On the Generalized Delay-Capacity Tradeoff of Mobile Networks with Lévy Flight Mobility

In the literature, scaling laws for wireless mobile networks have been characterized under various models of node mobility and several assumptions on how communication occurs between nodes. To improve the realism in the analysis of scaling laws, we propose a new analytical framework. The framework is the first to consider a L\'{e}vy flight mobility pattern, which is known to closely mimic human mobility patterns. Also, this is the first work that allows nodes to communicate while being mobile. Under this framework, delays ($\bar{D}$) to obtain various levels of per-node throughput $(\lambda)$ for L\'evy flight are suggested as $\bar{D}(\lambda) = O(\sqrt{\min (n^{1+\alpha} \lambda, n^2)})$, where L\'evy flight is a random walk of a power-law flight distribution with an exponent $\alpha \in (0,2]$. The same framework presents a new tighter tradeoff $\bar{D}(\lambda) = O(\sqrt{\max (1,n\lambda^3)})$ for \textit{i.i.d.} mobility, whose delays are lower than existing results for the same levels of per-node throughput.

[1]  Andrea J. Goldsmith,et al.  Large wireless networks under fading, mobility, and delay constraints , 2004, IEEE INFOCOM 2004.

[2]  Michael J. Neely,et al.  Dynamic power allocation and routing for satellite and wireless networks with time varying channels , 2003 .

[3]  Panganamala Ramana Kumar,et al.  Capacity bounds for ad hoc and hybrid wireless networks , 2004, CCRV.

[4]  Zhen Liu,et al.  Capacity, delay and mobility in wireless ad-hoc networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[5]  Ravi Mazumdar,et al.  Scaling laws for capacity and delay in wireless ad hoc networks with random mobility , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[6]  Injong Rhee,et al.  SLAW: A New Mobility Model for Human Walks , 2009, IEEE INFOCOM 2009.

[7]  David Tse,et al.  Mobility increases the capacity of ad-hoc wireless networks , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[8]  Devavrat Shah,et al.  Optimal throughput-delay scaling in wireless networks - part I: the fluid model , 2006, IEEE Transactions on Information Theory.

[9]  M Ferraro,et al.  Mean number of visits to sites in Levy flights. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Ness B. Shroff,et al.  The Fundamental Capacity-Delay Tradeoff in Large Mobile Ad Hoc Networks , 2004 .

[11]  Zygmunt J. Haas,et al.  Multipath routing in mobile ad hoc networks or how to route in the presence of frequent topology changes , 2001, 2001 MILCOM Proceedings Communications for Network-Centric Operations: Creating the Information Force (Cat. No.01CH37277).

[12]  Ness B. Shroff,et al.  Degenerate delay-capacity tradeoffs in ad-hoc networks with Brownian mobility , 2006, IEEE Transactions on Information Theory.

[13]  P. R. Kumar,et al.  Internets in the sky: capacity of 3D wireless networks , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[14]  Eytan Modiano,et al.  Capacity and delay tradeoffs for ad hoc mobile networks , 2005, IEEE Trans. Inf. Theory.

[15]  Eytan Modiano,et al.  Erratum to "Capacity and Delay Tradeoffs for Ad Hoc Mobile Networks" , 2005, IEEE Transactions on Information Theory.

[16]  Ravi R. Mazumdar,et al.  Delay and Capacity Trade-o in Wireless Ad Hoc Networks with Random Mobility , 2004 .

[17]  Injong Rhee,et al.  Delay-capacity tradeoffs for mobile networks with Lévy walks and Lévy flights , 2011, 2011 Proceedings IEEE INFOCOM.

[18]  P. A. Robinson,et al.  LEVY RANDOM WALKS IN FINITE SYSTEMS , 1998 .

[19]  Kyunghan Lee,et al.  On the Levy-Walk Nature of Human Mobility , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

[20]  Panganamala Ramana Kumar,et al.  RHEINISCH-WESTFÄLISCHE TECHNISCHE HOCHSCHULE AACHEN , 2001 .

[21]  J. L. Nolan.  Stable Distributions. Models for Heavy Tailed Data , 2001 .

[22]  Rick S. Blum,et al.  Delay limited capacity of ad hoc networks: asymptotically optimal transmission and relaying strategy , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[23]  G. Sharma,et al.  On Achievable Delay / Capacity Trade-offs in Mobile Ad Hoc Networks , 2004 .