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Networks with cascading overloads
1. | Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, Ontario K1N 6M8, Canada, Canada |
2. | Industrial and Systems Engineering, Georgia Institute of Technology, Groseclose Building, Room 428, Atlanta GA 30332-0205, United States |
References:
[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.
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, (1628). Google Scholar |
[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.
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.
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.
|
[7] |
R. D. Foley and D. R. McDonald, Large deviations of amodified jackson network: Stability and rough asymptotics,, Ann. Appl. Probab., 15 (2004), 519.
doi: 10.1214/105051604000000666. |
[8] |
R. D. Foley and D. R. McDonald, Bridges and networks: Exact asymptotics,, Annals of Applied Probability, 15 (2005).
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., (). Google Scholar |
[10] |
I. Ignatiouk-Robert and C. Loree, Martin boundary of a killed random walk on a quadrant,, Ann. Probab, 38 (2010), 1106.
doi: 10.1214/09-AOP506. |
[11] |
T. G. Kurtz, Strong approximation theorems for density dependent Markov chains,, Stoch. Proc. Appl., 6 (1978), 223.
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., (2008). Google Scholar |
[13] |
S. P. Meyn and R. L. Tweedie, "Markov Chains and Stochastic Stability,", Springer-Verlag, (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.
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). Google Scholar |
show all references
References:
[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.
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, (1628). Google Scholar |
[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.
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.
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.
|
[7] |
R. D. Foley and D. R. McDonald, Large deviations of amodified jackson network: Stability and rough asymptotics,, Ann. Appl. Probab., 15 (2004), 519.
doi: 10.1214/105051604000000666. |
[8] |
R. D. Foley and D. R. McDonald, Bridges and networks: Exact asymptotics,, Annals of Applied Probability, 15 (2005).
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., (). Google Scholar |
[10] |
I. Ignatiouk-Robert and C. Loree, Martin boundary of a killed random walk on a quadrant,, Ann. Probab, 38 (2010), 1106.
doi: 10.1214/09-AOP506. |
[11] |
T. G. Kurtz, Strong approximation theorems for density dependent Markov chains,, Stoch. Proc. Appl., 6 (1978), 223.
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., (2008). Google Scholar |
[13] |
S. P. Meyn and R. L. Tweedie, "Markov Chains and Stochastic Stability,", Springer-Verlag, (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.
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). Google Scholar |
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