Spatio-temporal dynamics of random-access networks : an interacting particle approach

• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

[1]  Martin E. Dyer,et al.  On Markov Chains for Independent Sets , 2000, J. Algorithms.

[2]  Do Young Eun,et al.  A High-Order Markov-Chain-Based Scheduling Algorithm for Low Delay in CSMA Networks , 2016, IEEE/ACM Transactions on Networking.

[3]  Soung Chang Liew,et al.  Back-of-the-Envelope Computation of Throughput Distributions in CSMA Wireless Networks , 2007, 2009 IEEE International Conference on Communications.

[4]  Julian Keilson,et al.  A Limit Theorem for Passage Times in Ergodic Regenerative Processes , 1966 .

[5]  Devavrat Shah,et al.  Network adiabatic theorem: an efficient randomized protocol for contention resolution , 2009, SIGMETRICS '09.

[6]  Devavrat Shah,et al.  Delay optimal queue-based CSMA , 2010, SIGMETRICS '10.

[7]  Prasad Tetali,et al.  Slow mixing of Glauber dynamics for the hard-core model on the hypercube , 2004, SODA '04.

[8]  Patrick Thiran,et al.  Border Effects, Fairness, and Phase Transition in Large Wireless Networks , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

[9]  R. Baxter,et al.  Hard hexagons: exact solution , 1980 .

[10]  Jaume Barceló,et al.  On the Interactions Between Multiple Overlapping WLANs Using Channel Bonding , 2014, IEEE Transactions on Vehicular Technology.

[11]  Rudolf Grübel,et al.  Rarity and exponentiality: an extension of Keilson's theorem, with applications , 2005, Journal of Applied Probability.

[12]  Norman M. Abramson,et al.  THE ALOHA SYSTEM: another alternative for computer communications , 1899, AFIPS '70 (Fall).

[13]  J. Keilson.  A review of transient behavior in regular diffusion and birth-death processes , 1964 .

[14]  Kavita Ramanan,et al.  Nonmonotonicity of phase transitions in a loss network with controls , 2006, math/0610321.

[15]  Jean C. Walrand,et al.  Stability and delay of distributed scheduling algorithms for networks of conflicting queues , 2012, Queueing Syst. Theory Appl..

[16]  AARON KERSHENBAUM,et al.  An Algorithm for Evaluation of Throughput in Multihop Packet Radio Networks with Complex Topologies , 1987, IEEE J. Sel. Areas Commun..

[17]  John N. Tsitsiklis,et al.  Hardness of Low Delay Network Scheduling , 2011, IEEE Transactions on Information Theory.

[18]  Boris Bellalta,et al.  Analysis of Dynamic Channel Bonding in Dense Networks of WLANs , 2015, IEEE Transactions on Mobile Computing.

[19]  R. Schonmann,et al.  Behavior of droplets for a class of Glauber dynamics at very low temperature , 1992 .

[20]  Eric Vigoda,et al.  Fast convergence of the Glauber dynamics for sampling independent sets , 1999, Random Struct. Algorithms.

[21]  Julian Keilson.  Log-concavity and log-convexity in passage time densities of diffusion and birth-death processes , 1971 .

[22]  C. Landim,et al.  Tunneling and Metastability of Continuous Time Markov Chains , 2009, 0910.4088.

[23]  Ole J. Heilmann,et al.  Phase transition of hard hexagons on a triangular lattice , 1973 .

[24]  Devavrat Shah,et al.  Randomized Scheduling Algorithm for Queueing Networks , 2009, ArXiv.

[25]  Patrick Thiran,et al.  Modeling the 802.11 Protocol Under Different Capture and Sensing Capabilities , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[26]  G. Guidotti,et al.  Throughput analysis in multihop packet radio networks , 1991, MILCOM 91 - Conference record.

[27]  Francesca R. Nardi,et al.  On the Essential Features of Metastability: Tunnelling Time and Critical Configurations , 2004 .

[28]  Leonard Kleinrock,et al.  On the capacity of wireless CSMA/CA multihop networks , 2013, 2013 Proceedings IEEE INFOCOM.

[29]  Sem C. Borst,et al.  Delay performance in random-access networks , 2014, Queueing Syst. Theory Appl..

[30]  O. Catoni.  Rough Large Deviation Estimates for Simulated Annealing: Application to Exponential Schedules , 1992 .

[31]  Yung Yi,et al.  From Glauber dynamics to Metropolis algorithm: Smaller delay in optimal CSMA , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[32]  Jinwoo Shin,et al.  Optimal CSMA: A survey , 2012, 2012 IEEE International Conference on Communication Systems (ICCS).

[33]  R. Srikant,et al.  The Impact of Access Probabilities on the Delay Performance of Q-CSMA Algorithms in Wireless Networks , 2013, IEEE/ACM Transactions on Networking.

[34]  Richard J. Gibbens,et al.  Bistability in Communication Networks , 2010 .

[35]  E. Olivieri,et al.  Low temperature stochastic dynamics for an Ising model with alternating field , 1996 .

[36]  S. Borst,et al.  Hitting Time Asymptotics for Hard-Core Interactions on Grids , 2015, 1503.06757.

[37]  Anisotropy Effects in Nucleation for Conservative Dynamics , 2005 .

[38]  Partha P. Mitra,et al.  Markov random field models of multicasting in tree networks , 2002, Advances in Applied Probability.

[39]  A. Trouvé.  Rough Large Deviation Estimates for the Optimal Convergence Speed Exponent of Generalized Simulated , 1994 .

[40]  E. Olivieri,et al.  Markov chains with exponentially small transition probabilities: First exit problem from a general domain. I. The reversible case , 1995 .

[41]  Claudio Landim,et al.  Metastability of reversible finite state Markov processes , 2010 .

[42]  Jean C. Walrand,et al.  Distributed Random Access Algorithm: Scheduling and Congestion Control , 2009, IEEE Transactions on Information Theory.

[43]  E.N.M. Cirillo,et al.  Metastability in the Two-Dimensional Ising Model with Free Boundary Conditions , 1998 .

[44]  Yechiam Yemini.  Astatistical Mechanics of Distributed Resource Sharing Mechanisms , 1983, INFOCOM.

[45]  C. Landim,et al.  Hitting Times of Rare Events in Markov Chains , 2013 .

[46]  David Galvin,et al.  Sampling independent sets in the discrete torus , 2008, Random Struct. Algorithms.

[47]  V. Climenhaga.  Markov chains and mixing times , 2013 .

[48]  Jian Ni,et al.  Q-CSMA: Queue-Length-Based CSMA/CA Algorithms for Achieving Maximum Throughput and Low Delay in Wireless Networks , 2009, IEEE/ACM Transactions on Networking.

[49]  Basil S. Maglaris,et al.  Throughput Analysis in Multihop CSMA Packet Radio Networks , 1987, IEEE Trans. Commun..

[50]  E. Cirillo,et al.  Metastability for a Stochastic Dynamics with a Parallel Heat Bath Updating Rule , 2009, 0907.1796.

[51]  Yuri M. Suhov,et al.  A Hard-Core Model on a Cayley Tree: An Example of a Loss Network , 2004, Queueing Syst. Theory Appl..

[52]  Lisa Zhang,et al.  Utility optimization in heterogeneous networks via CSMA-based algorithms , 2013, 2013 11th International Symposium and Workshops on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt).

[53]  Samuel Karlin,et al.  COINCIDENT PROPERTIES OF BIRTH AND DEATH PROCESSES , 1959 .

[54]  O. Catoni,et al.  The exit path of a Markov chain with rare transitions , 1997 .

[55]  Fabio Martinelli,et al.  Fast mixing for independent sets, colorings, and other models on trees , 2004, SODA '04.

[56]  Sem C. Borst,et al.  Throughput of CSMA networks with buffer dynamics , 2014, Perform. Evaluation.

[57]  O. Catoni.  Simulated annealing algorithms and Markov chains with rare transitions , 1999 .

[58]  Metastability for General Dynamics with Rare Transitions: Escape Time and Critical Configurations , 2014, 1412.7923.

[59]  Magnús M. Halldórsson,et al.  How Well Can Graphs Represent Wireless Interference? , 2014, STOC.

[60]  J. Lebowitz,et al.  Phase Transitions in Binary Lattice Gases , 1971 .

[61]  E. Cirillo,et al.  A comparison between different cycle decompositions for Metropolis dynamics , 2014, 1401.3522.

[62]  David Ruelle,et al.  A phase transition in a continuous classical system , 1971 .

[63]  Do Young Eun,et al.  Exploiting the past to reduce delay in CSMA scheduling: a high-order markov chain approach , 2013, SIGMETRICS '13.

[64]  G. Andrews,et al.  The hard-hexagon model and Rogers-Ramanujan type identities. , 1981, Proceedings of the National Academy of Sciences of the United States of America.

[65]  Xiaojun Lin,et al.  Improving the delay performance of CSMA algorithms: A Virtual Multi-Channel approach , 2013, 2013 Proceedings IEEE INFOCOM.

[66]  E. Olivieri,et al.  Metastability and nucleation for conservative dynamics , 2000 .

[67]  Patrick Thiran,et al.  A Packing Approach to Compare Slotted and Non-Slotted Medium Access Control , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[68]  Sem C. Borst,et al.  Delay performance in random-access grid networks , 2013, Perform. Evaluation.

[69]  V. Stefanov,et al.  A note on integrals for birth-death processes. , 2000, Mathematical biosciences.

[70]  Claude Berge.  Minimax relations for the partial q- colorings of a graph , 1989, Discret. Math..

[71]  Jean C. Walrand,et al.  A Distributed CSMA Algorithm for Throughput and Utility Maximization in Wireless Networks , 2010, IEEE/ACM Transactions on Networking.

[72]  S. Zachary,et al.  Loss networks , 2009, 0903.0640.

[73]  Alan M. Frieze,et al.  Torpid mixing of some Monte Carlo Markov chain algorithms in statistical physics , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[74]  Stan Zachary,et al.  Loss networks and Markov random fields , 1999 .

[75]  Cristian Spitoni,et al.  Metastability for Reversible Probabilistic Cellular Automata with Self-Interaction , 2007 .

[76]  Jean C. Walrand,et al.  Fast Mixing of Parallel Glauber Dynamics and Low-Delay CSMA Scheduling , 2010, IEEE Transactions on Information Theory.

[77]  Renormalization and graph methods for Markov chains , 1995 .

[78]  Olle Häggström,et al.  Nonmonotonic Behavior in Hard-Core and Widom–Rowlinson Models , 1999 .

[79]  Dana Randall,et al.  Slow Mixing of Markov Chains Using Fault Lines and Fat Contours , 2010, Algorithmica.

[80]  Philippe Robert,et al.  Stochastic networks with multiple stable points. , 2006, math/0601296.

[81]  Anthony Unwin,et al.  Reversibility and Stochastic Networks , 1980 .

[82]  Leandros Tassiulas,et al.  Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks , 1992 .

[83]  Philippe Robert,et al.  Metastability of CDMA cellular systems , 2006, MobiCom '06.

[84]  Patrick Thiran,et al.  On the fairness of large CSMA networks , 2009, IEEE Journal on Selected Areas in Communications.

[85]  F. Kelly.  One-Dimensional Circuit-Switched Networks , 1987 .

[86]  L. Kleinrock,et al.  Spatial reuse in multihop packet radio networks , 1987, Proceedings of the IEEE.

[87]  A. Sokal,et al.  Bounds on the ² spectrum for Markov chains and Markov processes: a generalization of Cheeger’s inequality , 1988 .

[88]  D. Stroock,et al.  Simulated annealing via Sobolev inequalities , 1988 .

[89]  S. Borst,et al.  Slow Transitions and Starvation in Dense Random-Access Networks , 2015 .

[90]  Koushik Kar,et al.  Throughput modelling and fairness issues in CSMA/CA based ad-hoc networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[91]  Yves Dallery,et al.  Moments of first passage times in general birth–death processes , 2008, Math. Methods Oper. Res..

[92]  R. Kotecḱy,et al.  Shapes of growing droplets—A model of escape from a metastable phase , 1994 .

[93]  PadhyeJitendra,et al.  Impact of interference on multi-hop wireless network performance , 2005 .

[94]  Jiaping Liu,et al.  Towards utility-optimal random access without message passing , 2010, CMC 2010.

[95]  Yechiam Yemini,et al.  The Asymptotic Analysis of Some Packet Radio Networks , 1986, IEEE J. Sel. Areas Commun..

[96]  Alexandre Proutière,et al.  Resource Allocation over Network Dynamics without Timescale Separation , 2010, 2010 Proceedings IEEE INFOCOM.

[97]  Sem C. Borst,et al.  Mixing properties of CSMA networks on partite graphs , 2012, 6th International ICST Conference on Performance Evaluation Methodologies and Tools.

[98]  Prasad Tetali,et al.  Slow mixing of Glauber dynamics for the hard‐core model on regular bipartite graphs , 2006, Random Struct. Algorithms.

[99]  G. Reuter,et al.  Spectral theory for the differential equations of simple birth and death processes , 1954, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[100]  Vladimir Marbukh.  Loss circuit switched communication network-performance analysis and dynamic routing , 1993, Queueing Syst. Theory Appl..

[101]  Massimo Franceschetti,et al.  Closing the Gap in the Capacity of Wireless Networks Via Percolation Theory , 2007, IEEE Transactions on Information Theory.

[102]  E. Scoppola,et al.  Asymptotically exponential hitting times and metastability: a pathwise approach without reversibility , 2014, 1406.2637.

[103]  David Aldous,et al.  Inequalities for rare events in time-reversible Markov chains II , 1993 .

[104]  Murat Alanyali,et al.  Delay performance of CSMA in networks with bounded degree conflict graphs , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[105]  Droplet growth for three-dimensional Kawasaki dynamics , 2003 .

[106]  Sem C. Borst,et al.  Insensitivity and stability of random-access networks , 2010, Perform. Evaluation.

[107]  Michele Garetto,et al.  Modeling Per-Flow Throughput and Capturing Starvation in CSMA Multi-Hop Wireless Networks , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[108]  Antonio Galves,et al.  Metastable behavior of stochastic dynamics: A pathwise approach , 1984 .

[109]  A. Girotra,et al.  Performance Analysis of the IEEE 802 . 11 Distributed Coordination Function , 2005 .

[110]  Dana Randall,et al.  Slow mixing of glauber dynamics via topological obstructions , 2006, SODA '06.

[111]  Lili Qiu,et al.  Impact of Interference on Multi-Hop Wireless Network Performance , 2003, MobiCom '03.

[112]  J. Keilson.  Markov Chain Models--Rarity And Exponentiality , 1979 .

[113]  A. Bovier,et al.  Metastability and Low Lying Spectra¶in Reversible Markov Chains , 2000, math/0007160.

[114]  Minghua Chen,et al.  Analysis of Frequency-Agile CSMA Wireless Networks , 2010, ArXiv.

[115]  Nucleation pattern at low temperature for local Kawasaki dynamicsin two dimensions , 2005 .

[116]  R. Srikant,et al.  On the design of efficient CSMA algorithms for wireless networks , 2010, 49th IEEE Conference on Decision and Control (CDC).

[117]  L. Kleinrock,et al.  Packet Switching in Radio Channels: Part I - Carrier Sense Multiple-Access Modes and Their Throughput-Delay Characteristics , 1975, IEEE Transactions on Communications.

[118]  Peter Marbach,et al.  Throughput-optimal random access with order-optimal delay , 2010, 2011 Proceedings IEEE INFOCOM.

[119]  E. Cirillo,et al.  Relaxation Height in Energy Landscapes: An Application to Multiple Metastable States , 2012, 1205.5647.

[120]  By DAVID J. ALDOUS,et al.  INEQUALITIES FOR RARE EVENTS IN TIME-REVERSIBLE MARKOV CHAINS I , 1992 .

[121]  A. Bovier,et al.  Metastability in reversible diffusion processes II. Precise asymptotics for small eigenvalues , 2005 .

[122]  A. Bovier,et al.  Metastability in Reversible Diffusion Processes I: Sharp Asymptotics for Capacities and Exit Times , 2004 .

[123]  D. Aldous.  Markov chains with almost exponential hitting times , 1982 .

[124]  Frank Kelly,et al.  Limit theorems for loss networks with diverse routing , 1989, Advances in Applied Probability.

[125]  Kathie Cameron,et al.  A min-max relation for the partial q- colourings of a graph. Part II: Box perfection , 1989, Discret. Math..

[126]  G. B. Arous,et al.  Metastability of the Three Dimensional Ising Model on a Torus at Very Low Temperatures , 1996 .

[127]  Metastability and nucleation for the Blume-Capel model. Different mechanisms of transition , 1995, hep-th/9505055.

[128]  Minghua Chen,et al.  Mixing time and temporal starvation of general CSMA networks with multiple frequency agility , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[129]  Roberto H. Schonmann,et al.  Critical droplets and metastability for a Glauber dynamics at very low temperatures , 1991 .

[130]  Fabio Martinelli,et al.  The Multistate Hard Core Model on a Regular Tree , 2011, SIAM J. Discret. Math..

[131]  E. Lieb,et al.  Phase transition in a continuum classical system with finite interactions , 1972 .

[132]  Ordering and demixing transitions in multicomponent Widom-Rowlinson models. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[133]  D. S. Gaunt,et al.  Hard‐Sphere Lattice Gases. I. Plane‐Square Lattice , 1965 .

[134]  J. Berg,et al.  Percolation and the hard-core lattice gas model , 1994 .

[135]  Frank Kelly,et al.  Stochastic Models of Computer Communication Systems , 1985 .

[136]  R. Kotecḱy,et al.  Droplet dynamics for asymmetric Ising model , 1993 .

[137]  Elisabetta Scoppola,et al.  Markov chains with exponentially small transition probabilities: First exit problem from a general domain. II. The general case , 1995 .

[138]  Jennifer Chayes,et al.  The analysis of the Widom-Rowlinson model by stochastic geometric methods , 1995 .

[139]  Lawrence G. Roberts,et al.  ALOHA packet system with and without slots and capture , 1975, CCRV.

[140]  John S. Rowlinson,et al.  New Model for the Study of Liquid–Vapor Phase Transitions , 1970 .

[141]  Gang Wang,et al.  Practical conflict graphs for dynamic spectrum distribution , 2013, SIGMETRICS '13.

[142]  L. Miclo.  ABOUT RELAXATION TIME OF FINITE GENERALIZED METROPOLIS ALGORITHMS , 2002 .