A Hierarchical Approach to Robust Stability of Multiclass Queueing Networks

Published Online:https://doi.org/10.1287/opre.2023.0147

References

  • Bernard A, Kharroubi AE (1991) Regulations déterminates et stochastiques dans le premier “orthant” de RN. Stochastics 34(3–4):149–167.Google Scholar
  • Bramson M (1998a) State space collapse for queueing networks. Proc. Internat. Congress Math. (Berlin).Google Scholar
  • Bramson M (1998b) State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems 30(1):89–140.CrossrefGoogle Scholar
  • Bramson M (2008) Stability of Queueing Networks (Springer, Berlin, Heidelberg).Google Scholar
  • Chen H (1996) A sufficient condition for the positive recurrence of a semimartingale reflecting Brownian motion in an orthant. Ann. Appl. Probab. 6(3):758–765.CrossrefGoogle Scholar
  • Chen H, Ye HQ (2001) Existence condition for the diffusion approximations of multiclass priority queueing networks. Queueing Systems 38(4):435–470.CrossrefGoogle Scholar
  • Chen H, Ye HQ (2002) Piecewise linear Lyapunov function for the stability of multiclass priority fluid networks. IEEE Trans. Automat. Control 47(4):564–575.CrossrefGoogle Scholar
  • Chen H, Zhang H (2000) A sufficient condition and a necessary condition for the diffusion approximations of multiclass queueing networks under priority service disciplines. Queueing Systems 34(1):237–268.CrossrefGoogle 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.CrossrefGoogle Scholar
  • Dai J, Harrison JM (2020) Processing Networks: Fluid Models and Stability (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Dai JG, Vande Vate JH (1996) Global stability of two-station queueing networks. Stochastic Networks (Springer, New York), 1–26.Google Scholar
  • Dai JG, Vande Vate JH (2000) The stability of two-station multitype fluid networks. Oper. Res. 48(5):721–744.LinkGoogle Scholar
  • Dai JG, Weiss G (1996) Stability and instability of fluid models for reentrant lines. Math. Oper. Res. 21(1):115–134.LinkGoogle Scholar
  • Dai JG, Hasenbein JJ, Vande Vate JH (1999) Stability of a three-station fluid network. Queueing Systems 33(4):293–325.CrossrefGoogle Scholar
  • Dai JG, Hasenbein JJ, Vande Vate JH (2004) Stability and instability of a two-station queueing network. Ann. Appl. Probab. 14(1):326–377.CrossrefGoogle Scholar
  • Delgado R (2010) State space collapse and stability of queueing networks. Math. Methods Oper. Res. 72(3):477–499.CrossrefGoogle Scholar
  • Down D, Meyn SP (1997) Piecewise linear test functions for stability and instability of queueing networks. Queueing Systems 27(3):205–226.CrossrefGoogle Scholar
  • Dumas V (1997) A multiclass network with non-linear, non-convex, non-monotonic stability conditions. Queueing Systems 25(1):1–43.CrossrefGoogle 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.LinkGoogle Scholar
  • Gurvich I, Whitt W (2009) Scheduling flexible servers with convex delay costs in many-server service systems. Manufacturing Service Oper. Management 11(2):237–253.LinkGoogle Scholar
  • Gurvich I, Whitt W (2010) Service-level differentiation in many-server service systems via queue-ratio routing. Oper. Res. 58(2):316–328.LinkGoogle Scholar
  • Hasenbein JJ (1997) Necessary conditions for global stability of multiclass queueing networks. Oper. Res. Lett. 21(2):87–94.CrossrefGoogle Scholar
  • Kumar P, Seidman T (1990) Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems. IEEE Trans. Automatic Control 35(3):289–298.CrossrefGoogle Scholar
  • Mandelbaum A, Van der Heyden A (1987) Complementarity and reflection. Unpublished work 1:987.Google Scholar
  • Rybko AN, Stolyar AL (1992) Ergodicity of stochastic processes describing the operation of open queueing networks. Problemy Peredachi Informatsii 28(3):3–26.Google Scholar
  • Stolyar AL (1995) On the stability of multiclass queueing networks: A relaxed sufficient condition via limiting fluid processes. Markov Processes Related Fields 1(4):491–512.Google Scholar
  • Williams RJ (1998) Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse. Queueing Systems 30(1):27–88.CrossrefGoogle Scholar
  • Ye HQ, Yao DD (2018) Justifying diffusion approximations for multiclass queueing networks under a moment condition. Ann. Appl. Probab. 28(6):3652–3697.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.