Distributed Potential Field Based Routing and Autonomous Load ...

IEEE COMMUNICATIONS LETTERS, VOL. 13, NO. 6, JUNE 2009

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Distributed Potential Field Based Routing and Autonomous Load Balancing for Wireless Mesh Networks Sangsu Jung, Student Member, IEEE, Malaz Kserawi, Dujeong Lee, and June-Koo Kevin Rhee, Member, IEEE

Abstract—Congested hot spots and node failures severely degrade the performance of wireless mesh networks. However, conventional routing schemes are inefficient in mitigation of the problems. Considering analogy to physics, we propose a novel distributed potential-field-based routing scheme for anycast wireless mesh networks, which is robust to sudden traffic and network perturbations, effectively balancing load among multiple gateways and mesh nodes with little control overhead. Simulation results exhibit autonomous load balancing and failure-tolerant performance in wireless mesh networking. Index Terms—Field based routing, load balancing routing, physics-inspired approach, wireless mesh network.

I. I NTRODUCTION

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IRELESS mesh networks have been expected to play a significant role in future network environments. In wireless mesh networks, mesh nodes relay packets to mesh gateways (mesh portals) for Internet access. In traditional routing schemes such as AODV [1], when a congested hot spot forms in a path, which is responsible for long delays and frequent packet losses, the congestion sustains until new routes for majority of traffic are established. Furthermore, a node failure generates requests for route re-establishment, which incur high traffic volume; hence, it degrades the performance of networks. Even though geographic routing such as GPSR [2] requires no route maintenance process, it generates congested hot spots increasing wireless contentions and delays as well. On the other hand, HWMP [3], which has been proposed for wireless mesh networks in the IEEE 802.11s draft, has similar limitations because it is based on AODV. Furthermore, it still experiences trouble even in the proactive mode to construct a tree topology because reconstructing a tree spends large network resources. In wireless mesh networks, routing topology is typically a hub-and-spoke type, where a gateway as a hub serves many stations. As an advanced model, anycast routing [4] can be utilized to host multiple gateways. For such networks we propose a novel potential-field-based routing [5] scheme based on an electrostatic potential to provide a robust and scalable routing with autonomous load balancing and failure recovery. In conventional field-based routing, scalar values are assigned to each node to form a field gradient, so the packets are forwarded to a node with the lowest gradient. The scalar

Manuscript received September 13, 2008. The associate editor coordinating the review of this letter and approving it for publication was N. Nikolaou. This work was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-313-D00685). The authors are with the Department of Electrical Engineering and the Department of Information and Communications Engineering, KAIST, Daejeon, Rep. of Korea (e-mail:{s.jung, malaz, dj.lee, rhee.jk}@kaist.ac.kr). Digital Object Identifier 10.1109/LCOMM.2009.090110

field value at every node is assigned mainly considering a distance to a destination [4][6]. In contrast, our scalar field value is implicitly determined by a distance to a destination and a degree of congestion. Although traffic-aware potentialfield-based routing suggested in [7] demonstrates a similar concept, our novel approach develops a robust network-wide stable routing model provided by a distributed approach. Notably, our protocol refers to only one-hop neighbors’ potential information in achieving the global congestion control. In detail, the contributions of our work are as follows: First, we map a network to a potential field in physics to reflect proximity and traffic volume; employing Poisson’s equation, which has been verified to be robustly stable in nature. Second, we apply a finite element method (FEM), which is one of numerical analysis techniques, to assign a potential value to each node of an arbitrary mesh network topology in a distributed way. To the best of our knowledge, this is the first approach to utilize an FEM for a network protocol. Finally, we propose a novel potential-field-based routing protocol, which achieves autonomous load balancing for congestion and robustness to node failures with little overhead. II. P OTENTIAL -F IELD -BASED ROUTING We model a network with an undirected graph G=(V, L) where V is the set of vertices (nodes) and L is the set of edges (links) between nodes which are assumed to be symmetric. Additionally, every node v has the set of its neighboring nodes, Z(v) where v∈V. Because a potential field system governed by Poisson’s equation (1) is already known to have naturally stable states in electrostatic systems such as solid state devices, physics, and other areas for the past centuries [5][8][9], our approach is to develop an analogy between physics and a network routing problem so as to find an efficient and stable solution for a throughput-maximizing anycast mesh network: ∇2 φ = −ηρ

(1)

where φ represents a potential, η is a coefficient that reflects the efficiency of source charge ρ. To implement dynamic autonomous traffic load balancing, we model a packet traffic volume (the number of packets remaining in the queue), ρ(v), as the source charge and take φ(v) as the potential(scalar) of each node v. Distinctively from previous works [4]-[7], we aim to develop a completely distributed routing protocol by the use of an FEM [8][9]—a numerical analysis technique to approximate the solution of a partial differential equation decomposing complex domains—widely used for electromagnetic, thermodynamics, and mechanics systems. For an FEM, each node v constructs triangles with Z(v): E0,v , · · ·, Ei,v , Ei+1,v ,

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IEEE COMMUNICATIONS LETTERS, VOL. 13, NO. 6, JUNE 2009

(a)

Fig. 1. FEM element geometry model. Every node is required to have its geographical location information. The index m is cyclically wrapped around to index 0.

· · ·, Em-1,v ; which are interpreted as the one-hop neighbor elements to affect φ(v) where node v has m one-hop neighbors of a geometry model as shown in Fig. 1. Applying a typical FEM formulation of a Poisson’s equation [8][9], one can find a primitive solution for a single triangle element Ek,v : φ(v)rk,v − rk+1,v 2 = (φk+1,v rk,v − φk,v rk+1,v )· (rk,v − rk+1,v ) + ηΔk ρ(v)

(2)

We modify the conventional notations of bi and ci of [8] and → [9] with real-space vectors − r k,v . The virtual source charge at a node can contribute to all neighbor triangle elements. Further, we introduce a fractional coefficient Δk , which accounts for the portion of the source contribution to element k, thus k Δk = 1. In order to consider impacts from all neighbor elements, a typical FEM formulation assembles (2) of all neighbors in Fig. 1 into the following form [9]: rk,v − φk,v rk+1,v ) · (rk,v φ(v) = {Σm−1 k=0 (φk+1,v

− rk+1,v ) + ηρ(v)}/(Σm−1 rk,v − rk+1,v 2 ) k=0

(3)

This formula is evaluated iteratively at every node independently to find the global potential field. The global convergence of a distributed iterative manner has been widely studied in the context of a local equilibrium method of FEM [10]. Here, the distance vector comes from the real space, but it can also be mapped to a link cost between neighbors. In our routing scheme, autonomous load-balancing fieldbased anycast routing (ALFA), a mesh node v forwards a packet to a neighbor node which has the lowest potential (steepest gradient), arg minzj (v)∈Z(v) φ(zj (v)), among one-hop neighbor nodes where j=0, · · ·, m-1. When a network is initiated, all mesh nodes except mesh gateways are assigned to have zero potential values and mesh gateway potentials are assigned to a pre-defined minimum potential value to enable any packet to drain at a mesh gateway. Then, each node starts exchanging its potential value with its one-hop neighbors and re-calculates its potential based on (3) iteratively to achieve potential convergence by the local equilibrium method. After 10 to 15 iterations during a convergence period, all nodes converge to 90% of their steady state potentials in the meansquare-root-error sense. The boundary condition of a potential field is given as φ(B) = 0, where B is the set of the boundary nodes and B⊂V, to produce a uniform ‘field gradient’ from

(b)

Fig. 2. Potential distribution derived from distributed formulation; (a) uncongested case, (b) congested case. Dots indicate the positions of mesh nodes. Letter marking G and H represent for mesh gateway and congested node, respectively.

mesh nodes to gateways. An example of a mesh model used in this work is presented in Fig. 2. Once mesh nodes start transmitting packets, the potential distribution according to (3), reaches a steady state of Fig. 2(a) after a few iterations. Here, packets are considered to have positive charges. When congestion happens, for example, at node H shown in Fig. 2(b), the potential of the node increases so that the potential distribution of the neighbor nodes also increases by (3). Thus, a new routing pattern is formed based on the changed potential, as the traffic tends to avoid the congested high potential area. This property enables a network to achieve autonomous distributed load balancing. In the case of node failures, ALFA continuously provides forwarding with no route re-establishment process, similarly to geographic routing, where the potential field is rapidly reformed in a localized manner. Because ALFA is a family of field-(gradient)-based routing, it is loop free [4][7]. Furthermore, it also maintains consistency of routing due to the nature of Poisson’s equation. Even though it has the stateless property, the potential field does not fluctuate. Additionally, the potential sensitivity to congestion can be controlled by the choice of a value for η. III. P ERFORMANCE E VALUATION In this section, we evaluate the performance of our protocol, ALFA, compared with traditional shortest path routing (SPR), which is a basis for AODV and HWMP, and geographic greedy forwarding routing (GFR), using NS-2 [11] to incorporate PHY/MAC models of the IEEE 802.11. In the simulation, 100 mesh nodes with a transmission range of 250m are randomly distributed in a 1000m×1000m geometric region with two mesh gateways. We assume that most traffic is generated from the mesh nodes at around x=500m (Fig. 2). At a mesh gateway, φ(v) is assigned to a certain lowest value (e.g. -50) and η is set to 10. Potential information is updated every second, as a one-hop broadcast message. Each data packet (UDP) is 512 bytes long and sent at the rate of 2 to 10 packets per second under the bandwidth of 2Mbits/s. To estimate the robustness against congested hot spots, we measure the throughput per mesh node of three schemes with respect to the sending rates as shown in Fig. 3(a). Compared with SPR and GFR, ALFA shows the highest throughput— more than 100% improvement on the maximum—because


JUNG et al.: DISTRIBUTED POTENTIAL FIELD BASED ROUTING AND AUTONOMOUS LOAD BALANCING FOR WIRELESS MESH NETWORKS

(a) Fig. 3.

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Performance comparison; (a)robustness for congested hot spots, (b)robustness for node failures, (c)network-wide control overhead.

ALFA naturally avoids congested nodes whereas SPR and GFR maintain congested hot spots in its paths until new paths are established. As we increase the sending rate of transmitting packets, we observe that SPR and GFR do not increase the throughput for each source; ALFA continuously increases it. This implies that the available bandwidths of SPR and GFR are limited by sub-networks’ traffic-insensitive routing; whereas ALFA autonomously routes packets via other efficient paths more effectively utilizing mesh nodes and mesh gateways until approaching the theoretical bandwidth limit of a network. We validate the performance of the protocols under node failure situations at the sending rate of 4 packets per second as depicted in Fig. 3(b). We randomly choose failed nodes in the valley region of Fig. 2(a). Until three forwarding nodes are failed, the three protocols still show similar performance. However, when four node failures happen, the performance of SPR and GFR starts being significantly degraded whereas that of ALFA has little change—outperforming 130% and 350% higher than SPR and GFR, respectively—because a critical forwarding node failure causes a route re-establishment process carrying a large amount of control overhead in SPR and voids or dead-ends in GFR; whereas, ALFA does not require additional overhead for route re-establishment or for discovery of an efficient path without voids and dead-ends. (Fig. 3(c)) Conclusively, ALFA is well suited for future wireless mesh networks with the help of its rapid fault-tolerance mechanism and autonomous load balancing effect. IV. C ONCLUSIONS In this letter, we propose an autonomous load balancing field-based anycast routing scheme for wireless mesh networks in analogy to a physics system. We develop a distributed routing protocol using an FEM formulation, which is a widely

used numerical analysis technique, to assign a potential value to each node. Distinguished from previous protocols, our potential value reflects not only a distance to a destination but also a traffic volume at each node. Furthermore, our protocol autonomously avoids traffic congestion at a far node only by exchanging local information with one-hop neighboring nodes. Due to the stateless property of our protocol, a rapid faulttolerance mechanism is also provided. Through simulations, we show that our protocol is robust against congested hot spots and node failures in wireless mesh networking. R EFERENCES [1] C. E. Perkins, E. Belding-Royer, and S. R. Das, “Ad hoc on-demand distance vector (AODV) routing,” http://www.ietf.org/rfc/rfc3561.txt, July 2003, RFC 3561. [2] B. Karp and H. T. Kung, “GPSR: Greedy Perimeter Stateless Routing for wireless networks,” in Proc. MobiCom, Boston, MA, USA, 2000. [3] A. Joshi, et al., “HWMP Specification,” IEEE P802.11 Wireless LANs, document IEEE 802.11-061778r1, Nov. 2006. [4] V. Lenders, M. May, and B. Plattner, “Density-based vs. proximity-based anycast routing for mobile networks,” in Proc. IEEE Infocom, Barcelona, Spain, 2006. [5] S. Toumpis, “Mother nature knows best: a survey of recent results on wireless networks based on analogies with physics,” Computer Networks, vol. 52, no. 2, 2008, pp. 360-383. [6] J. Na, D. Soroker, and C. K. Kim, “Greedy geographic routing using dynamic potential field for wireless ad hoc networks,” IEEE Communications Letters, vol. 11, no. 3, 2007, pp. 243-245. [7] A. Basu, A. Lin, and S. Ramanathan, “Routing using potentials: a dynamic traffic-aware routing algorithm,” in Proc. ACM Sigcomm, Karlsruhe, Germany, 2003. [8] L. J. Segerlind, Applied Finite Element Analysis, 2nd ed., ch. 5. John Wiley&Sons, 1984. [9] J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics, ch. 4. IEEE Press, 1998. [10] Z. Li and M. B. Reed, “Convergence analysis for an element-by-element finite element method,” Computer Methods in Applied Mechanics and Engineering, vol. 123, 1995, pp. 33-42. [11] NS-2, http://www.isi.edu/nsnam/ns/.
