Closed Queueing Networks Under Congestion: Nonbottleneck Independence and Bottleneck Convergence

Published Online:https://doi.org/10.1287/moor.1120.0583

References

  • Anselmi J, Cremonesi P. A unified framework for the bottleneck analysis of multiclass queueing networks. Perform. Eval. (2010) 67(4):218–234CrossrefGoogle Scholar
  • Anselmi J, Cremonesi P, Amaldi E. Service consolidation with end-to-end response time constraints. Euromicro-SEAA, IEEE (2008) 345–352CrossrefGoogle Scholar
  • Balbo G, Serazzi G. Asymptotic analysis of multiclass closed queueing networks: Multiple bottlenecks. Perform. Eval. (1997) 30(3):115–152CrossrefGoogle Scholar
  • Baskett F, Chandy KM, Muntz RR, Palacios FG. Open, closed, and mixed networks of queues with different classes of customers. J. ACM (1975) 22(2):248–260CrossrefGoogle Scholar
  • Berger A, Bregman L, Kogan Y. Bottleneck analysis in multiclass closed queueing networks and its application. Queueing Syst. Theory Appl. (1999) 31(3–4):217–237CrossrefGoogle Scholar
  • Bolch G, Greiner S, de Meer H, Trivedi KS. Queueing Networks and Markov Chains (2005) (Wiley-Interscience, Hoboken, NJ) Google Scholar
  • Bramson M. Convergence to equilibria for fluid models of head-of-the-line proportional processor sharing queueing networks. Queueing Systems (1996) 23:1–26CrossrefGoogle Scholar
  • Brown TC, Pollett PK. Some distributional approximations in Markovian queueing networks. Adv. Appl. Probab. (1982) 14(3):654–671CrossrefGoogle Scholar
  • Casale G. A generalized method of moments for closed queueing networks. Perform. Eval. (2011) 68(2):180–200CrossrefGoogle Scholar
  • Casale G, Serazzi G. Bottlenecks identification in multiclass queueing networks using convex polytopes. MASCOTS '04 (2004) (IEEE Computer Society, Washington, DC) 223–230CrossrefGoogle Scholar
  • Chandy KM, Neuse D. Linearizer: A heuristic algorithm for queueing network models of computing systems. Commun. ACM (1982) 25(2):126–134CrossrefGoogle Scholar
  • Chen H, Mandelbaum A. Stochastic discrete flow networks: Diffusion approximations and bottlenecks. Ann. Probab. (1991) 19(4):1463–1519CrossrefGoogle Scholar
  • Chen H, Yao DD. Fundamentals of Queueing Networks (2001) (Springer-Verlag, New York) CrossrefGoogle Scholar
  • Cover TM, Thomas JA. Elements of Information Theory (1991) (Wiley-Interscience, Hoboken, NJ) CrossrefGoogle Scholar
  • Dupuis P, Fischer M. (2012) . On the construction of Lyapunov functions for nonlinear Markov processes via relative entropyGoogle Scholar
  • George DK, Xia CH, Squillante MS. Exact-order asymptotic analysis of closed queueing networks. J. Appl. Probab. (2012) CrossrefGoogle Scholar
  • Goodman JB, Massey WA. The nonergodic Jackson network. J. Appl. Probab. (1984) 21(4):860–869CrossrefGoogle Scholar
  • Gordon WJ, Newell GF. Closed queueing systems with exponential servers. Oper. Res. (1967) 15(2):254–265LinkGoogle Scholar
  • Harrison PG, Coury S. On the asymptotic behaviour of closed multiclass queueing networks. Perform. Eval. (2002) 47(2):131–138CrossrefGoogle Scholar
  • Kaspi H, Mandelbaum A. Regenerative closed queueing networks. Stochastics Stochastics Rep. (1992) 39(4):239–258CrossrefGoogle Scholar
  • Kelly FP. Reversibility and Stochastic Networks (1979) (Wiley, Chicester, UK) Google Scholar
  • Kelly FP. Charging and rate control for elastic traffic. Eur. Trans. Telecomm. (1997) 8:33–37CrossrefGoogle Scholar
  • Kelly FP, Massoulié L, Walton NS. Resource pooling in congested networks: Proportional fairness and product form. Queueing Syst. Theory Appl. (2009) 63:165–194CrossrefGoogle Scholar
  • Kelly FP, Maulloo AK, Tan DKH. Rate control in communication networks: Shadow prices, proportional fairness and stability. J. Oper. Res. Soc. (1998) 49:237–252CrossrefGoogle Scholar
  • Knessl C, Tier C. Asymptotic expansion for large closed queuing networks. J. ACM (1990) 37(1):144–174CrossrefGoogle Scholar
  • Knessl C, Tier C. Asymptotic expansions for large closed queueing networks with multiple job classes. IEEE Trans. Comput. (1992) 41(4):480–488CrossrefGoogle Scholar
  • Kumar PR, Seidman TI. Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems. IEEE Trans. Automatic Control (1990) 35:289–298CrossrefGoogle Scholar
  • Lipsky L, Lieu C-M H, Tehranipour A, van de Liefvoort A. On the asymptotic behavior of time-sharing systems. Commun. ACM (1982) 25(10):707–714CrossrefGoogle Scholar
  • McKenna J, Mitra D. Asymptotic expansions and integral representations of moments of queue lengths in closed Markovian networks. J. ACM (1984) 31(2):346–360CrossrefGoogle Scholar
  • McKenna J, Mitra D. Asymptotic expansions for closed Markovian networks with state-dependent service rates. J. ACM (1986) 33(3):568–592CrossrefGoogle Scholar
  • Pattipati KR, Kostreva MM, Teele JL. Approximate mean value analysis algorithms for queuing networks: Existence, uniqueness, and convergence results. J. ACM (1990) 37(3):643–673CrossrefGoogle Scholar
  • Pittel B. Closed exponential networks of queues with saturation: The Jackson-type stationary distribution and its asymptotic analysis. Math. Oper. Res. (1979) 4(4):357–378LinkGoogle Scholar
  • Pollett PK. Modelling congestion in closed queueing networks. Internat. Trans. Oper. Res. (2000) 7(45):319–330CrossrefGoogle Scholar
  • Reiser M, Kobayashi H. Queueing networks with multiple closed chains: Theory and computational algorithms. IBM J. Res. Dev. (1975) 19(3):283–294CrossrefGoogle Scholar
  • Reiser M, Lavenberg SS. Mean-value analysis of closed multichain queueing networks. J. ACM (1980) 27(2):313–322CrossrefGoogle Scholar
  • Robert P. Stochastic Networks and Queues (2003) (Springer-Verlag, Berlin, Heidelberg) CrossrefGoogle Scholar
  • Schweitzer P. Approximate analysis of multiclass closed networks of queues. Proc. Internat. Conf. Stochastic Control Optim. (1979) (Free University, Amsterdam) Google Scholar
  • Schweitzer P. Bottleneck determination in networks of queues. Proc. ORSA/TIMS Special Interest Conf. Appl. Probab.—Comput. Sci., The Interface (1981) Boca Raton, FL:471–485Google Scholar
  • Schweitzer P, Serazzi G, Broglia M. A survey of bottleneck analysis in closed queues. Performance Evaluation of Computer and Communication Systems (1993) (Springer-Verlag, Berlin, Heidelberg) 491–508Lecture Notes in Computer Science, Vol. 729CrossrefGoogle Scholar
  • Spitzer F. Random fields and interacting particle systems: Notes on lectures given at the 1971 MAA Summer Seminar, Williams College, Williamstown, Massachusetts (1971) (Mathematical Association of America, Oberlin, OH) Google Scholar
  • Srikant R. The Mathematics of Internet Congestion Control (2004) (Birkhauser, Boston) CrossrefGoogle Scholar
  • Urgaonkar B, Pacifici G, Shenoy P, Spreitzer M, Tantawi A. An analytical model for multi-tier Internet services and its applications. ACM SIGMETRICS (2005) (ACM, New York) 291–302CrossrefGoogle Scholar
  • Walton NS. Proportional fairness and its relationship with multiclass queueing networks. Ann. Appl. Probab. (2009) 19(6):2301–2333CrossrefGoogle Scholar
  • Wang H, Sevcik K, Serazzi G, Wang S. The general form linearizer algorithms: A new family of approximate mean value analysis algorithms. Perform. Eval. (2008) 65(2):129–151CrossrefGoogle Scholar
  • Whitt W. Open and closed models for networks of queues. AT&T Bell Laboraties Technical J. (1984) 63(9):1911–1979CrossrefGoogle 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.