Jumping Fluid Models and Delay Stability of Max-Weight Dynamics Under Heavy-Tailed Traffic

Published Online:https://doi.org/10.1287/stsy.2023.0110

References

  • Anantharam V (1989) How large delays build up in a GI/G/1 queue. Queueing Systems 5(4):345–367.Google Scholar
  • Anthony M, Bartlett PL (2009) Neural Network Learning: Theoretical Foundations (Cambridge University Press, New York).Google Scholar
  • Asmussen S (1996) Rare events in the presence of heavy tails. Glasserman P, Sigman K, Yao DD, eds. Stochastic Networks (Springer, New York), 197–214.Google Scholar
  • Bertsimas D, Gamarnik D, Tsitsiklis JN (2001) Performance of multiclass Markovian queueing networks via piecewise linear Lyapunov functions. Ann. Appl. Probab. 11(4):1384–1428.Google Scholar
  • Borst S, Boxma O, Jelenković P (2003) Reduced-load equivalence and induced burstiness in GPS queues with long-tailed traffic flows. Queueing Systems 43(4):273–306.Google Scholar
  • Chen B, Blanchet J, Rhee CH, Zwart B (2019) Efficient rare-event simulation for multiple jump events in regularly varying random walks and compound Poisson processes. Math. Oper. Res. 44(3):919–942.LinkGoogle Scholar
  • Durrett R (1980) Conditioned limit theorems for random walks with negative drift. Zeitschrift Wahrscheinlichkeitstheorie Verwandte Gebiete 52(3):277–287.Google Scholar
  • Foss S, Korshunov D (2012) On large delays in multi-server queues with heavy tails. Math. Oper. Res. 37(2):201–218.LinkGoogle Scholar
  • Foss S, Korshunov D, Zachary S (2011) An Introduction to Heavy-Tailed and Subexponential Distributions (Springer, New York).Google Scholar
  • Georgiadis L, Neely MJ, Tassiulas L (2006) Resource Allocation and Cross-Layer Control in Wireless Networks (Now Publishers Inc., Hanover, MA).Google Scholar
  • Jelenković P, Momčilović P (2003) Asymptotic loss probability in a finite buffer fluid queue with hetergeneous heavy-tailed on–off processes. Ann. Appl. Probab. 13(2):576–603.Google Scholar
  • Maguluri ST, Burle SK, Srikant R (2016) Optimal heavy-traffic queue length scaling in an incompletely saturated switch. ACM SIGMETRICS Performance Evaluation Rev. 44(1):13–24.Google Scholar
  • Markakis MG (2013) Scheduling in switched queueing networks with heavy-tailed traffic. Unpublished PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
  • Markakis MG, Modiano E, Tsitsiklis JN (2014) Max-weight scheduling in queueing networks with heavy-tailed traffic. IEEE/ACM Trans. Networking 22(1):257–270.Google Scholar
  • Markakis MG, Modiano E, Tsitsiklis JN (2018) Delay analysis of the max-weight policy under heavy-tailed traffic via fluid approximations. Math. Oper. Res. 43(2):460–493.LinkGoogle Scholar
  • Nair J, Jagannathan K, Wierman A (2015) When heavy-tailed and light-tailed flows compete: The response time tail under generalized max-weight scheduling. IEEE/ACM Trans. Networking 24(2):982–995.Google Scholar
  • Nair J, Wierman A, Zwart B (2020) The Fundamentals of Heavy Tails: Properties, Emergence, and Estimation (Cambridge University Press, Cambridge, UK).Google Scholar
  • Neely MJ (2010) Stochastic Network Optimization with Application to Communication and Queueing Systems. Ying L, ed., Synthesis Lectures on Communication Networks and Algorithms 3.1 (Springer Nature, Cham, Switzerland).Google Scholar
  • Pakes A (1975) On the tails of waiting-time distributions. J. Appl. Probab. 12(3):555–564.Google Scholar
  • Shah D, Wischik D (2012) Switched networks with maximum weight policies: Fluid approximation and multiplicative state space collapse. Ann. Appl. Probab. 22(1):70–127.Google Scholar
  • Sharifnassab A, Tsitsiklis JN, Golestani SJ (2019) Sensitivity to cumulative perturbations for a class of piecewise constant hybrid systems. IEEE Trans. Automatic Control 65(3):1057–1072.Google Scholar
  • Sharifnassab A, Tsitsiklis JN, Golestani SJ (2020) Fluctuation bounds for the max-weight policy with applications to state space collapse. Stochastic Systems 10(3):223–250.LinkGoogle Scholar
  • 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.Google Scholar
  • Veraverbeke N (1977) Asymptotic behaviour of Wiener-Hopf factors of a random walk. Stochastic Processes Appl. 5(1):27–37.Google Scholar
  • Zwart B, Borst S, Mandjes M (2004) Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows. Ann. Appl. Probab. 14(2):903–957.Google Scholar
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