Spatial networks with wireless applications

Carl P. Dettmann; Orestis Georgiou; Pete Pratt

doi:10.1016/j.crhy.2018.10.001

Spatial networks with wireless applications
[Réseaux spatiaux appliqués aux télécommunications sans fil]

Carl P. Dettmann ¹ ; Orestis Georgiou ^1,² ; Pete Pratt ¹

¹ School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK
² Ultrahaptics, The West Wing, Glass Wharf, Bristol, BS2 0EL, UK

Comptes Rendus. Physique, Volume 19 (2018) no. 4, pp. 187-204.

Résumé
Abstract

De nombreux réseaux sont constitués de nœuds situés dans l'espace physique, avec des liens plus fréquents entre des paires de nœuds peu distants. Par exemple, pour un réseau maillé sans fil, les nœuds représentent des appareils sans fil et les liens des canaux de communication. Nous décrivons des travaux récents impliquant de tels réseaux, en considérant les effets dus à la géométrie (convexe, non convexe et fractale), à la distribution spatiale des nœuds, à la probabilité de liaisons dépendant de la distance, à la mobilité, à la directivité et aux interférences.

Many networks have nodes located in physical space, with links more common between closely spaced pairs of nodes. For example, the nodes could be wireless devices and links communication channels in a wireless mesh network. We describe recent work involving such networks, considering effects due to the geometry (convex, non-convex, and fractal), node distribution, distance-dependent link probability, mobility, directivity, and interference.

Publié le : 2018-05-01

DOI : 10.1016/j.crhy.2018.10.001

Keywords: Wireless networks, Telecommunications, Probabilities, Random graphs
Mot clés : Réseaux sans fil, Télécommunications, Probabilités, Graphes aléatoires

Affiliations des auteurs :

Carl P. Dettmann ¹ ; Orestis Georgiou ^{1, 2} ; Pete Pratt ¹

¹ School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK
² Ultrahaptics, The West Wing, Glass Wharf, Bristol, BS2 0EL, UK

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Carl P. Dettmann; Orestis Georgiou; Pete Pratt. Spatial networks with wireless applications. Comptes Rendus. Physique, Volume 19 (2018) no. 4, pp. 187-204. doi : 10.1016/j.crhy.2018.10.001. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2018.10.001/

Bibliographie
Cité par

[1] E.N. Gilbert Random plane networks, J. Soc. Ind. Appl. Math., Volume 9 (1961), pp. 533-543

[2] D.S. Johnson; C.R. Aragon; L.A. McGeoch; C. Schevon Optimization by simulated annealing: an experimental evaluation; part I, graph partitioning, Oper. Res., Volume 37 (1989), pp. 865-892

[3] M. Penrose Random Geometric Graphs, Oxford University Press, 2003

[4] M. Haenggi Stochastic Geometry for Wireless Networks, Cambridge University Press, 2012

[5] M. Barthélemy Spatial networks, Phys. Rep., Volume 499 (2011), pp. 1-101

[6] M. Walters Random geometric graphs, Surv. Comb., Volume 392 (2011), pp. 365-402

[7] Y. Chen; R. Li; Z. Zhao; H. Zhang On the capacity of D2D social networks with fractal communications, ICT, IEEE (2018), pp. 486-492

[8] C.P. Dettmann Isolation and connectivity in random geometric graphs with self-similar intensity measures, J. Stat. Phys., Volume 172 (2018), pp. 679-700

[9] A. Soshnikov Determinantal random point fields, Russ. Math. Surv., Volume 55 (2000), pp. 923-975

[10] S. Torquato; A. Scardicchio; C.E. Zachary Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory, J. Stat. Mech. Theory Exp., Volume 2008 (2008)

[11] F. Baccelli; B. Błaszczyszyn et al. Stochastic geometry and wireless networks: volume II applications, Found. Trends Netw., Volume 4 (2010), pp. 1-312

[12] W.S. Kendall; I.S. Molchanov New Perspectives in Stochastic Geometry, Oxford University Press, 2010

[13] V. Schmidt Stochastic Geometry, Spatial Statistics and Random Fields, Springer, 2014

[14] A. Kulesza; B. Taskar et al. Determinantal point processes for machine learning, Found. Trends Mach. Learn., Volume 5 (2012), pp. 123-286

[15] F. Baccelli; M. Klein; M. Lebourges; S. Zuyev Stochastic geometry and architecture of communication networks, Telecommun. Syst., Volume 7 (1997), pp. 209-227

[16] M. Haenggi; J.G. Andrews; F. Baccelli; O. Dousse; M. Franceschetti Stochastic geometry and random graphs for the analysis and design of wireless networks, IEEE J. Sel. Areas Commun., Volume 27 (2009), pp. 1029-1046

[17] D. Ring; W. Young The hexagonal cells concept, Bell Labs Tech. J. (1947)

[18] W. Lu; M. Di Renzo Stochastic geometry modeling of cellular networks: analysis, simulation and experimental validation, Proceedings of the 18th ACM International Conference on Modeling, Analysis and Simulation of Wireless and Mobile Systems, ACM, 2015, pp. 179-188

[19] G. Last; M. Penrose Lectures on the Poisson Process, vol. 7, Cambridge University Press, 2017

[20] F. Baccelli; B. Błaszczyszyn (Foundations and Trends(r) in Networking: Vol. 3: No. 3–4) (2010), pp. 249-449 | DOI

[21] U. Schilcher; S. Toumpis; M. Haenggi; A. Crismani; G. Brandner; C. Bettstetter Interference functionals in Poisson networks, IEEE Trans. Inf. Theory, Volume 62 (2016), pp. 370-383

[22] J.G. Andrews; F. Baccelli; R.K. Ganti A tractable approach to coverage and rate in cellular networks, IEEE Trans. Commun., Volume 59 (2011), pp. 3122-3134

[23] M.D. Penrose Connectivity of soft random geometric graphs, Ann. Appl. Probab., Volume 26 (2016), pp. 986-1028

[24] D. Stoyan; A. Penttinen Recent applications of point process methods in forestry statistics, Stat. Sci. (2000), pp. 61-78

[25] D. Dereudre Introduction to the theory of Gibbs point processes, 2017 (arXiv preprint) | arXiv

[26] D.B. Taylor; H.S. Dhillon; T.D. Novlan; J.G. Andrews Pairwise interaction processes for modeling cellular network topology, GLOBECOM, IEEE (2012), pp. 4524-4529

[27] A. Guo; M. Haenggi Spatial stochastic models and metrics for the structure of base stations in cellular networks, IEEE Trans. Wirel. Commun., Volume 12 (2013), pp. 5800-5812

[28] A. Goldman et al. The Palm measure and the Voronoi tessellation for the Ginibre process, Ann. Appl. Probab., Volume 20 (2010), pp. 90-128

[29] T. Shirai; N. Miyoshi A cellular network model with Ginibre configured base stations, Adv. Appl. Probab., Volume 46 (2014), pp. 832-845

[30] N. Deng; W. Zhou; M. Haenggi The Ginibre point process as a model for wireless networks with repulsion, IEEE Trans. Wirel. Commun., Volume 14 (2015), pp. 107-121

[31] O. Macchi The coincidence approach to stochastic point processes, Adv. Appl. Probab., Volume 7 (1975), pp. 83-122

[32] O. Macchi The fermion process—a model of stochastic point process with repulsive points, Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians, Springer, 1977, pp. 391-398

[33] L. Decreusefond; I. Flint; N. Privault; G.L. Torrisi Determinantal point processes, Stochastic Analysis for Poisson Point Processes, Springer, 2016, pp. 311-342

[34] J.B. Hough; M. Krishnapur; Y. Peres; B. Virág et al. Determinantal processes and independence, Probab. Surv., Volume 3 (2006), pp. 206-229

[35] J. Ginibre Statistical ensembles of complex, quaternion, and real matrices, J. Math. Phys., Volume 6 (1965), pp. 440-449

[36] B. Błaszczyszyn; M. Haenggi; P. Keeler; S. Mukherjee Stochastic Geometry Analysis of Cellular Networks, Cambridge University Press, 2018

[37] F. Lavancier; J. Møller; E. Rubak Determinantal point process models and statistical inference, J. R. Stat. Soc., Ser. B, Stat. Methodol., Volume 77 (2015), pp. 853-877

[38] Y. Li; F. Baccelli; H.S. Dhillon; J.G. Andrews Statistical modeling and probabilistic analysis of cellular networks with determinantal point processes, IEEE Trans. Commun., Volume 63 (2015), pp. 3405-3422

[39] B. Matérn Spatial Variation, vol. 36, Springer Science & Business Media, 2013

[40] Q. Ying; Z. Zhao; Y. Zhou; R. Li; X. Zhou; H. Zhang Characterizing spatial patterns of base stations in cellular networks, ICCC, IEEE (2014), pp. 490-495

[41] J. Grandell Doubly Stochastic Poisson Processes, vol. 529, Springer, 2006

[42] J. Møller Properties of Spatial Cox Process Models, Department of Mathematical Sciences, Aalborg University, 2006

[43] V.V. Chetlur; H.S. Dhillon Coverage analysis of a vehicular network modeled as cox process driven by Poisson line process, IEEE Trans. Wirel. Commun., Volume 17 (2018), pp. 4401-4416

[44] R.K. Ganti; M. Haenggi Interference and outage in clustered wireless ad hoc networks, IEEE Trans. Inf. Theory, Volume 55 (2009), pp. 4067-4086

[45] Y. Zhong; W. Zhang Multi-channel hybrid access femtocells: a stochastic geometric analysis, IEEE Trans. Commun., Volume 61 (2013), pp. 3016-3026

[46] D. Li; H. Du; P.-J. Wan; X. Gao; Z. Zhang; W. Wu Construction of strongly connected dominating sets in asymmetric multihop wireless networks, Theor. Comput. Sci., Volume 410 (2009), pp. 661-669

[47] Y. Shang On the degree sequence of random geometric digraphs, Appl. Math. Sci., Volume 4 (2010), pp. 2001-2012

[48] R. Ferrero; M.V. Bueno-Delgado; F. Gandino In-and out-degree distributions of nodes and coverage in random sector graphs, IEEE Trans. Wirel. Commun., Volume 13 (2014), pp. 2074-2085

[49] L. Gugelmann; K. Panagiotou; U. Peter Random hyperbolic graphs: degree sequence and clustering, Autom. Lang. Program. (2012), pp. 573-585

[50] L. Daqing; K. Kosmidis; A. Bunde; S. Havlin Dimension of spatially embedded networks, Nat. Phys., Volume 7 (2011), pp. 481-484

[51] A. Cvetkovski; M. Crovella Hyperbolic embedding and routing for dynamic graphs, INFOCOM 2009, IEEE, IEEE, 2009, pp. 1647-1655

[52] B.M. Waxman Routing of multipoint connections, IEEE J. Sel. Areas Commun., Volume 6 (1988), pp. 1617-1622

[53] M.D. Penrose On a continuum percolation model, Adv. Appl. Probab., Volume 23 (1991), pp. 536-556

[54] K.S. Alexander Finite clusters in high-density continuous percolation: compression and sphericality, Probab. Theory Relat. Fields, Volume 97 (1993), pp. 35-63

[55] D. Krioukov Clustering implies geometry in networks, Phys. Rev. Lett., Volume 116 (2016)

[56] T. Müller; P. Prałat The acquaintance time of (percolated) random geometric graphs, Eur. J. Comb., Volume 48 (2015), pp. 198-214

[57] M. Bradonjić Outbreak of infectious diseases through the weighted random connection model, Math. Model. Nat. Phenom., Volume 9 (2014), pp. 82-88

[58] S.K. Iyer The random connection model: connectivity, edge lengths, and degree distributions, Random Struct. Algorithms, Volume 52 (2018), pp. 283-300

[59] G. Mao Connectivity of Communication Networks, Springer, 2017

[60] L. Barnett; E. Di Paolo; S. Bullock Spatially embedded random networks, Phys. Rev. E, Volume 76 (2007)

[61] E. Parsonage; M. Roughan Fast generation of spatially embedded random networks, IEEE Trans. Netw. Sci. Eng., Volume 4 (2017), pp. 112-119

[62] J. Hackl; B.T. Adey Generation of spatially embedded random networks to model complex transportation networks, 14th International Probabilistic Workshop, Springer, 2017, pp. 217-230

[63] N. Abramson The aloha system: another alternative for computer communications, Proceedings of the November 17–19, 1970, Fall Joint Computer Conference, ACM, 1970, pp. 281-285

[64] O. Georgiou; S. Wang; M.Z. Bocus; C.P. Dettmann; J.P. Coon Location, location, location: border effects in interference limited ad hoc networks, WiOpt, IEEE (2015), pp. 568-575

[65] C.P. Dettmann; O. Georgiou Random geometric graphs with general connection functions, Phys. Rev. E, Volume 93 (2016)

[66] C.P. Dettmann; O. Georgiou Isolation statistics in temporal spatial networks, Europhys. Lett., Volume 119 (2017)

[67] G. Sharma; R. Mazumdar Hybrid sensor networks: a small world, Proceedings of the 6th ACM International Symposium on Mobile Ad Hoc Networking and Computing, ACM, 2005, pp. 366-377

[68] M. Wiedermann; J.F. Donges; J. Kurths; R.V. Donner Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes, Phys. Rev. E, Volume 93 (2016)

[69] M.Z. Bocus; C.P. Dettmann; J.P. Coon An approximation of the first order Marcum Q-function with application to network connectivity analysis, IEEE Commun. Lett., Volume 17 (2013), pp. 499-502

[70] J. Coon; C.P. Dettmann; O. Georgiou Full connectivity: corners, edges and faces, J. Stat. Phys., Volume 147 (2012), pp. 758-778

[71] O. Georgiou; C.P. Dettmann; J.P. Coon Network connectivity: stochastic vs. deterministic wireless channels, IEEE ICC 2014, 2014, pp. 77-82

[72] J.P. Coon; C.P. Dettmann On the connectivity of 2-D random networks with anisotropically radiating nodes, IEEE Commun. Lett., Volume 17 (2013), pp. 321-324

[73] O. Georgiou; C.P. Dettmann; J.P. Coon Connectivity of confined 3D networks with anisotropically radiating nodes, IEEE Trans. Wirel. Commun., Volume 13 (2014), pp. 4534-4546

[74] T.J. Shepard A channel access scheme for large dense packet radio networks, ACM SIGCOMM Comput. Commun. Rev., Volume 26 (1996), pp. 219-230

[75] J.P. Coon; O. Georgiou; C.P. Dettmann Connectivity scaling laws in wireless networks, IEEE Wirel. Commun. Lett., Volume 4 (2015), pp. 629-632

[76] C.M. Newman; L.S. Schulman One dimensional $1 / | j - i |^{s}$ percolation models: the existence of a transition for $s ≦ 2$ , Commun. Math. Phys., Volume 104 (1986), pp. 547-571

[77] G. Grimmett What is percolation?, Percolation, Springer, 1999, pp. 1-31

[78] S.R. Broadbent; J.M. Hammersley Percolation processes: I. Crystals and mazes, Mathematical Proceedings of the Cambridge Philosophical Society, vol. 53, Cambridge University Press, 1957, pp. 629-641

[79] H. Kesten Percolation Theory for Mathematicians, Springer, 1982

[80] M.B. Isichenko Percolation, statistical topography, and transport in random media, Rev. Mod. Phys., Volume 64 (1992), p. 961

[81] A. Bug; S. Safran; G.S. Grest; I. Webman Do interactions raise or lower a percolation threshold?, Phys. Rev. Lett., Volume 55 (1985), p. 1896

[82] I. Balberg; N. Binenbaum Invariant properties of the percolation thresholds in the soft-core–hard-core transition, Phys. Rev. A, Volume 35 (1987), p. 5174

[83] M. Franceschetti; O. Dousse; D.N. Tse; P. Thiran Closing the gap in the capacity of wireless networks via percolation theory, IEEE Trans. Inf. Theory, Volume 53 (2007), pp. 1009-1018

[84] O. Dousse; M. Franceschetti; N. Macris; R. Meester; P. Thiran Percolation in the signal to interference ratio graph, J. Appl. Probab., Volume 43 (2006), pp. 552-562

[85] R. Vaze Percolation and connectivity on the signal to interference ratio graph, INFOCOM, 2012 Proceedings IEEE, IEEE, 2012, pp. 513-521

[86] P. Pratt; C.P. Dettmann; O. Georgiou How does mobility affect the connectivity of interference-limited ad hoc networks?, WiOpt, IEEE (2016), pp. 1-8

[87] G. Mao; B.D. Anderson Connectivity of large wireless networks under a general connection model, IEEE Trans. Inf. Theory, Volume 59 (2013), pp. 1761-1772

[88] B. Bollobás Random graphs, Modern Graph Theory, Springer, 1998, pp. 215-252

[89] P. Erdos; A. Rényi On the evolution of random graphs, Publ. Math. Inst. Hung. Acad. Sci., Volume 5 (1960), pp. 17-60

[90] G. Mao; B. Anderson Towards a better understanding of large-scale network models, IEEE/ACM Trans. Netw. (TON), Volume 20 (2012), pp. 408-421

[91] C. Bettstetter; C. Hartmann; C. Moser How does randomized beamforming improve the connectivity of ad hoc networks?, ICC 2005, Volume vol. 5, IEEE (2005), pp. 3380-3385

[92] J. Coon; C.P. Dettmann; O. Georgiou Impact of boundaries on fully connected random geometric networks, Phys. Rev. E, Volume 85 (2012)

[93] J.P. Coon; O. Georgiou; C.P. Dettmann Connectivity in dense networks confined within right prisms, Proceedings of SPASWIN 2014: International Workshop on Spatial Stochastic Models for Wireless Networks, 2014

[94] Z. Khalid; S. Durrani; J. Guo A tractable framework for exact probability of node isolation and minimum node degree distribution in finite multihop networks, IEEE Trans. Veh. Technol., Volume 63 (2014), pp. 2836-2847

[95] Z. Khalid; S. Durrani Connectivity of three dimensional wireless sensor networks using geometrical probability, AusCTW, IEEE (2013), pp. 47-51

[96] L. Devroye Laws of the iterated logarithm for order statistics of uniform spacings, Ann. Probab., Volume 9 (1981), pp. 860-867

[97] A.M. Makowski; G. Han et al. On the sensitivity of the critical transmission range: lessons from the lonely dimension, Found. Trends Netw., Volume 6 (2013), pp. 287-399

[98] L.A. Laranjeira; G.N. Rodrigues Border effect analysis for reliability assurance and continuous connectivity of wireless sensor networks in the presence of sensor failures, IEEE Trans. Wirel. Commun., Volume 13 (2014), pp. 4232-4246

[99] J.P. Coon Modelling trust in random wireless networks, ISWCS, IEEE (2014), pp. 976-981

[100] K. Koufos; C.P. Dettmann Boundaries as an enhancement technique for physical layer security, IEEE Trans. Inf. Forensics Secur., Volume 14 (2019), pp. 61-74

[101] L. Fu; X. Wang; P. Kumar Are we connected? Optimal determination of source–destination connectivity in random networks, IEEE/ACM Trans. Netw. (TON), Volume 25 (2017), pp. 751-764

[102] C. Nguyen; O. Georgiou; Y. Doi Maximum likelihood based multihop localization in wireless sensor networks, ICC, IEEE (2015), pp. 6663-6668

[103] S. Funke; C. Klein Hole detection or: how much geometry hides in connectivity?, Proceedings of the Twenty-Second Annual Symposium on Computational Geometry, ACM, 2006, pp. 377-385

[104] E. Estrada; S. Meloni; M. Sheerin; Y. Moreno Epidemic spreading in random rectangular networks, Phys. Rev. E, Volume 94 (2016)

[105] K.R. Schaubach; N. Davis; T.S. Rappaport A ray tracing method for predicting path loss and delay spread in microcellular environments, Vehicular Technology Conference, 1992, IEEE 42nd, IEEE, 1992, pp. 932-935

[106] S. Marano; F. Palmieri; G. Franceschetti Statistical characterization of ray propagation in a random lattice, J. Opt. Soc. Am. A, Volume 16 (1999), pp. 2459-2464

[107] T. Bai; R. Vaze; R.W. Heath Analysis of blockage effects on urban cellular networks, IEEE Trans. Wirel. Commun., Volume 13 (2014), pp. 5070-5083

[108] O. Georgiou; C.P. Dettmann; J.P. Coon Network connectivity through small openings, ISWCS 2013, VDE (2013), pp. 1-5

[109] A.P. Giles; O. Georgiou; C.P. Dettmann Connectivity of soft random geometric graphs over annuli, J. Stat. Phys., Volume 162 (2016), pp. 1068-1083

[110] O. Georgiou; M.Z. Bocus; M.R. Rahman; C.P. Dettmann; J.P. Coon Network connectivity in non-convex domains with reflections, IEEE Commun. Lett., Volume 19 (2015), pp. 427-430

[111] C.A. Balanis Antenna theory: a review, Proc. IEEE, Volume 80 (1992), pp. 7-23

[112] C.A. Balanis Modern Antenna Handbook, John Wiley & Sons, 2011

[113] H.-N. Dai; K.-W. Ng; M.-Y. Wu On busy-tone based mac protocol for wireless networks with directional antennas, Wirel. Pers. Commun., Volume 73 (2013), pp. 611-636

[114] P. Li; C. Zhang; Y. Fang The capacity of wireless ad hoc networks using directional antennas, IEEE Trans. Mob. Comput., Volume 10 (2011), pp. 1374-1387

[115] Q. Wang; H.-N. Dai; Z. Zheng; M. Imran; A.V. Vasilakos On connectivity of wireless sensor networks with directional antennas, Sensors, Volume 17 (2017), p. 134

[116] S. Yi; Y. Pei; S. Kalyanaraman On the capacity improvement of ad hoc wireless networks using directional antennas, Proceedings of the 4th ACM International Symposium on Mobile Ad Hoc Networking & Computing, ACM, 2003, pp. 108-116

[117] A. Nasipuri; K. Li; U.R. Sappidi Power consumption and throughput in mobile ad hoc networks using directional antennas, Eleventh International Conference on Computer Communications and Networks, 2002, Proceedings, IEEE, 2002, pp. 620-626

[118] L. Hu; D. Evans Using directional antennas to prevent wormhole attacks, NDSS, 2004, pp. 241-245

[119] S. Singh; R. Mudumbai; U. Madhow Interference analysis for highly directional 60-GHz mesh networks: the case for rethinking medium access control, IEEE/ACM Trans. Netw. (TON), Volume 19 (2011), pp. 1513-1527

[120] H. Koskinen Analytical study of connectivity in wireless multihop networks utilizing beamforming, Proceedings of the 9th ACM International Symposium on Modeling Analysis and Simulation of Wireless and Mobile Systems, ACM, 2006, pp. 212-218

[121] O. Georgiou; C. Nguyen Multihop connectivity of ad hoc networks with randomly oriented directional antennas, IEEE Wirel. Commun. Lett., Volume 4 (2015), pp. 369-372

[122] Y.-B. Ko; V. Shankarkumar; N.H. Vaidya Medium access control protocols using directional antennas in ad hoc networks, INFOCOM 2000, Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies, Proceedings, IEEE, vol. 1, IEEE, 2000, pp. 13-21

[123] O. Georgiou; S. Wang; M.Z. Bocus; C.P. Dettmann; J.P. Coon Directional antennas improve the link-connectivity of interference limited ad hoc networks, PIMRC, IEEE (2015), pp. 1311-1316

[124] T. Bai; A. Alkhateeb; R.W. Heath Coverage and capacity of millimeter-wave cellular networks, IEEE Commun. Mag., Volume 52 (2014), pp. 70-77

[125] X. Zhou; R.K. Ganti; J.G. Andrews Secure wireless network connectivity with multi-antenna transmission, IEEE Trans. Wirel. Commun., Volume 10 (2011), pp. 425-430

[126] T. Bai; R.W. Heath Coverage and rate analysis for millimeter-wave cellular networks, IEEE Trans. Wirel. Commun., Volume 14 (2015), pp. 1100-1114

[127] K. Venugopal; M.C. Valenti; R.W. Heath Interference in finite-sized highly dense millimeter wave networks, Information Theory and Applications Workshop (ITA), 2015, IEEE, 2015, pp. 175-180

[128] T. Bai; R.W. Heath Coverage analysis for millimeter wave cellular networks with blockage effects, GlobalSIP, IEEE (2013), pp. 727-730

[129] A. Kansal; J. Hsu; S. Zahedi; M.B. Srivastava Power management in energy harvesting sensor networks, ACM Trans. Embed. Comput. Syst. (TECS), Volume 6 (2007), p. 32

[130] I. Krikidis; S. Timotheou; S. Nikolaou; G. Zheng; D.W.K. Ng; R. Schober Simultaneous wireless information and power transfer in modern communication systems, IEEE Commun. Mag., Volume 52 (2014), pp. 104-110

[131] M. Di Renzo; W. Lu System-level analysis and optimization of cellular networks with simultaneous wireless information and power transfer: stochastic geometry modeling, IEEE Trans. Veh. Technol., Volume 66 (2017), pp. 2251-2275

[132] O. Georgiou Simultaneous wireless information and power transfer in cellular networks with directional antennas, IEEE Commun. Lett., Volume 21 (2017), pp. 885-888

[133] S.E. Tajbakhsh; J.P. Coon; D.E. Simmons Accessibility and delay in random temporal networks, Phys. Rev. E, Volume 96 (2017)

[134] L. Bracciale, M. Bonola, P. Loreti, G. Bianchi, R. Amici, A. Rabuffi, Crawdad dataset roma/taxi (v. 2014-07-17), CRAWDAD wireless network data archive, 2014.

[135] P. Holme; J. Saramäki Temporal networks, Phys. Rep., Volume 519 (2012), pp. 97-125

[136] S. Boccaletti; G. Bianconi; R. Criado; C.I. Del Genio; J. Gómez-Gardenes; M. Romance; I. Sendina-Nadal; Z. Wang; M. Zanin The structure and dynamics of multilayer networks, Phys. Rep., Volume 544 (2014), pp. 1-122

[137] R.K. Ganti; M. Haenggi Bounds on the information propagation delay in interference-limited aloha networks, WiOPT 2009, IEEE (2009), pp. 1-7

[138] F. Baccelli; B. Blaszczyszyn A new phase transitions for local delays in MANETs, INFOCOM, 2010 Proceedings IEEE, IEEE, 2010, pp. 1-9

[139] M. Haenggi The local delay in Poisson networks, IEEE Trans. Inf. Theory, Volume 59 (2013), pp. 1788-1802

[140] F. Baccelli; B. Błaszczyszyn; M.-O. Haji-Mirsadeghi Optimal paths on the space–time SINR random graph, Adv. Appl. Probab., Volume 43 (2011), pp. 131-150

[141] D. Helen; D. Arivazhagan Applications, advantages and challenges of ad hoc networks, J. Artif. Intell. Res., Volume 2 (2014), pp. 453-457

[142] P. Gupta; P.R. Kumar The capacity of wireless networks, IEEE Trans. Inf. Theory, Volume 46 (2000), pp. 388-404

[143] M. Grossglauser; D. Tse Mobility increases the capacity of ad-hoc wireless networks, INFOCOM 2001, Twentieth Annual Joint Conference of the IEEE Computer and Communications Societies, Proceedings, IEEE, vol. 3, IEEE, 2001, pp. 1360-1369

[144] X. Lin; N.B. Shroff The fundamental capacity-delay tradeoff in large mobile ad hoc networks, Third Annual Mediterranean Ad Hoc Networking Workshop, 2004

[145] G. Sharma; R.R. Mazumdar Scaling laws for capacity and delay in wireless ad hoc networks with random mobility, 2004 IEEE International Conference on Communications, vol. 7, IEEE, 2004, pp. 3869-3873

[146] M.J. Neely; E. Modiano Capacity and delay tradeoffs for ad hoc mobile networks, IEEE Trans. Inf. Theory, Volume 51 (2005), pp. 1917-1937

[147] U. Schilcher; G. Brandner; C. Bettstetter Quantifying inhomogeneity of spatial point patterns, Comput. Netw., Volume 115 (2017), pp. 65-81

[148] S. Bandyopadhyay; E.J. Coyle; T. Falck Stochastic properties of mobility models in mobile ad hoc networks, IEEE Trans. Mob. Comput., Volume 6 (2007)

[149] Z. Gong; M. Haenggi Interference and outage in mobile random networks: expectation, distribution, and correlation, IEEE Trans. Mob. Comput., Volume 13 (2014), pp. 337-349

[150] C. Bettstetter; G. Resta; P. Santi The node distribution of the random waypoint mobility model for wireless ad hoc networks, IEEE Trans. Mob. Comput., Volume 2 (2003), pp. 257-269

[151] E. Hyytia; P. Lassila; J. Virtamo Spatial node distribution of the random waypoint mobility model with applications, IEEE Trans. Mob. Comput., Volume 5 (2006), pp. 680-694

[152] A.P. Giles; O. Georgiou; C.P. Dettmann Betweenness centrality in dense random geometric networks, ICC, IEEE (2015), pp. 6450-6455

[153] K. Koufos; C.P. Dettmann Temporal correlation of interference in bounded mobile ad hoc networks with blockage, IEEE Commun. Lett., Volume 20 (2016), pp. 2494-2497

[154] K. Koufos; C.P. Dettmann; J.P. Coon Correlated interference from uncorrelated users in bounded ad hoc networks with blockage, IEEE Wirel. Commun. Lett., Volume 6 (2017), pp. 114-117

[155] S. Benhamou How many animals really do the levy walk?, Ecology, Volume 88 (2007), pp. 1962-1969

[156] R.N. Mantegna; H.E. Stanley Stochastic process with ultraslow convergence to a Gaussian: the truncated Lévy flight, Phys. Rev. Lett., Volume 73 (1994), p. 2946

[157] D. Brockmann; L. Hufnagel; T. Geisel The scaling laws of human travel, Nature, Volume 439 (2006), pp. 462-465

[158] K. Lee; Y. Kim; S. Chong; I. Rhee; Y. Yi Delay-capacity tradeoffs for mobile networks with Lévy walks and Lévy flights, INFOCOM, 2011 Proceedings IEEE, IEEE, 2011, pp. 3128-3136

[159] B.D. Hughes Random Walks and Random Environments, vol. 2, Clarendon Press, Oxford, UK, 1996

[160] A.V. Chechkin; V.Y. Gonchar; J. Klafter; R. Metzler Fundamentals of Lévy flight processes, Fractals, Diffusion, and Relaxation in Disordered Complex Systems: Advances in Chemical Physics, Part B, vol. 133, 2006, pp. 439-496

[161] I. Rhee; M. Shin; S. Hong; K. Lee; S.J. Kim; S. Chong On the levy-walk nature of human mobility, IEEE/ACM Trans. Netw. (TON), Volume 19 (2011), pp. 630-643

[162] A.N. Kolmogorov; B.V. Gnedenko Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, 1968

[163] A.V. Chechkin; R. Metzler; J. Klafter; V.Y. Gonchar et al. Introduction to the theory of Lévy flights, Anomalous Transport: Foundations and Applications, 2008, pp. 129-162

[164] C.P. Dettmann; J. Coon; M. Di Renzo; O. Georgiou Random graphs and wireless communication networks, part 8: mobility http://www.eng.ox.ac.uk/sen/files/course2016/lec8.pdf (Accessed 2017-9-10)

[165] N. Lu; X.S. Shen Scaling laws for throughput capacity and delay in wireless networks—a survey, IEEE Commun. Surv. Tutor., Volume 16 (2014), pp. 642-657

[166] M.F. Shlesinger; J. Klafter Lévy walks versus Lévy flights, On Growth and Form, Springer, 1986, pp. 279-283

[167] K. Lee; S. Hong; S.J. Kim; I. Rhee; S. Chong Slaw: self-similar least-action human walk, IEEE/ACM Trans. Netw. (TON), Volume 20 (2012), pp. 515-529

[168] P. Santi The critical transmitting range for connectivity in mobile ad hoc networks, IEEE Trans. Mob. Comput., Volume 4 (2005), pp. 310-317

[169] L.F. Richardson The problem of contiguity: an appendix to statistics of deadly quarrels, Gen. Syst. Yearb., Volume 6 (1961), pp. 139-187

[170] B. Mandelbrot How long is the coast of britain? Statistical self-similarity and fractional dimension, Science, Volume 156 (1967), pp. 636-638

[171] T.F. Nonnenmacher; G.A. Losa; E.R. Weibel Fractals in Biology and Medicine, Birkhäuser, 2013

[172] G. Shen Fractal dimension and fractal growth of urbanized areas, Int. J. Geogr. Inf. Sci., Volume 16 (2002), pp. 419-437

[173] X. Ge; Y. Qiu; J. Chen; M. Huang; H. Xu; J. Xu; W. Zhang; Y. Yang; C.-X. Wang; J. Thompson Wireless fractal cellular networks, IEEE Wirel. Commun., Volume 23 (2016), pp. 110-119

[174] K. Lee; S. Hong; S.J. Kim; I. Rhee; S. Chong Slaw: a new mobility model for human walks, INFOCOM 2009, IEEE, IEEE, 2009, pp. 855-863

[175] C.P. Dettmann; O. Georgiou; J.P. Coon More is less: connectivity in fractal regions, Proc. IEEE ISWCS 2015, 2015, pp. 636-640

[176] J.E. Hutchinson Fractals and Self Similarity, Department of Mathematics, University of Melbourne, 1979

[177] K. Falconer Dimensions of self-affine sets: a survey, Further Developments in Fractals and Related Fields, Springer, 2013, pp. 115-134

[178] A. Bunde; S. Havlin Fractals and Disordered Systems, Springer Science & Business Media, 2012

[179] K. Tchoumatchenko; S. Zuyev Aggregate and fractal tessellations, Probab. Theory Relat. Fields, Volume 121 (2001), pp. 198-218

[180] R.K. Ganti; J.G. Andrews Correlation of link outages in low-mobility spatial wireless networks, ASILOMAR, IEEE (2010), pp. 312-316

[181] M. Haenggi The meta distribution of the SIR in Poisson bipolar and cellular networks, IEEE Trans. Wirel. Commun., Volume 15 (2016), pp. 2577-2589

[182] R.M. Mnatsakanov Hausdorff moment problem: reconstruction of probability density functions, Stat. Probab. Lett., Volume 78 (2008), pp. 1869-1877

[183] N. Rashevsky Life, information theory, and topology, Bull. Math. Biol., Volume 17 (1955), pp. 229-235

[184] M. Dehmer; A. Mowshowitz A history of graph entropy measures, Inf. Sci., Volume 181 (2011), pp. 57-78

[185] A. Holzinger; B. Ofner; C. Stocker; A.C. Valdez; A.K. Schaar; M. Ziefle; M. Dehmer On graph entropy measures for knowledge discovery from publication network data, International Conference on Availability, Reliability, and Security, Springer, 2013, pp. 354-362

[186] W.-K. Ang; P. Jowitt Some observations on energy loss and network entropy in water distribution networks, Eng. Optim., Volume 35 (2003), pp. 375-389

[187] A.V. Cruz; N. Mallet; P.J. Magill; P. Brown; B.B. Averbeck Effects of dopamine depletion on network entropy in the external globus pallidus, J. Neurophysiol., Volume 102 (2009), pp. 1092-1102

[188] L. Ji; W. Bing-Hong; W. Wen-Xu; Z. Tao Network entropy based on topology configuration and its computation to random networks, Chin. Phys. Lett., Volume 25 (2008), p. 4177

[189] G. Bianconi Entropy of network ensembles, Phys. Rev. E, Volume 79 (2009)

[190] R. Timo; K. Blackmore; L. Hanlen On entropy measures for dynamic network topologies: limits to MANET, 6th Australian Communications Theory Workshop, 2005, Proceedings, IEEE, 2005, pp. 95-101

[191] A. Halu; S. Mukherjee; G. Bianconi Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting network ensembles, Phys. Rev. E, Volume 89 (2014)

[192] J.P. Coon Topological uncertainty in wireless networks, IEEE Globecom 2016, 2016 (in press) | DOI

[193] J.P. Coon; C.P. Dettmann; O. Georgiou Entropy of spatial network ensembles, Phys. Rev. E, Volume 97 (2018)

[194] J.P. Coon; P.J. Smith Topological entropy in wireless networks subject to composite fading, ICC, IEEE (2017), pp. 1-7

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