Asymptotic Product-Form Steady State for Generalized Jackson Networks in Multiscale Heavy Traffic

References

• Ata B, Harrison JM, Si N (2025) Drift control of high-dimensional reflected Brownian motion: A computational method based on neural networks. Stochastic Systems 15(2):111–146.Link, Google Scholar
• Blanchet J, Chen X, Si N, Glynn PW (2021) Efficient steady-state simulation of high-dimensional stochastic networks. Stochastic Systems 11(2):174–192.Link, Google Scholar
• Braverman A, Dai J, Miyazawa M (2017) Heavy traffic approximation for the stationary distribution of a generalized Jackson network: The BAR approach. Stochastic Systems 7(1):143–196.Link, Google Scholar
• Braverman A, Dai J, Miyazawa M (2025) The BAR approach for multiclass queueing networks with SBP service policies. Stochastic Systems 15(1):1–49.Link, Google Scholar
• Budhiraja A, Lee C (2009) Stationary distribution convergence for generalized Jackson networks in heavy traffic. Math. Oper. Res. 34(1):45–56.Link, Google Scholar
• Chen H, Mandelbaum A (1991) Discrete flow networks: Bottleneck analysis and fluid approximations. Math. Oper. Res. 16(2):408–446.Link, Google Scholar
• Chen H, Yao D (2001) Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization (Springer-Verlag, New York).Crossref, Google Scholar
• Dai JG (1995) On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. Ann. Appl. Probab. 5(1):49–77.Crossref, Google Scholar
• Dai JG, Harrison JM (1992) Reflected Brownian motion in an orthant: Numerical methods for steady-state analysis. Ann. Appl. Probab. 2(1):65–86.Crossref, Google Scholar
• Dai JG, Harrison JM (2020) Processing Networks: Fluid Models and Stability (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Dai JG, Huo D (2024) Asymptotic product-form steady-state for multiclass queueing networks with SBP service policies in multi-scale heavy traffic. Preprint, submitted March 6, https://arxiv.org/abs/2403.04090.Google Scholar
• Dai JG, Nguyen V, Reiman MI (1994) Sequential bottleneck decomposition: An approximation method for open queueing networks. Oper. Res. 42(1):119–136.Link, Google Scholar
• DeGroot MH, Schervish MJ (2011) Probability and Statistics, 4th ed. (Pearson, Boston).Google Scholar
• Gamarnik D, Zeevi A (2006) Validity of heavy traffic steady-state approximation in generalized Jackson networks. Ann. Appl. Probab. 16(1):56–90.Crossref, Google Scholar
• Guang J, Chen X, Dai JG (2024) Uniform moment bounds for generalized Jackson networks in multiscale heavy traffic. Preprint, submitted January 26, https://doi.org/10.48550/arXiv.2401.14647.Google Scholar
• Guang J, Chen X, Dai JG (2025) Uniform moment bounds for generalized Jackson networks in multiscale heavy traffic. Math. Oper. Res. 51(1):668–685.Google Scholar
• Gurvich I (2014) Validity of heavy-traffic steady-state approximations in multiclass queueing networks: The case of queue-ratio disciplines. Math. Oper. Res. 39(1):121–162.Link, Google Scholar
• Harrison JM (1978) The diffusion approximation for tandem queues in heavy traffic. Adv. Appl. Probab. 10(4):886–905.Crossref, Google Scholar
• Harrison JM (1988) Brownian models of queueing networks with heterogeneous customer populations. Fleming W, Lions PL, eds. Stochastic Differential Systems, Stochastic Control Theory and Applications, IMA Volumes in Mathematics and Its Applications, vol. 10 (Springer, New York), 147–186.Crossref, Google Scholar
• Harrison JM, Nguyen V (1993) Brownian models of multiclass queueing networks: Current status and open problems. Queueing Systems Theory Appl. 13(1–3):5–40.Crossref, Google Scholar
• Harrison JM, Reiman MI (1981) Reflected Brownian motion on an orthant. Ann. Probab. 9(2):302–308. Crossref, Google Scholar
• Harrison JM, Williams RJ (1987a) Brownian models of open queueing networks with homogeneous customer populations. Stochastics 22(2):77–115.Crossref, Google Scholar
• Harrison JM, Williams RJ (1987b) Multidimensional reflected Brownian motions having exponential stationary distributions. Ann. Probab. 15(1):115–137.Crossref, Google Scholar
• Jackson JR (1957) Networks of waiting lines. Oper. Res. 5(4):518–521.Link, Google Scholar
• Johnson DP (1983) Diffusion approximations for optimal filtering of jump processes and for queueing networks. PhD thesis, University of Wisconsin, Madison.Google Scholar
• Kang WN, Kelly FP, Lee NH, Williams RJ (2009) State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy. Ann. Appl. Probab. 19(5):1719–1780.Crossref, Google Scholar
• Koops DT, Boxma OJ, Mandjes MRH (2016) A tandem fluid network with Lévy input in heavy traffic. Queueing Systems 84(3):355–379.Google Scholar
• Reiman MI (1984) Open queueing networks in heavy traffic. Math. Oper. Res. 9(3):441–458.Link, Google Scholar
• Shen X, Chen H, Dai JG, Dai W (2002) The finite element method for computing the stationary distribution of an SRBM in a hypercube with applications to finite buffer queueing networks. Queueing Systems 42(1):33–62. Crossref, Google Scholar
• Whitt W (1983) The queueing network analyzer. Bell System Tech. J. 62(9):2779–2815.Crossref, Google Scholar
• Whitt W (1989) Planning queueing simulations. Management Sci. 35(11):1341–1366.Link, Google Scholar
• Whitt W, You W (2022) A robust queueing network analyzer based on indices of dispersion. Naval Res. Logist. 69(1):36–56.Crossref, Google Scholar
• Williams RJ (2016) Stochastic processing networks. Annu. Rev. Statist. Appl. 3:323–345.Crossref, Google Scholar
• Xu Y (2022) WWTA load-balancing for parallel-server systems with heterogeneous servers and multi-scale heavy traffic limits for generalized Jackson networks. PhD thesis, Cornell University, Ithaca, NY.Google Scholar
• Ye HQ, Yao DD (2018) Justifying diffusion approximations for multiclass queueing networks under a moment condition. Ann. Appl. Probab. 28(6):3652–3697.Crossref, Google Scholar