Heavy-Traffic Analysis of Queueing Systems with No Complete Resource Pooling

References

• [1] Bell SL, Williams RJ (2001) Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: Asymptotic optimality of a threshold policy. Ann. Appl. Probab. 11(3):608–649.Crossref, Google Scholar
• [2] Benson T, Akella A, Maltz DA (2010) Network traffic characteristics of data centers in the wild. Proc. 10th ACM SIGCOMM Conf. Internet Measurement (Association of Computer Machinery, New York), 267–280.Google Scholar
• [3] Bertsimas D, Tsitsiklis JN (1997) Introduction to Linear Optimization, vol. 6 (Athena Scientific, Belmont, MA).Google Scholar
• [4] Bertsimas D, Paschalidis IC, Tsitsiklis JN (1994) Optimization of multiclass queueing networks: Polyhedral and nonlinear characterizations of achievable performance. Ann. Appl. Probab. 4(1):43–75.Crossref, Google Scholar
• [5] Dai J, Lin W (2008) Asymptotic optimality of maximum pressure policies in stochastic processing networks. Ann. Appl. Probab. 18(6):2239–2299.Crossref, Google Scholar
• [6] Dimakis A, Walrand J (2006) Sufficient conditions for stability of longest queue first scheduling. Adv. Appl. Prob. 38(2):505–521.Crossref, Google Scholar
• [7] Eryilmaz A, Srikant R (2012) Asymptotically tight steady-state queue length bounds implied by drift conditions. Queueing Systems 72(3–4):311–359.Crossref, Google Scholar
• [8] Garnett O, Mandelbaum A (2000) An introduction to skills-based routing and its operational complexities. Teaching notes.Google Scholar
• [9] Ghamami S, Ward AR (2013) Dynamic scheduling of a two-server parallel server system with complete resource pooling and reneging in heavy traffic: Asymptotic optimality of a two-threshold policy. Math. Oper. Res. 38(4):761–824.Link, Google Scholar
• [10] Gupta G, Shroff N (2010) Delay analysis for wireless networks with single hop traffic and general interference constraints. IEEE/ACM Trans. Networking 18(2):393–405.Crossref, Google Scholar
• [11] Hajek B (1982) Hitting-time and occupation-time bounds implied by drift analysis with applications. Adv. Appl. Probab. 14(3):502–525.Crossref, Google Scholar
• [12] Harrison J (1998) Heavy traffic analysis of a system with parallel servers: Asymptotic optimality of discrete review policies. Ann. App. Probab. 8(3):822–848.Crossref, Google Scholar
• [13] Harrison J (2013) Brownian Models of Performance and Control (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• [14] Harrison J, López M (1999) Heavy traffic resource pooling in parallel-server systems. Queueing Systems 33:339–368.Crossref, Google Scholar
• [15] Kandula S, Sengupta S, Greenberg A, Patel P, Chaiken R (2009) The nature of data center traffic: Measurements & analysis. Proc. Ninth ACM SIGCOMM Conf. Internet Measurement (Association of Computer Machinery, New York), 202–208.Google Scholar
• [16] Kang W, Williams R (2012) Diffusion approximation for an input-queued switch operating under a maximum weight matching policy. Stochastic Systems 2(2):277–321.Link, Google Scholar
• [17] Kang X, Wang W, Jaramillo JJ, Ying L (2014) On the performance of largest-deficit-first for scheduling real-time traffic in wireless networks. IEEE/ACM Trans. Networking 24(1):72–84.Crossref, Google Scholar
• [18] Kingman J (1962) Some inequalities for the queue GI/G/1. Biometrika 49(3/4):315–324.Crossref, Google Scholar
• [19] Kumar S, Kumar PR (1994) Performance bounds for queueing networks and scheduling policies. IEEE Trans. Automatic Control 39(8):1600–1611.Crossref, Google Scholar
• [20] Maguluri ST, Srikant R (2016) Heavy traffic queue length behavior in a switch under the MaxWeight algorithm. Stochastic Systems 6(1):211–250.Link, Google Scholar
• [21] Maguluri ST, Burle S, Srikant R (2018) Optimal heavy-traffic queue length scaling in an incompletely saturated switch. Queueing Systems 88(3–4):279–309.Crossref, Google Scholar
• [22] Maguluri ST, Hajek B, Srikant R (2014) The stability of longest-queue-first scheduling with variable packet sizes. IEEE Transactions on Automatic Control 59(8):2295–2300.Google Scholar
• [23] Meyn S (2009) Stability and asymptotic optimality of generalized maxweight policies. SIAM J. Control Optim. 47(6):3259–3294.Crossref, Google Scholar
• [24] Shah D, Tsitsiklis J, Zhong Y (2011) Optimal scaling of average queue sizes in an input-queued switch: An open problem. Queueing Systems 68(3–4):375–384.Crossref, Google Scholar
• [25] Shi C, Wei Y, Zhong Y (2019) Process flexibility for multiperiod production systems. Oper. Res. 67(5):1300–1320.Link, Google Scholar
• [26] Stolyar A (2004) MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic. Ann. Appl. Probab. 14(1):1–53.Crossref, Google Scholar
• [27] Tassiulas L, Ephremides A (1992) Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks. IEEE Trans. Automatic Control 37(12):1936–1948.Crossref, Google Scholar
• [28] Wang W, Maguluri S, Srikant R, Ying L (2022) Heavy-traffic insensitive bounds for weighted proportionally fair bandwidth sharing policies. Math. Oper. Res., ePub ahead of print February 7, https://doi.org/10.1287/moor.2021.1225.Google Scholar
• [29] Williams R (2000) On dynamic scheduling of a parallel server system with complete resource pooling. McDonald DR, Turner SRE, eds. Analysis of Communication Networks: Call Centres, Traffic and Performance, Fields Institute Communications, vol. 28 (American Mathematical Society), 49–71.Crossref, Google Scholar
• [30] Williams R (2016) Stochastic processing networks. Annual. Rev. Statist. Appl. 3:323–345.Crossref, Google Scholar