Mean-Field Limits for Large-Scale Random-Access Networks

References

• Atzori L, Iera A, Morabito G (2010) The Internet of Things: A survey. Comput. Networks 54(15):2787–2805.Google Scholar
• Bertsimas D, Nazakato D (1995) The distributional Little’s Law and its applications. Oper. Res. 43(2):298–310.Link, Google Scholar
• Bianchi G (2000) Performance analysis of the IEEE 802.11 distributed coordination function. IEEE J. Selected Areas Comm. 18(3):535–547.Google Scholar
• Billingsley P (1968) Convergence of Probability Measures, 1st ed. (John Wiley & Sons, New York).Google Scholar
• Billingsley P (1999) Convergence of Probability Measures, 2nd ed. (John Wiley & Sons, New York).Google Scholar
• Boorstyn RR, Kershenbaum A, Maglaris B, Sahin V (1987) Throughput analysis in multihop CSMA packet radio networks. IEEE Trans. Comm. 35:267–274.Google Scholar
• Bordenave C, McDonald D, Proutiere A (2008) Performance of random medium access control, an asymptotic approach. Performance Evaluation Rev. 36(1):1–12.Google Scholar
• Boxma OJ, Weststrate JA (1989) Waiting times in polling systems with Markovian server routing. Proc. Messung, Modellierung Bewertung Rechensystemen Netzen, Informatik-Fachberichte, vol. 218 (Springer, Berlin), 89–105. Google Scholar
• Bramson M (1998) State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems 30(1–2):89–140.Google Scholar
• Cecchi F (2018) Mean-field limits for ultra-dense random-access networks. PhD thesis, Eindhoven University of Technology, Eindhoven, Netherlands.Google Scholar
• Cecchi F, Borst SC, van Leeuwaarden JSH (2014) Throughput of CSMA networks with buffer dynamics. Performance Evaluation 79:216–234.Google Scholar
• Cecchi F, Borst SC, van Leeuwaarden JSH, Whiting PA (2016) CSMA networks in a many-sources regime: A mean-field approach. IEEE INFOCOM 2016: 35th Annual IEEE Internat. Conf. Comput. Comm. (IEEE, Piscataway, NJ), 1–9.Google Scholar
• Cho J, Le Boudec JY, Jiang Y (2012) On the asymptotic validity of the decoupling assumption for analyzing 802.11 MAC protocol. IEEE Trans. Inform. Theory 58(11):6879–6893.Google Scholar
• Dai JG, Meyn SP (1995) Stability and convergence of moments for multiclass queueing networks via fluid limit models. IEEE Trans. Automatic Control 40(11):1889–1904.Google Scholar
• De Biasi FS, Pianigiani G (1986) Uniqueness for differential equations implies continuous dependence only in finite dimension. Bull. London Math. Soc. 18(4):379–382.Google Scholar
• Down D (1998) On the stability of polling models with multiple servers. J. Appl. Probab. 34(4):925–935.Google Scholar
• Duffy KR (2010) Mean field Markov models of wireless local area networks. Markov Processes Related Fields 16(2):295–328.Google Scholar
• Ethier SN, Kurtz TG (1986) Markov Processes: Characterization and Convergence, Wiley Series in Probability and Mathematical Statistics (John Wiley & Sons, New York).Google Scholar
• Evans D (2011) The Internet of things. How the next evolution of the Internet is changing everything. White paper, Cisco Internet Business Solutions Group (IBSG).Google Scholar
• Feuillet M, Robert P (2014) A scaling analysis of a transient stochastic network. Adv. Appl. Probab. 46(2):516–535.Google Scholar
• Fricker C, Jaibi MR (1998) Stability of multi-server polling models. INRIA Research Report No. 3347, INRIA, France.Google Scholar
• Gamarnik D, Zeevi A (2006) Validity of heavy traffic steady-state approximations in generalized Jackson networks. Ann. Appl. Probab. 16(1):56–90.Google Scholar
• Halldorsson M, Tonoyan T (2015) How well can graphs represent wireless interference? Proc. 47th Annual ACM Sympos. Theory Comput., 635–644.Google Scholar
• Hunt PJ, Kurtz TG (1994) Large loss networks. Stochastic Process. Appl. 53(2):363–378.Google Scholar
• Jiang L, Walrand J (2010) A distributed CSMA algorithm for throughput and utility maximization in wireless networks. IEEE/ACM Trans. Networking 18(3):960–972.Google Scholar
• Kang W, Ramanan K (2012) Asymptotic approximations for stationary distributions of many-server queues with abandonment. Ann. Appl. Probab. 22(2):477–521.Google Scholar
• Kurtz TG (1980) Representations of Markov processes as multiparameter time changes. Ann. Appl. Probab. 8(4):682–715.Google Scholar
• Liew SC, Kai CH, Leung J, Wong B (2010) Back-of-the-envelope computation of throughput distributions in CSMA wireless networks. IEEE Trans. Mobile Comput. 9(9):1319–1331.Google Scholar
• Revuz D, Yor M (2013) Continuous Martingales and Brownian Motion, 3rd ed., Grundlehren der mathematischen Wissenschaften, vol. 293 (Springer, Berlin).Google Scholar
• Rudin W (1976) Principles of Mathematical Analysis, 3rd ed., International Series in Pure and Applied Mathematics (McGraw-Hill Education, New York).Google Scholar
• Sharma G, Ganesh A, Key PB (2009) Performance analysis of contention based medium access control protocols. IEEE Trans. Inform. Theory 55(4):1665–1682.Google Scholar
• Stolyar A (2005) On the asymptotic optimality of the gradient scheduling algorithm for multiuser throughput allocation. Oper. Res. 53(1):12–25.Link, Google Scholar
• van de Ven PM, Borst SC, van Leeuwaarden JSH, Proutiere A (2010) Insensitivity and stability of random-access networks. Performance Evaluation 67(11):1230–1242.Google Scholar
• van de Ven PM, Janssen AJEM, van Leeuwaarden JSH, Borst SC (2011) Achieving target throughputs in random-access networks. Performance Evaluation 68(11):1103–1117.Google Scholar
• Wang X, Kar K (2005) Throughput modeling and fairness issues in CSMA/CA based ad-hoc networks. Proc. IEEE 24th Annual Joint Conf. IEEE Comput. Comm. Soc. (IEEE, Piscataway, NJ), 23–34.Google Scholar
• Whitt W (1985) Blocking when service is required from several facilities simultaneously. ATT Tech. J. 64(8):1807–1856.Google Scholar
• Zhou X, Zhang Z, Wang G, Yu X, Zhao BY, Zheng H (2013) Practical conflict graphs for dynamic spectrum distribution. Proc. ACM SIGMETRICS (ACM, New York), 5–16.Google Scholar