References
- Bertsimas , D. , Paschalidis , I. and Tsitsiklis , J.N. 1998 . “On the large deviation behaviour of acyclic networks of G/G/1 queues” . Ann. Appl. Probab. , 8 (4)
- Bertsimas , D. , Paschalidis , I. and Tsitsiklis , J.N. 1998 . “Asymptotic buffer overflow probabilities in multiclass multiplexers: an optimal control approach” . IEEE Trans. Autom. Control , 43 : 315 – 335 .
- Bertsimas , D. , Paschalidis , I. and Tsitsiklis , J.N. 1999 . “Large deviations analysis of the generalized processor sharing policy” . Queueing Syst. , 32 : 319 – 349 .
- Borovkov , A.A. 1976 . Random Processes in Queueing Theory , Berlin : Springer .
- Chang , C.S. 1994 . “Stability, queue length and delay of deterministic and stochastic queueing networks” . IEEE Trans. Autom. Control , 39 : 913 – 931 .
- Chang , C.S. 1995 . “Sample path large deviations and intree networks” . Queueing Syst. , 20 : 7 – 36 .
- Chang , C.S. and Zajic , T. 1995 . “Effective bandwidths of departure processes from queues with time varying capacities” . INFOCOM .
- Cramér , H. 1954 . “On some questions connected with mathematical risk” . Univ. Calif. Publ. Statist. , 2 : 99 – 125 .
- Dembo , A. and Zajic , T. 1995 . “Large deviations: from empirical mean and measure to partial sums process” . Stoch. Proc. Appl. , 57 : 191 – 224 .
- Dembo , A. and Zeitouni , O. 1993 . Large Deviations Techniques and Applications , Boston : Jones and Bartlett .
- Deuschel , J.-D. and Stroock , D.W. 1989 . Large Deviations , New York : Academic Press .
- de Veciana , G. , Courcoubetis , C. and Walrand , J. 1994 . “Decoupling bandwidths for networks: a decomposition approach to resource management” . INFOCOM .
- Dobrushin , R.L. and Pechersky , E.A. 1998 . “Large deviations for random processes with independent increments on infinite intervals” . Probl. Inform. Transm. , 34 : 354 – 384 .
- Duffield , N.G. and O'Connell , N. 1995 . “Large deviations and overflow probabilities for the general single server queue, with applications” . Proc. Camb. Phil. Soc. , 118 (1)
- Eichelsbacher , P. and O'Connell , N. 1999 . “Sample path large deviations in finer topologies” . Stochastics Stochastic Rep. , 67 : 231 – 254 .
- Ganesh , A. and Anantharam , V. 1996 . “Stationary tail probabilities in exponential server tandems with renewal arrivals” . Queueing Syst. , 22 : 203 – 247 .
- Glynn , P.W. and Whitt , W. 1994 . “Logarithmic asymptotics for steady-state tail probabilities in a single-server queue” . J. Appl. Prob. , 31A : 131 – 156 .
- Majewski , K. 1998 . “Heavy traffic approximations of large deviations of feed-forward queueing networks” . Queueing Syst. , 28 : 125 – 155 .
- Mogulskii , A.A. 1976 . “Large deviations for trajectories of multi dimensional random walks” . Th. Prob. Appl. , 21 : 300 – 315 .
- O'Connell , N. 1996 . “Queue lengths and departures at single-server resources” . In Stochastic Networks: Theory and Applications , Edited by: Kelly , F.P. , Zachary , S. and Ziedins , I. Oxford : Clarendon Press .
- O'Connell , N. 1997 . “Large deviations for departures from a shared buffer” . J. Appl. Prob. , 34 : 753 – 766 .
- O'Connell , N. 1998 . “Large deviations for queue lengths at a multi-buffered resource” . J. Appl. Prob. , 35 : 240 – 245 .
- Ramanan , K. and Dupuis , P. 1998 . “Large deviation properties of data streams that share a buffer” . Annu. Appl. Probab. , 8 (4) : 1
- Toomey , F. 1998 . “Bursty traffic and finite capacity queues” . Annu. Oper. Res. , 79 : 45 – 62 .
- Varadhan , S.R. 1966 . “Asymptotic probabilities and differential equations” . Comm. Pure Appl. Math. , 19 : 261 – 286 .