Project Euclid

References

• [1] Asmussen, S. (2003). Applied Probability and Queues, 2nd ed. Springer, New York.
  Mathematical Reviews (MathSciNet): MR1978607
  
• [2] Birkhoff, G. (1946). Three observations on linear algebra. Univ. Nac. Tucumán. Revista A. 5 147–151.
  Mathematical Reviews (MathSciNet): MR20547
  
• [3] Bonald, T. and Proutière, A. (2002). Insensitivity in processor-sharing networks. Perform. Eval. 49 193–209.
• [4] Bonald, T. and Proutière, A. (2003). Insensitive bandwidth sharing in data networks. Queueing Syst. 44 69–100.
  Mathematical Reviews (MathSciNet): MR1989867
  Digital Object Identifier: doi:10.1023/A:1024094807532
  
• [5] Bramson, M. (1998). State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Syst. 30 89–148.
  Mathematical Reviews (MathSciNet): MR1663763
  Digital Object Identifier: doi:10.1023/A:1019160803783
  
• [6] Dai, J. G. and Lin, W. (2005). Maximum pressure policies in stochastic processing networks. Oper. Res. 53 197–218.
  Mathematical Reviews (MathSciNet): MR2131925
  Digital Object Identifier: doi:10.1287/opre.1040.0170
  
• [7] Dai, J. G. and Lin, W. (2008). Asymptotic optimality of maximum pressure policies in stochastic processing networks. Ann. Appl. Probab. 18 2239–2299.
  Mathematical Reviews (MathSciNet): MR2473656
  Digital Object Identifier: doi:10.1214/08-AAP522
  Project Euclid: euclid.aoap/1227708918
  
• [8] Dai, J. G. and Prabhakar, B. (2000). The throughput of switches with and without speed-up. In Proceedings of IEEE Infocom 556–564. IEEE, New York.
• [9] Demers, A., Keshav, S. and Shenker, S. (1990). Analysis and simulation of a fair queuing algorithm. Internetworking: Research and Experience 1 3–26.
• [10] El Gamal, A., Mammen, J., Prabhakar, B. and Shah, D. (2006). Optimal throughput-delay scaling in wireless networks. II. Constant-size packets. IEEE Trans. Inform. Theory 52 5111–5116.
  Mathematical Reviews (MathSciNet): MR2300378
  Digital Object Identifier: doi:10.1109/TIT.2006.883548
  
• [11] Foss, S. and Konstantopoulos, T. (2004). An overview of some stochastic stability methods. J. Oper. Res. Soc. Japan 47 275–303.
  Mathematical Reviews (MathSciNet): MR2174067
  
• [12] Gallager, R. and Parekh, A. (1993). A generalized processor sharing approach to flow control in integrated services networks: The single-node case. IEEE/ACM Transactions on Networking 1 344–357.
• [13] Ganesh, A., O’Connell, N. and Wischik, D. (2004). Big Queues. Springer, Berlin.
  Mathematical Reviews (MathSciNet): MR2045489
  
• [14] Harrison, J. M. (1995). Balanced fluid models of multiclass queueing networks: A heavy traffic conjecture. In Stochastic Networks. IMA Vol. Math. Appl. 71 1–20. Springer, New York.
  Mathematical Reviews (MathSciNet): MR1381003
  Digital Object Identifier: doi:10.1007/978-1-4757-2418-9_1
  
• [15] Harrison, J. M. (2000). Brownian models of open processing networks: Canonical representation of workload. Ann. Appl. Probab. 10 75–103.
  Mathematical Reviews (MathSciNet): MR1765204
  Digital Object Identifier: doi:10.1214/aoap/1019737665
  Project Euclid: euclid.aoap/1019737665
  
• [16] Harrison, J. M. (2003). Correction: “Brownian models of open processing networks: Canonical representation of workload” [Ann. Appl. Probab. 10 (2000), no. 1, 75–103; MR1765204 (2001g:60230)]. Ann. Appl. Probab. 13 390–393.
  Mathematical Reviews (MathSciNet): MR1765204
  Digital Object Identifier: doi:10.1214/aoap/1019737665
  Project Euclid: euclid.aoap/1019737665
  
• [17] Jagabathula, S. and Shah, D. (2008). Optimal delay scheduling in networks with arbitrary constraints. In Proceedings of the 2008 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems 395–406. ACM, New York.
• [18] Kang, W. N., Kelly, F. P., Lee, N. H. and Williams, R. J. (2009). State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy. Ann. Appl. Probab. 19 1719–1780.
  Mathematical Reviews (MathSciNet): MR2569806
  Digital Object Identifier: doi:10.1214/08-AAP591
  Project Euclid: euclid.aoap/1255699542
  
• [19] Kelly, F. P. (1979). Reversibility and Stochastic Networks. Wiley, Chichester.
  Mathematical Reviews (MathSciNet): MR554920
  
• [20] Kelly, F. P., Massoulié, L. and Walton, N. S. (2009). Resource pooling in congested networks: Proportional fairness and product form. Queueing Syst. 63 165–194.
  Mathematical Reviews (MathSciNet): MR2576010
  Digital Object Identifier: doi:10.1007/s11134-009-9143-8
  
• [21] Kingman, J. F. C. (1962). On queues in heavy traffic. J. Roy. Statist. Soc. Ser. B 24 383–392.
  Mathematical Reviews (MathSciNet): MR148146
  
• [22] Matoušek, J. (2002). Lectures on Discrete Geometry. Springer, New York.
  Mathematical Reviews (MathSciNet): MR1899299
  
• [23] Meyn, S. (2009). Stability and asymptotic optimality of generalized maxweight policies. SIAM J. Control Optim. 47 3259–3294.
  Mathematical Reviews (MathSciNet): MR2476439
  Digital Object Identifier: doi:10.1137/06067746X
  
• [24] Meyn, S. P. and Tweedie, R. L. (1993). Markov Chains and Stochastic Stability. Springer, London.
  Mathematical Reviews (MathSciNet): MR1287609
  
• [25] Neely, M., Modiano, E. and Cheng, Y. (2007). Logarithmic delay for $n\times n$ packet switches under the crossbar constraint. IEEE/ACM Transactions on Networking (TON) 15 657–668.
• [26] Proutière, A. (2003). Insensitivity and stochastic bounds in queuing netwokrs—applications to flow level traffic modelling in telecommunication networks. Ph.D. thesis, Ecole Doctorale, de l’Ecole Polytechnique.
• [27] Shah, D., Tsitsiklis, J. N. and Zhong, Y. Queue-size scaling for input-queued switches. Unpublished manuscript.
• [28] Shah, D., Tsitsiklis, J. N. and Zhong, Y. (2010). Qualitative properties of $\alpha$-weighted scheduling policies. In ACM SIGMETRICS Performance Evaluation Review 239–250. ACM, New York.
• [29] Shah, D., Tsitsiklis, J. N. and Zhong, Y. (2011). Optimal scaling of average queue sizes in an input-queued switch: An open problem. Queueing Syst. 68 375–384.
  Mathematical Reviews (MathSciNet): MR2834209
  Digital Object Identifier: doi:10.1007/s11134-011-9234-1
  
• [30] Shah, D., Tsitsiklis, J. N. and Zhong, Y. (2014). Qualitative properties of $\alpha$-fair policies in bandwidth-sharing networks. Ann. Appl. Probab. 24 76–113.
  Mathematical Reviews (MathSciNet): MR3161642
  Digital Object Identifier: doi:10.1214/12-AAP915
  Project Euclid: euclid.aoap/1389278720
  
• [31] Shah, D. and Wischik, D. (2011). Fluid models of congestion collapse in overloaded switched networks. Queueing Syst. 69 121–143.
  Mathematical Reviews (MathSciNet): MR2836736
  Digital Object Identifier: doi:10.1007/s11134-011-9250-1
  
• [32] Shah, D. and Wischik, D. (2012). Switched networks with maximum weight policies: Fluid approximation and multiplicative state space collapse. Ann. Appl. Probab. 22 70–127.
  Mathematical Reviews (MathSciNet): MR2932543
  Digital Object Identifier: doi:10.1214/11-AAP759
  Project Euclid: euclid.aoap/1328623696
  
• [33] Stolyar, A. L. (2004). Maxweight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic. Ann. Appl. Probab. 14 1–53.
  Mathematical Reviews (MathSciNet): MR2023015
  Digital Object Identifier: doi:10.1214/aoap/1075828046
  Project Euclid: euclid.aoap/1075828046
  
• [34] Stolyar, A. L. (2008). Large deviations of queues sharing a randomly time-varying server. Queueing Syst. 59 1–35.
  Mathematical Reviews (MathSciNet): MR2429895
  Digital Object Identifier: doi:10.1007/s11134-008-9072-y
  
• [35] Tassiulas, L. and Ephremides, A. (1992). Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks. IEEE Trans. Automat. Control 37 1936–1948.
  Mathematical Reviews (MathSciNet): MR1200609
  Digital Object Identifier: doi:10.1109/9.182479
  
• [36] Venkataramanan, V. J. and Lin, X. (2007). Structural properties of LDP for queue-length based wireless scheduling algorithms. In 45th Annual Allerton Conference on Communication, Control, and Computing 759–766. IEEE, New York.
• [37] von Neumann, J. (1953). A certain zero-sum two-person game equivalent to the optimal assignment problem. In Contributions to the Theory of Games. 5–12. Princeton Univ. Press, Princeton, NJ.
  Mathematical Reviews (MathSciNet): MR54920
  
• [38] Walton, N. S. (2009). Proportional fairness and its relationship with multi-class queueing networks. Ann. Appl. Probab. 19 2301–2333.
  Mathematical Reviews (MathSciNet): MR2588246
  Digital Object Identifier: doi:10.1214/09-AAP612
  Project Euclid: euclid.aoap/1259158773
  
• [39] Whitt, W. (2002). Stochastic-Process Limits. Springer, New York.
  Mathematical Reviews (MathSciNet): MR1876437
  
• [40] Williams, R. J. (1998). Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse. Queueing Syst. 30 27–88.
  Mathematical Reviews (MathSciNet): MR1663759
  Digital Object Identifier: doi:10.1023/A:1019108819713
  
• [41] Zachary, S. (2007). A note on insensitivity in stochastic networks. J. Appl. Probab. 44 238–248.
  Mathematical Reviews (MathSciNet): MR2312999
  Digital Object Identifier: doi:10.1239/jap/1175267175
  Project Euclid: euclid.jap/1175267175