Abstract
The paper presents a new approach investigating mobile ad hoc network connectivity. It is shown how to define and evaluate the connectivity probability of a mobile network where the position of the nodes and the link quality changes over time. The connectivity probability is a measure that can capture the impact of the node movement on the network connectivity. A number of mobility models is considered ranging from the classical Random Direction model to the Virtual World model based on the mobility measurements of a multi–player game. We introduce an Attractor model as a simple way to model non–homogeneous node distribution by incorporating viscosity regions in the simulation area. Methods of ergodic theory are used to show the correctness of the approach and to reduce the computational time. Simulation results show how the node density distribution affects the network connectivity.
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References
C. Bettstetter, “Smooth is Better than Sharp: A Random Mobility Model for Simulation of Wireless Networks”, In Proceedings of the 4th ACM International Workshop on Modelling, Analysis, and Simulation of Wireless and Mobile Systems, Italy, July 2001.
T. Camp, J. Boleng, and V. Davies, “A Survey of Mobility Models for Ad hoc Network Research”, WCMC: Special Issue on Mobile Ad Hoc Networking, Vol. 2, No. 5, pp. 483–502, 2002.
F. Fitzek, L. Badia, M. Zorzi, G. Schulte, P. Seeling, and T. Henderson, “Mobility and Stability Evaluation in Wireless Multi-Hop Networks Using Multi-Player Games”, In Proceedings of NETGAMES'03, May 2003.
C. Bettstetter, “On the Minimum Node Degree and Connectivity of a Wireless Multihop Network”, In Proceedings of the 3rd ACM International Symposium on Mobile Ad hoc Networking & Computing, June 2002.
D. Turgut, S.K. Das, and M. Chatterjee, “Longevity of Routes in Mobile Ad Hoc Networks”, In Proceeding of IEEE 53rd Vehicular Technology Conference, May 2001.
H. Koskinen, “Statistical Model Describing Connectivity in Ad Hoc Networks”, In Proceedings of WiOpt'04, March 2004.
P. Santi and M.D. Blough, “The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks”, IEEE Transactions on Mobile Computing, Vol. 2, No. 1, pp. 25-39, January 2003.
F.H.P. Fitzek, T.K. Madsen, R. Prasad, and M. Katz, “Impact of Node Mobility on the Protocol Design of Self-Organizing Networks”, In Proceedings of Wireless World Research Forum 11, June 2004.
P. Panchapakesan and D. Manjunath, “On the Transmission Range in Dense Ad Hoc Radio Networks”, In Proceedings of IEEE SPCOM'01. 2001.
P. Gupta and P.R. Kumar, “Critical Power for Asymptotic Connectivity in Wireless Networks”, Stochastic Analysis, Control, Optimization and Applications. Boston: Birkhauser, pp. 547–566, 1998.
O. Dousse, P. Thiran, and M. Hasler, “Connectivity in Ad Hoc and Hybrid Networks”, In Proceedings of INFOCOM 2002, 2002.
B. Bui-Xuan, A. Ferreira, and A. Jarry, “Evolving Graphs and Least Cost Journeys in Dynamic Networks”, In Proceedings of WiOpt'03 – Modeling and Optimization in Mobile, Ad-Hoc and Wireless Networks, Sophia Antipolis, March 2003.
V. Arnold and A. Avec, “Ergodic Problems of Classical Mechanics”, Benjamin, New York, 1968.
T.K. Madsen, F. Fitzek, and R. Prasad, “Impact of Different Mobility Models on Connectivity Probability of a Wireless Ad Hoc Network”, In Proceedings of International Workshop on Wireless Ad Hoc Networks. June 2004.
T.K. Madsen, F. Fitzek, and R. Prasad, “Simulating Mobile Ad Hoc Networks: Estimation of Connectivity Probability”, In Proceedings of WPMC'04, 2004.
A. Jardosh, E.M. Belding-Royer, K.C. Almeroth, and S. Suri, “Towards Realistic Mobility Models for Mobile Ad Hoc Networks”, In Proceedings of the 9th Annual International Conference on Mobile Computing and Networking, September 2003.
D. Yu and H. Li, “Influence of Mobility Models on Node Distribution in Ad Hoc Networks”, In Proceedings of ICCT'03, 2003.
J. Yoon, M. Liu, and B. Noble, “Random Waypoint Considered Harmful”, In Proceedings of INFOCOM 2003, April 2003.
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Tatiana K. Madsen was born in Moscow, Russia, in 1975. She is an Assistant Professor in the Department of Communication Technology, University of Aalborg, Denmark. She received her M.Sc. and Ph.D. degrees in Mathematics from Moscow State University, Russia in 1997 and 2000, respectively. The area of her Ph.D. studies was dynamical systems, their ergodic properties and integrability. Her current research interests lies within the areas of ad hoc networks with the focus on realistic mobility models and ad hoc routing and 4G wireless communications including QoS support for multimedia services and IP header compression techniques for wireless networks.
Frank H.P. Fitzek was born in Berlin, Germany in 1971. He is an Associate Professor in the Department of Communication Technology, University of Aalborg, Denmark heading the Future Vision group. He received his diploma (Dipl.-Ing.) degree in electrical engineering from the University of Technology – Rheinisch-Westfälische Technische Hochschule (RWTH) – Aachen, Germany, in 1997 and his Ph.D. (Dr.-Ing.) in Electrical Engineering from the Technical University Berlin, Germany in 2002. As a visiting student at the Arizona State University he conducted research in the field of video services over wireless networks. He co-founded the start-up company acticom GmbH in Berlin in 1999. In 2002 he was Adjunct Professor at the University of Ferrara, Italy giving lectures on wireless communications and conducting research on multi-hop networks. His current research interests are in the areas of 4G wireless communication, QoS support for multimedia services, access techniques, security for wireless communication, and the integration of multi hop networks in cellular systems. Dr. Fitzek serves on the Editorial Board of the IEEE Communications Surveys & Tutorials. He is the program chair for the International Conference on Advances in Computer Entertainment Technology (ACE2004) and serves in the program committee for VTC2003, VTC2004, ACE2004, and IEEE MWN2004.
Ramjee Prasad received a B.Sc. (eng) degree from Bihar Institute of Technology, Sindri, India, and M.Sc. (Eng) and Ph.D. degrees from Birla Institute of Technology (BIT), Ranchi, India, in 1968, 1970 and 1979, respectively. During February 1988 May 1999 he has been with the Telecommunications and Traffic-Control Systems Group of Delft University of Technology (DUT), The Netherlands, where he was actively involved in the area of wireless personal and multimedia communications (WPMC). He was head of the Transmission Research Section of International research Centre for Telecommunications Transmission and Radar (IRCTR) and also Program Director of the Centre for Wireless Personal Communications (CEWPC). As from June 1999 Ramjee Prasad joined as the Wireless Information Multimedia Communications chair and co-director of Center for PersonKommunikation at Aalborg University, Denmark. From January 2004 he is Director of the, Center for Teleinfrastruktur (CTIF). He has published over 500 technical papers, and authored and co-edited a series of book about Wireless Multimedia Communications (Artech House). His research interest lies in wireless networks, packet communications, multiple access protocols, adaptive equalizers, spread-spectrum CDMA systems and multimedia communications. He is a fellow of the IEE, a fellow of IETE, a senior member of IEEE, a member of NERG, and a member of the Danish Engineering Society (IDA).
Jan Gerrit Schulte is the CEO of acticom mobile networks GmbH in Berlin, Germany. He studied electrical engineering at the Technical University Berlin from 1989 until 2001, while the main focus were telecommunication networks, the project alpha core dealt with “Internet Measurements and Characterists”, and the Diploma thesis was about routing and stability in wireless ad-hoc networks. From 1996 until 2000 he worked as student researcher at the Telekommunications Network Group at TU-Berlin. From there Gerrit Schulte changed to SIEMENS AG WM where he worked within Bluetooth Development and Design. In 2001 Gerrit Schulte began to work as CEO of acticom, a company that he also co-founded in 1999 and which is developing software for wireless telecommunication networks and devices, such as mobile phones and cellular networks.
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Madsen, T.K., Fitzek, F.H.P., Prasad, R. et al. Connectivity Probability of Wireless Ad Hoc Networks: Definition, Evaluation, Comparison. Wireless Pers Commun 35, 135–151 (2005). https://doi.org/10.1007/s11277-005-8745-7
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DOI: https://doi.org/10.1007/s11277-005-8745-7