On the Approximation Error of Mean-Field Models

Published Online:https://doi.org/10.1287/stsy.2018.0012

References

  • Adlakha S, Johari R (2013) Mean field equilibrium in dynamic games with strategic complementarities. Oper. Res. 61(4):971–989.LinkGoogle Scholar
  • Anantharam V, Benchekroun M (1993) A technique for computing sojourn times in large networks of interacting queues. Probab. Engrg. Inform. Sci. 7(4):441–464.Google Scholar
  • Baccelli F, Karpelevich F, Kelbert MY, Puhalskii A, Rybko A, Suhov YM (1992) A mean-field limit for a class of queueing networks. J. Statist. Phys. 66(3–4):803–825.Google Scholar
  • Bailey NTJ (1975) The Mathematical Theory of Infectious Diseases and Its Applications (Hafner Press, New York).Google Scholar
  • Barbour AD (1988) Steins’s method and Poisson process convergence. J. Appl. Probab. 25(A):175–184.Google Scholar
  • Barbour AD, Chen LH (2005) An Introduction to Stein’s Method, Vol. 4 (World Scientific, Singapore).Google Scholar
  • Bordenave C, Mcdonald D, Proutière A (2010) A particle system in interaction with a rapidly varying environment: Mean field limits and applications. Networks and Heterogeneous Media 5(1):31–62.Google Scholar
  • Bortolussi L, Hayden RA (2013) Bounds on the deviation of discrete-time markov chains from their mean-field model. Performance Evaluation 70(10):736–749.Google Scholar
  • Bramson M, Lu Y, Prabhakar B (2012) Asymptotic independence of queues under randomized load balancing. Queueing Systems 71(3):247–292.Google Scholar
  • Braverman A, Dai JG (2017) Stein’s method for steady-state diffusion approximations of m/Ph/n + m systems. Ann. Appl. Probab. 27(1):550–581.Google Scholar
  • Braverman A, Dai JG, Feng J (2016) Steins method for steady-state diffusion approximations: An introduction through the Erlang-A and Erlang-C models. Stoch. Syst. 6(2):301–366.LinkGoogle Scholar
  • Cecchi F, Borst SC, van Leeuwaardena JSH (2015) Mean-field analysis of ultra-dense csma networks. ACM SIGMETRICS Performance Evaluation Rev. 43(2):13–15.Google Scholar
  • Chaintreau A, Le Boudec J-Y, Ristanovic N (2009) The age of gossip: Spatial mean field regime. Lin B, Xu J, Sengupta S, Shah D, eds. Proc. ACM SIGMETRICS Internat. Conf. Measurement Model. Comput. Systems (ACM, New York), 109–120.Google Scholar
  • Gotze F (1991) On the rate of convergence in the multivariate CLT. Ann. Probab. 19(2):724–739.Google Scholar
  • Gurvich Iet al. (2014) Diffusion models and steady-state approximations for exponentially ergodic markovian queues. Adv. Appl. Probab. 24(6):2527–2559.Google Scholar
  • Kadanoff LP (2009) More is the same; phase transitions and mean field theories. J. Statist. Phys. 137(5–6):777–797.Google Scholar
  • Khalil HK (2001) Nonlinear Systems (Prentice Hall, Upper Saddle River, NJ).Google Scholar
  • Kurtz TG (1971) Limit theorems for sequences of jump markov processes approximating ordinary differential processes. J. Appl. Probab. 8(2):344–356.Google Scholar
  • Kurtz TG (1981) Approximation of Population Processes, Vol. 36 (SIAM, Philadelphia).Google Scholar
  • Lasry J-M, Lions P-L (2007) Mean field games. Japanese J. Math. 2(1):229–260.Google Scholar
  • Lu Y, Xie Q, Kliot G, Geller A, Larus JR, Greenberg A (2011) Join-Idle-Queue: A novel load balancing algorithm for dynamically scalable web services. Performance Evaluation 68(11):1056–1071.Google Scholar
  • Manjrekar M, Ramaswamy V, Shakkottai S (2014) A mean field game approach to scheduling in cellular systems. Proc. IEEE Conf. Comput. Comm. (INFOCOM) (IEEE, Piscataway, NJ), 1554–1562.Google Scholar
  • Mitzenmacher M (1996) The power of two choices in randomized load balancing. Ph.D. thesis, University of California at Berkeley.Google Scholar
  • Mukhopadhyay A, Mazumdar RR (2013) Analysis of load balancing in large heterogeneous processor sharing systems. Preprint https://arxiv.org/abs/1311.5806.Google Scholar
  • Mukhopadhyay A, Karthik A, Mazumdar RR, Guillemin F (2015) Mean field and propagation of chaos in multi-class heterogeneous loss models. Perform. Eval. 91:117–131.Google Scholar
  • Norman MF (1974) A central limit theorem for Markov processes that move by small steps. Ann. Probab. 2(6):1065–1074.Google Scholar
  • Norman MF (1975) Limit theorems for stationary distributions. Ann. Appl. Probab. 15(1):561–575.Google Scholar
  • Stein C (1972) A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. Proc. Sixth Berkeley Symp. Math. Stat. Prob. (University of California Press, Berkeley, CA), 583–602.Google Scholar
  • Stein C (1986) Approximate Computation of Expectations. Lecture Notes-Monograph Ser., Vol. 7 (Institute of Mathematical Statistics, Hayward, CA).Google Scholar
  • Stolyar A (2015a) Pull-based load distribution in large-scale heterogeneous service systems. Queueing Systems 80(4):341–361.Google Scholar
  • Stolyar A (2015b) Tightness of stationary distributions of a flexible-server system in the Halfin-Whitt asymptotic regime. Stochastic Systems 5(2):239–267.LinkGoogle Scholar
  • Sznitman A-S (1991) Topics in propagation of chaos. Hennequin PL, ed. Ecole d’Eté de Probabilités de Saint-Flour XIX–1989 Lecture Notes in Mathematics, Vol. 1464 (Springer, Berlin), 165–251.Google Scholar
  • Tsitsiklis JN, Xu K (2012) On the power of (even a little) resource pooling. Stochastic Systems 2(1):1–66.LinkGoogle Scholar
  • Vvedenskaya ND, Dobrushin RL, Karpelevich FI (1996) Queueing system with selection of the shortest of two queues: An asymptotic approach. Problemy Peredachi Informatsii 32(1):20–34.Google Scholar
  • Xie Q, Dong X, Lu Y, Srikant R (2015) Power of d choices for large-scale bin packing: A loss model. Proc. ACM SIGMETRICS Internat. Conf. Measuring Model. Comput. Systems (ACM, New York), 321–334.Google Scholar
  • Ying L, Srikant R, Kang X (2015) The power of slightly more than one sample in randomized load balancing. Proc. IEEE Conf. Comput. Comm. (INFOCOM) (IEEE, Piscataway, NJ), 1131–1139.Google 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.