson Networks and Noncrossing Probabilities

References

• Abate J., Whitt W. Simple spectral representations for the M/M/1 queue. Queueing Systems: Theory Appl. (1988) 3(4):321–346Crossref, Google Scholar
• Abramowitz M., Stegun I.Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (1965) (Dover Publications, New York) Google Scholar
• Arvesú J., Coussement J., Van Assche W. Some discrete multiple orthogonal polynomials. J. Comput. Appl. Math. (2003) 153:19–45Crossref, Google Scholar
• Baccelli F., Massey W. A. A transient analysis of the two-node series Jackson network. (1988) . Technical Report 852, INRIA, Sophia Antipolis, FranceGoogle Scholar
• Biane P., Bougerol P., O'Connell N. Littelmann paths and Brownian paths. Duke Math. J. (2005) 130:127–167Crossref, Google Scholar
• Blanc J. P. C. The relaxation time of two queueing systems in series. Stochastic Models (1985) 1:1–16Crossref, Google Scholar
• Böhm W., Mohanty S. G. On the Karlin-McGregor theorem and applications. Ann. Appl. Probab. (1997) 7:314–325Crossref, Google Scholar
• Böhm W., Jain J. L., Mohanty S. G. On zero-avoiding transition probabilities of an r-node tandem queue: A combinatorial approach. J. Appl. Probab. (1993) 30:737–741Crossref, Google Scholar
• Dembo A., Zeitouni O.Large Deviations Techniques and Applications (1998) 2nd ed.(Springer, New York) Crossref, Google Scholar
• Dieker A. B., Warren J. Determinantal transition kernels for some interacting particles on the line. Ann. Inst. Henri Poincaré Probab. Statist. (2008) 44(6):1162–1172Crossref, Google Scholar
• Glynn P., Mandjes M., Norros I. On convergence to stationarity of fractional Brownian storage. Ann. Appl. Probab. (2009) 19:1385–1403Crossref, Google Scholar
• Johansson K. Random matrices and determinantal processes. (2005) . Accessed June 14, 2007, http://arxiv.org/abs/math-ph/0510038v1Google Scholar
• Karlin S., McGregor J. Coincidence probabilities. Pacific J. Math. (1959) 9:1141–1164Crossref, Google Scholar
• Kroese D., Scheinhardt W., Taylor P. Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process. Ann. Appl. Probab. (2004) 14:2057–2089Crossref, Google Scholar
• Massey W. A. Calculating exit times for series Jackson networks. J. Appl. Probab. (1987) 24:226–234Crossref, Google Scholar
• O'Connell N. A path-transformation for random walks and the Robinson-Schensted correspondence. Trans. Amer. Math. Soc. (2003a) 355:3669–3697Crossref, Google Scholar
• O'Connell N. Conditioned random walks and the RSK correspondence. J. Phys. A: Math. Gen (2003b) 36:3049–3066Crossref, Google Scholar
• O'Connell N., Yor M. A representation for non-colliding random walks. Electronic Comm. Probab. (2002) 7:1–12Crossref, Google Scholar
• Puchała Z., Rolski T. The exact asymptotic of the collision time tail distribution for independent Brownian particles with different drifts. Probab. Theory Related Fields (2008) 142(3–4):595–617Crossref, Google Scholar
• Rákos A., Schütz G. Bethe ansatz and current distribution for the TASEP with particle-dependent hopping rates. Markov Processes Related Fields (2006) 12:323–334Google Scholar
• Stanley R. P.Enumerative Combinatorics (1999) 2(Cambridge University Press, Cambridge, UK) Crossref, Google Scholar
• Warren J., Windridge P. Some examples of dynamics for Gelfand Tsetlin patterns. (2008) . Accessed December 1, 2008, http://arXiv.org/abs/0812.0022Google Scholar