Citation: |
[1] |
I. Adan, R. D. Foley and D. R. McDonald, Exact asymptotics for the stationary distribution of a Markov chain: A production model, Queueing Syst., 62 (2009), 311-344.doi: 10.1007/s11134-009-9140-y. |
[2] |
V. Anantharam, P. Heidelberger and P. Tsoucas, Analysis of rare events in continuous time Markov chains via time reversal and fluid approximation, Research Report, RC 16280, Computer Science Division, IBM T. J. Watson Center, Yorktown Heights, New York. |
[3] |
F. Baccelli and P. Bremaud, "Elements of Queueing Theory," Springer Verlag, 2003. |
[4] |
F. Baccelli and D. McDonald, Rare events for stationary processes, Stochastic Processes and their Applications, 89 (1997), 141-173.doi: 10.1016/S0304-4149(00)00018-1. |
[5] |
A. A. Borovkov and A. A. Mogul'skii, Limit theorems in the boundary hitting problem for a multidimensional random walk, Siberian Mathematical Journal, 4 (2001), 245-270.doi: 10.1023/A:1004832928857. |
[6] |
R. Foley and D. McDonald, Join the shortest queue: stability and exact asymptotics, Annals of Applied Probability, 11 (2001), 569-607. |
[7] |
R. D. Foley and D. R. McDonald, Large deviations of amodified jackson network: Stability and rough asymptotics, Ann. Appl. Probab., 15 (2004), 519-541.doi: 10.1214/105051604000000666. |
[8] |
R. D. Foley and D. R. McDonald, Bridges and networks: Exact asymptotics, Annals of Applied Probability, 15 (2005), 542-–586.doi: 10.1214/105051604000000675. |
[9] |
R. D. Foley and D. R. McDonald, Constructing a harmonic function for an irreducible non-negative matrix with convergence parameter $R > 1$, Accepted subject to revisions London Mathematical Society. |
[10] |
I. Ignatiouk-Robert and C. Loree, Martin boundary of a killed random walk on a quadrant, Ann. Probab, 38 (2010), 1106-1142.doi: 10.1214/09-AOP506. |
[11] |
T. G. Kurtz, Strong approximation theorems for density dependent Markov chains, Stoch. Proc. Appl., 6 (1978), 223-240.doi: 10.1016/0304-4149(78)90020-0. |
[12] |
K. Majewski and K. Ramanan, How large queue lengths build up in a Jackson network, preprint. 2008. |
[13] |
S. P. Meyn and R. L. Tweedie, "Markov Chains and Stochastic Stability," Springer-Verlag, London. 1993. |
[14] |
M. Miyazawa and Y. Q. Zhao, The stationary tail asymptotics in the GI/G/1-type queue with countably many background states, Advances in Applied Probability, 36 (2004), 1231-1251.doi: 10.1239/aap/1103662965. |
[15] |
V. Nicola and T. Zaburnenko, Efficient importance sampling heuristics for the simulation of population overflow in jackson networks, ACM Transactions on Modeling and Computer Simulation, 17 (2007). |