ETWORK PRESERVATIO THROUGH A TOPOLOGY COTROL ALGORITHM FOR WIRELESS MESH ETWORKS F. O. Aron, T. O. Olwal, A. Krien, Y. Hamam Tshwane University of Technology, Pretoria, Soth Africa. Dept of the French Soth African Technical Institte in Electronics The Meraka Institte, Concil of Scientific and Indstrial Research, Soth Africa jakajode@gmail.com, Thomas.olwal@gmail.com, krienam@tt.ac.za, hamama@tt.ac.za. ABSTRACT Wireless mesh networks (WMs) is becoming a promising new technology for extending coverage to farflng rral areas. This it achieves by linking the varios wireless LAS (WLAs) in distant locations ths providing a vital mode complimentary to the wireless infrastrctre-based networks. The benefits of WM deployments, however, come with certain challenges e.g., power management. While focssing on WM applications in rral areas, this paper explains the need for transmit power consmption control in WMs and proposes an Enhanced Local Minimm Shortest-path Tree (ELMST) algorithm for topology control for the WMs. The algorithm is distribted with each node sing only the information gathered locally to determine its own transmission power. In the first phase of its constrction, a minimm local shortest-path tree is obtained. The last phase then involves the removal of all nidirectional links. The performance of the algorithm is demonstrated via several simlation tests. The resltant network topology preserves network connectivity in addition to possessing other desirable featres sch as: (1) redction in the average node degree, (2) evenly distribted power consmption among the nodes as well as (3) a redced total power consmption leading to longer connectivity periods. KEY WORDS Topology Control, Wireless, Backbone, Mesh etwork, Energy Efficiency, Localized Algorithm. 1. ITRODUCTIO The efficient management of radio resorces (e.g., energy) in mltihop wireless networks (MWs) greatly impacts on the performance of sch networks [1]. Throgh transmission power control for instance, a network topology is affected, interference levels are adjsted and spatial channel re-se is enhanced. One way for efficient management is to have the network nodes select their appropriate logical neighbors (from a given physical topology network) according to some specified rles. For instance, there can be a coordinated decision making regarding each node s transmission power ranges with a goal of generating a network with some desired properties e.g., connectivity, redcing energy consmption and/or increasing network capacity [2]. This is referred to as topology control. Althogh several topology control techniqes e.g., [3], [], [5] with the aim of conserving power consmption have been proposed for other MWs like MAETs and wireless Sensor etworks (WSs), little attention has been drawn to sch needs in wireless mesh networks (WMs). This is mainly becase the backbone wireless mesh roters are static and have sally been assmed [6] to have electrical mains power spply and hence are prported not to have power constraints. However, with specific considerations to rral area applications of WMs, we arge that the mesh roters wold be stationary bt with power constraints. In rral areas, electrical mains power sorces are limited and/or often not available and the mesh nodes have to rely on exhastible and renewable means of energy spply sch as solar, battery or generator. Frthermore, the mesh clients are definitely power constrained [6]. With the aim of addressing these constraints, this paper proposes an energy-efficient topology control algorithm for WMs which comptes the best path based on the link weight fnctions. One advantage with this approach is that the channel conditions e.g., weather conditions are catered for since the link weights, as is shown later in this work (definition 2 and section B), is a fnction of the transmission power and the distances between nodes. The remainder of this paper is organized as follows. In section 2, the details of the network model is given. In section 3, previos related work is reviewed. The proposed algorithm is presented in section. Section 5 gives the simlation reslts and analysis. Finally, in section 6 the work is conclded and a sggestion for ftre work is given. 2. RELATED WORK Rodopl and Meng [7] describe the first algorithm which is based on the concept of relay region. A node decides to 603-080
relay throgh other nodes if less power will be consmed. The algorithm garantees the preservation of minimm energy paths between every pair of nodes connected in the original graph. Based on the reslts of [7], Li and Halpern [8] proposed an improved protocol which is comptationally simpler and better in performance with the reslting topology being a sb-network of the one generated by [7]. Li and Halpern [9] frther propose the small minimm energy commnication network (SMEC). In this algorithm, each node initially broadcasts hello message with some initial power and after reception of ACKs from the receiving nodes, checks if the crrent range covers the region of imal transmission range less the nion of the compliment of the relay regions of all the nodes reachable by node. The process terminates if node reaches its imal transmission power. The work in [7], [8] and [9], however, implicitly assme that a long link consmes more power than a shorter link, an assmption that is not practical for instance in heterogeneos networks according to [3]. In [10], [11], the concept of local neighborhood is first introdced. This concept proposes that a logical topological view of a node in a network be constrcted based only on its local information. This forms the basis of the family of the distribted and localized topology control algorithms. In the work of Li et al [10], a node bilds its local minimm spanning tree (LMST) based only on its one hop neighborhood information. It keeps only the one hop nodes as neighbors in the final topology. The reslting topology has been shown to be connected and with node degree bonded by six. In addition they provide an optional phase where the topology is transformed to one with bidirectional links only. However, LMST does not preserve the minimm energy paths. Another angle of approach is given by Li et al [12] for heterogeneos networks, in which the reslting network contains nidirectional links. Other old variants of topology control algorithms sch as in [13] also discss a distribted and localized algorithm to obtain a reliable high throghpt topology by adjsting a per node transmission power. However, their focs is not on minimizing the energy consmed in the network. All of the algorithms shown in [10], [11], [12], [13] have not been applied to WMs. It can not be generally assmed that the algorithms will atomatically fnction in WMs as the reqirements on network preservation, power efficiency and mobility are very different between WMs and other Mltihop etworks [6]. The algorithm proposed in this work consists of two phases with the reslting topology ensring connectivity and redced node logical ot degrees and is shown to apply for WMs. 3. ETWORK ARCHITECTURE AD SYSTEM MODEL In this section, the WM architectre considered in this paper is presented. Additionally a discssion is given on how the network is modelled. 3.1 Architectre A sample hybrid WM architectre modelled is as shown in figre 1. The network is composed of three grops of wireless network elements [6],[1]: (1) mesh gateways, mesh roter with gateway fnctionalities, are sed for relaying traffic between the WM and the internet, (2) Access Points, mesh roters, are the stationary nodes that act as wireless access points for the mesh clients and also form the mlti-hop wireless network infrastrctre and (3) Mesh clients are the end-ser 802.11 mesh nodes. They are either mobile or stationary. Internet Figre 1: An example of a mesh network architectre for a commnity mesh networking for resorce sharing with six MAPs where one acts as a Gateway to the internet. It is important to note that the mesh gateways can also fnction as mesh roters [15], [16]. Hence, the mesh gateway nodes and the access points form the backbone wireless mesh network and are sfficiently referred to as mesh access points (MAPs). Examples of WM applications [6] inclde commnity srveillance, commnity resorce sharing, broadband home networking, enterprise networking. These applications generate a large amont of client to client traffic as well as client to gateway traffic [15], [17]. Hence, it is sfficient to assme that most traffic appear at the backbone network. The focs of this work is therefore, to imize certain properties sch as network lifetime based on the backbone wireless mesh network ths allowing s to ignore the mesh clients. 3.2 System Model Consider a set V { v v,..., } AP/Gateway Access Point Mobile/stationary device Wireless link Wired link = 1, 2 v n of randomly distribted static Ms located on a 2D plane, each node V has a niqe id( i ) = i, where 1 i ( = V, nmber of nodes) and is specified by its coordinates
( x( ), y( )) at any instance. Each node V is assigned a power fnction p tx where p tx ( d ) is the minimm transmission power needed to establish a commnication link to another node v V located d distance away from. Two assmptions are made: (1) that the imm transmission power, p tx, V is the same and (2) that the imm distance, D, needed for any two nodes v V to commnicate directly is also the same. tx p tx Therefore, p ( D) =, V. At the beginning of p tx simlation, every node transmits with fll power and an indced graph modelled as a qasi Unit Disk Graph (qudg), G = ( V, E) is created. Here, V is the set of all nodes in the network and E is the set of all links/edges i.e., E = {( d( D}. The WM topology is modelled as a weight directed graph in which for each edge ( E, node v has to be within the transmission range of. The notation d( denotes the Eclidean distance between the nodes and v. The following gives a list of definitions to the terms sed in the paper. Definition 1 (Accessible eighborhood Set): The Accessible eighborhood Set,, is defined as the set A of all nodes that have a direct link with node, when transmits at imm transmission power. The set is given by = { v V d( D}. A Definition 2 (Weight Fnction): An edge ( has a weight given by the following expression: α w ( = t. d( + rx(, (1) where t is a threshold related to signal to noise ratio at node and α [ 2,5] is a constant real nmber depending on the wireless transmission environment. Both parts of (1) are smmed p to give the transmission power. The first part is the transmitter power consmed by transmitting a packet from node to v and rx( is the receiver power. Assming all receivers have the same threshold power for signal detection hence the vale of t becomes some appropriate constant. Definition 3 (Logical eighbor Set): A logical L L neighbor set of node is given by S. ode v S if and only if there exists an edge ( in the topology generated by the algorithm and = { v V v}. S L Definition (Flly Connected): A network is flly connected if and only if V, there exist either a direct path or a mltihop path from to every other node v V in the network. Definition 5 (Relay Region): Given a node v, let the physical location of v be denoted by Loc (. The relay region of the transmit-relay node pair (, is the physical region RL sch that relaying throgh v to v any other point in RL v consmes a lesser power than direct transmission to that point. Definition 6 (etwork Lifetime): Given a set of nodes V and for all v V an energy vale E (, the lifetime of node v is Lt = { t f ( t) E( } ntil when E ( = 0, v v where f v (t) is the energy consmed by v. The network lifetime LtV = Minv V ( Ltv ) i.e., the time taken till the first node goes off. Definition 7 (Bi-directionality): A topology G = ( V, E ) generated by the algorithm is bi-directional if, E = {( ( E( G ) and ( v, ) E( G )} and V = V.. PROPOSED ALGORITHM In this section, we present the algorithm design assmptions. Additionally, a two phased design algorithm i.e., constrction of a Local Minimm Shortest-path Tree and nidirectional links removal is proposed..1 Algorithm Design Assmptions The design of the algorithm assmes that: (1) each node se either a GPS receiver or other localization techniqes [20] to gather its location information, (2) each node ses an omni-directional antenna for both transmission and reception, (3) each node is able to adjst its own transmission power and () the initial topology graph G = ( V, E) is flly connected. The objective of the topology control algorithm is to find a sbgraph of the qudg, G = ( V, E), sch that the resltant topology preserves certain network reqirements namely, decrease in average node degree, an averagely low power consmption ths longer network lifetime and a maintenance of connectivity in the resltant network topology. Each node mst adjst its transmission radis to redce its power consmption while still maintaining the connectivity. Since the architectre is more of infrastrctre-less, the topology has to be constrcted in a distribted and localized manner to avoid flooding of the network. This implies that, each node mst establish its transmission power based only on the information of the nodes reachable by a small constant nmber of hops..2 The ELMST Algorithm Design Phases Phase 1: Constrction of Local Minimm Shortest path Tree (LM-SPT).
In this phase, each node gathers neighbor information and constrcts an LM-SPT (as depicted in Figre 2). The phase involves three stages: i. Information collection and exchange: - Each node in this step periodically broadcasts a beacon Hello messages sing imm power p. The ii. iii. tx information exchanged here incldes the node ID and the position in the 2D plane. This information is sed to calclate the node to node distance, the link weights and the path weights. The link weight represents the power reqired for transmission along a link, and the path weight represents the sm of all minimm link weights of a path from sorce to destination. The reslt of this stage is the Accessible eighborhood Set A for each node V. The Hello message is also sent by each node asynchronosly and periodically giving each node s information abot its neighbors. Constrction of a Logical Visible eighborhood Topology: - Each node applies the concept of the relay region in order to gather the nodes in the set of Logical Visible eighborhood. The set LV ( k) A at k = 1. If a node v A is in the relay region of another node w A then node v is moved to a new set of non neighbors called otbr. This is repeated for all the nodes i A. All nodes reachable via other nodes are moved ot of the set A and the remaining set is called LV( ). Each node then applies the Dijkstra s algorithm independently from a sorce node to all the other nodes in V in order to bild its LM-SPT. 1 2 3 5 a 6 7 8 Figre 2: (a) the topology from the point of view of node before topology control. (b) the view after topology control. Compting the transmission power: - Each node comptes its minimal transmission power to cover only all of the nodes contained in the set LV( k ), in which case, it determines which node among the nodes is frthest. The node then adjsts its transmission power to reach this node and ths all other nodes in the set LV ( k) are covered. The set is given by G = ( V, E ). From the information on the location of the nodes, the inter node distance is calclated. The distance is applied in the 1 2 3 5 b 7 6 8 propagation model formlas to obtain the minimm transmission power. The free space model is sed for short distances and the two ray grond reflection model is sed for longer distances depending on the vale of the Eclidean distance in relation to the cross over distance. The cross over distance is calclated sing the following expression: Cross _ over _ dist π h h t r =, (2) where h t = h r = 1.5, are the antenna heights of the transmitter and receiver respectively. Lambda λ, denotes the wavelength. For d( v ) < Cross_over_dist, the Free Space model is sed whereas if d( v ) Cross_over_dist, the Two-raygrond model is sed. The free-space propagation model is given by the following expression: λ 2 RxThresh(( π d ) L ) Pmin = 2. (3) G G λ The two ray grond reflection model is given by the following expression: RxThresh( d L ) t r Pmin =, () G G h h 2 2 t r t r where G t = G r = 1 is the transmitter and receiver Antenna gain respectively, L = 1 is path loss exponent and again the vales of h h = 1. 5. t = r Figre 2 shows an illstration of the operations of phase 1. ode broadcasts hello messages with fll transmission power and obtains responses from the nodes in the A sch as nodes 2,3,5,6 and 7. After stage 2, node establishes that node 7 is in the relay region of node 6 and node 2 is in the relay region of node 3 hence, LV () = {3,5,6} and otbr () = {2, 7}. In stage 2, node calclates its final transmission power as that sed to reach node 6 which is the frthest node in the LV() set. The LM-SPT is then bilt sing the Dijkstra s algorithm. Table 1 shows the algorithm that rns in each node V to compte the minimm transmission power. Let p ( be the minimm power reqired to transmit a data packet from node to node v at any time instance. Also let initial power p tx p = and F( p) be the region that node can reach if it broadcasts with power p. It is assmed that every node knows its terrain and antennae characteristics and is able to compte the region F ( p). The sets Accessible eighborhood ( A ), ot neighbor ( otbr ), and Logical Visible
eighborhood ( LV () ) of node are initialized to empty set,φ. ode broadcasts the Hello messages at fll transmission power p tx stating its position. It collects all the ACKs recording each nodes ID, and Location ( Loc ( ) in the Accessible eighborhood set A tx = { v Loc( F( p ), v } where Loc ( is the location of the node v and F ( p tx ) is the region covered by node at fll transmission power. Table 1. The Topology Control Algorithm Listing Phase 1: Inpt: the set, ) G = ( V E Otpt: Power assignment to node 001 002 p = p tx A initialize the imm power = φ accessible neighbors at 003 otbr = φ non neighbor set 00 LV( ) For every node v A, node comptes the distance d ( and the power p( and arranges them in ascending order. For every two nodes v,w A, if node v is in the relay region of node w i.e., Loc( RL w and p( + p( w, p( then node v is moved to the otbr set, otherwise it remains. If p = p tx = φ local Visible neighbors at p () Begin 005 broadcast Hello message with p = p tx 006 receive Acks and record the neighbors id and their locations in the set A 007 A = { v Loc( F( ptx ), v } 008 if ( A == φ ) 009 Retrn, 010 else 011 v A, calclate distance d ( 012 sort distance in ascending order. 013 calclate p (, v A sing d (, received power & propagation models. 01 sort A by p(, in increasing order, v A 015 for each v A do w A do Loc( RL && p( + p( w, p( otbr = otbr v 016 for each 017 if w then { } Loc RL otbr = otbr 018 else if ( v && p( + p( v, p( then { w} 019 LV() = A otbr 020 p( ) = { p( v LV( ), F p F p tx (, ) (, )} Loc( RL v and p( + p( v, p( then node w is moved to the otbr set otherwise it remains. The Logical Visible eighborhood of node i.e., LV () is therefore given by the set A less otbr set of node. Phase 2: Removal of Unidirectional links. Bi-directional links are qite important for link level acknowledgements and for packet transmissions and retransmissions over the nreliable wireless medim. In phase two of the algorithm, nidirectional links generated in phase 1 are removed so as to obtain bi-directional edges sing edge addition. The reslting topology is given by G = ( V, E ) where V = V, E = {( ( E( G ) and ( v, ) E( G )}. Table 2 depicts the algorithm sed. For every node v LV( ), if there is an edge v, then there mst be an edge v and node LV(. Table 2. Algorithm Listing For Unidirectional Links Removal Phase 2: Inpt: LV 1 hop ni/bi - directional link neighbors of. Otpt: () LV () new () 5. SIMULATIO AD RESULTS LV with bi-directional links Convert to bidirectional (*convert nidirectional links to bidirectional links*) 001 LV () 1 hop nidirectional neighbors of node 002 if 003 for each node k in ) 00 if edge k LV ( and LV(k) 005 then add edge k 006 then add node in LV (k) 007 repeat 2 6 for all V 008 Retrn ) LV ( In this section, some of the simlation reslts to verify the effectiveness of ELMST are presented. The performance of ELMST and IEEE 802.11b Maximm Power are compared. The topology control algorithm is implemented in S-2. The nodes are randomly distribted in a rectanglar region of 1200m x 1200m and are varied in nmber from 10 to 100 nodes. All the nodes have a imm transmission range D of 250m. A carrier freqency of 2.GHz and a transmission bandwidth of 2MHz is sed. It is assmed that the omni-directional antennas sed have a 0dB gain and are placed at a height of 1.5m above a node. OLSR is sed as the roting protocol in the simlations de to its distribtive natre. UDP traffic is sed as the application traffic sorce with the nmber of connections varying from 10, 20, 30 or 0.
The average connectivity is obtained by evalating the average node degree (the mean connectivity per node) sing the formla C = y /( ), where y is the nmber of nodes reachable by node and is the total nmber of nodes in the network. The average mean connectivity denoted by ψ is given by: 1 1 C = 0 ψ =, (5) which is eqivalent to smming p all the mean connectivity of every node in the entire network. The vale of C shold not be too large as this wold imply that a node commnicates even with very distant nodes and this increases interference and collision and also wastes energy. On the other hand, it shold not be made too small as this wold imply that longer paths have to be taken to reach destinations and this also increases the overall energy consmption in the network. Figre 3 shows a comparison of the average node degree levels. The ELMST algorithm records a great redction in the average node degree not exceeding 6.0 for the entire 10 to 100 nodes network, while maintaining node connectivity. This reslts from the fact that with redced power, a node s neighbors becomes only those that are closest to the node nless there is no relay node to a far neighbor. Figre : Performance comparisons between a conventional IEEE 802.11b at Max transmission power and ELMST in terms of network lifetime for a 50nodes network. Similarly, in figre 5, a network of 100nodes is simlated with 0 traffic connections at random times. As expected with controlled power, ELMST ensres the network remains connected p to 85s. This is becase, at redced per node transmission energy, channel contention is redced and a nodes total amont of processing power is redced as it only reaches few neighbors and eventally the overall consmed power in the network is redced. Figre 3: Performance comparisons between a conventional IEEE 802.11b at Max transmission power and ELMST in terms of Average ode Degree. odes range from 10 to 100. The lifetime of each of the network instances is also considered. This is measred in terms of the nmber of nodes that remain alive over a period of time. The simlations are based on the assmption that nodes are static and are rn for a period of 150 seconds. Figre shows the lifetime of a network of 50 nodes with 20 traffic connections at random times. A total of 102 packets were sent with 512bytes of data. It is noted that when sing imm power, the network gets disconnected after arond 52s. At a controlled power, the lifetime is extended to the 73s. Figre 5: Performance comparisons between a conventional IEEE 802.11b at Max transmission power and ELMST in terms of network lifetime for a 100 nodes network. 6. COCLUSIO In order to realize the effectiveness of WMs, the lifetime of the network is very critical. In this work, an enhanced minimm shortest-path tree based energy efficient topology control algorithm (ELMST) for wireless mesh networks with limited mobility was presented. The algorithm ses only the locally available information to determine the nodes that shold be its logical neighbors at any given time. The reslting
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