Optimal Hierarchical Energy Efficient Design for MANETs Wasim El-Hajj Western Michigan University Kalamazoo, MI

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1 Optimal Hierarchical Energ Efficient Design for MAETs Wasim El-Ha Western Michigan Universit Kalamaoo, MI Dionsios Kountanis Western Michigan Universit Kalamaoo, MI, USA Ala Al-Fuqaha Western Michigan Universit Kalamaoo, MI, USA Hani Harbi UAE Universit United Arab Emirates ABSTRACT Due to the groing interest in mobile ireless Ad-Hoc netors (MAETs applications, researchers have proposed man routing protocols that differ in their obective. Energ efficienc and scalabilit are to of the most important obectives. In our previous or, e proposed a fu based hierarchical energ efficient routing protocol (FEER for large scale MAETs that aims to maimie the netor s lifetime and increase its scalabilit. The problem has to parts: the clustering part and the routing part. In the first part, e cluster the netor into to levels of hierarch (cluster heads and normal nodes, connect the cluster heads (bacbone ith each other, and connect the normal nodes to the cluster heads hile maimiing the netor lifetime. In the second part, e design energ efficient routing that uses the hierarchical structure. We call the first part, the energ efficient clustering problem (EEC. In this paper, e formulate three variations of EEC as integer linear programming (ILP problems. We first consider a netor ith a full connected bacbone (EEC-FCB. Then, e rela the full connected constraint and consider a netor ith a connected bacbone (EEC-CB, not necessaril full connected. Finall, e consider a more reliable netor (EEC-R b electing a bacup cluster head for each cluster. Categories and Subect Descriptors C.2. [Computer-Communication etors]: etor Architecture and Design; C.4 [Computer Sstems Organiation]: Performance of Sstems. General Terms Design, performance, theor. Keords Mobile ireless ad-hoc netor, hierarchical design, energ efficienc, and integer linear programming.. ITRODUCTIO An Ad-Hoc netor is a collection of autonomous arbitraril located ireless hosts (also called nodes, in hich an infrastructure is absent. The netor consists of nodes, hich act as routers in the netor. In other ords, a node is not onl responsible for sending and receiving its on data, but it also has to forard traffic to other nodes. The maor advantages of Ad-Hoc netors are rapid deploment, robustness, fleibilit and support for mobilit, hich are useful in a ide range of applications. Ad-Hoc netors are suitable in situations here an infrastructure doesn t eist or is epensive to deplo. Permission to mae digital or hard copies of all or part of this or for personal or classroom use is granted ithout fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To cop otherise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. IWCMC 06, Jul 3 6, 2006, Vancouver, British Columbia, Canada. Copright 2006 ACM /06/ $5.00. A tpical application is disaster recover, here the communication netor infrastructure is destroed and restoring communication quicl is important. Another idel used application is militar communication in hostile environments (battlefield. Troops ill be able to set up a communication netor using light eight ireless equipment in rapidl changing environments. A critical issue in the design of routing protocols for mobile ireless Ad-Hoc netors (MAETs is the efficient utiliation of resources such as limited energ. The problem becomes more challenging if the netor is deploed in large scale. In order to utilie the limited energ resources and to overcome the scalabilit problem that is inherent in flat netors [, 2], e previousl designed a fu based hierarchical energ efficient routing protocol (FEER that aims to maimie the lifetime of the netor [3]. The lifetime of the netor is decided b the lifetime of the eaest node i.e. the node ith the shortest time to survive. FEER organies the netor into to levels of hierarch (normal nodes level and cluster heads level. Initiall, FEER elects some nodes in the netor to act as cluster heads (CHs. It interconnects CHs to each other forming the netor bacbone. Then, it associates each normal node ith a CH. And finall it designs the routing scheme. FEER has to maor components: ( the first component is to cluster the netor such that the initial bacbone nodes are poerful enough to handle the traffic demand; (2 the second component designs the routing scheme and the maintenance scheme. In this paper, e onl consider the first component (the clustering part. We define the optimal solution to the energ efficient clustering problem hen the netor has a full connected bacbone (EEC-FCB b formulating it as an ILP problem. To mae the problem more practical, an etension to EEC-FCB is made in order to reduce the bacbone connections (EEC-CB. The ILP solutions of EEC-FCB and EEC-CB are compared ith each other and the data are analed. We also introduce another etension in order to mae the netor more reliable (EEC-R. EEC-R introduces a bacup CH for each cluster. In a situation here the CH fails, eaens, or moves outside its cluster coverage, the bacup cluster head (BCH taes over immediatel. BCHs are ver useful in netors that are ver mobile. It is orth noting that the ILP formulation is used as a theoretical basis and it is not intended to be used in practice. Our proposed ILP formulation finds the optimal clustering solution. Researchers can then compare their clustering approaches to our ILP formulation in order to evaluate the performance of their schemes. The remainder of this paper is organied as follos. Section 2 includes some related or done in energ efficient routing in MAETs. Section 3 presents an overvie of FEER. Section 4 defines the energ efficient clustering problem ith a full connected bacbone (EEC-FCB and its ILP formulation. Section 5 defines the energ efficient clustering problem ith a relaed bacbone (EEC-CB and its formulation. Section 6 287

2 presents the performance evaluation of EEC-FCB and EEC-CB. Section 7 describes the reliable energ efficient clustering problem (EEC-R and its formulation. Section 8 concludes the paper and discusses future or. 2. RELATED WORK Researchers have proposed man routing protocols that address the limited energ constraint found in MAETs [4-4]. Some of this or focuses on minimiing the total energ consumption rate of the netor. Hoever, this can lead to some nodes in the netor being drained out of energ ver quicl. Hence, instead of tring to minimie the total energ consumption, routing to maimie the netor s lifetime is considered [4-8]. In [4] and [5], a rigorous formulation using linear programming is presented hich attempts to capture the issue of poer consumption more precisel. The obective as to design the routing hile maimiing the netor lifetime. The give heuristic algorithms to solve the linear program approimatel, but the proposed approach can perform arbitraril bad in the orst case. In a later paper [6], a centralied algorithm to determine the maimum lifetime is presented, based on the Garg-Koenemann [7] algorithm for multicommodit flo. In [8], the authors consider the routing problem in MAET ith the goal of maimiing the lifetime of the netor. The propose a distributed routing algorithm that reaches the optimal (centralied solution to ithin an asmptoticall small relative error. Their approach is based on the formulation of multicommodit flo, and it allos considering different poer consumption models and bandidth constraints. It ors for both static and slol changing dnamic netors. Our energ efficient approach has some similarities ith other approaches in the sense that it designs the netor in a hierarchical fashion and then it achieves interconnectivit beteen various parts of the netor. But to our noledge nobod formulated this design problem as an ILP problem and analed its performance. In the net section, e give a brief overvie about FEER. 3. FEER OVERVIEW FEER protocol [3] is a hierarchical energ efficient routing scheme for large scale mobile ad-hoc netors that aims to maimie the netor s lifetime. Each node in the netor is characteried b its residual energ, traffic, mobilit, and degree. In [3], e developed a fu logic controller that combines these parameters, eeping in mind the snerg beteen them. Having non the qualit of each node, a centralied algorithm is used to cluster the netor into to groups (cluster members and cluster heads and then route messages beteen nodes. FEER also creates an etra tpe of nodes called guest nodes that are beneficial in minimiing cluster maintenance. In this paper e remove the guest nodes in order to reduce the compleit of the ILP formulation. FEER differs from other approaches in the folloing aspects: ( it uses a fu logic controller to evaluate the strength of each node. (2 It designs a fault tolerant bacbone that satisfies the netor communication demand. (3 It designs energ efficient routing that maimies netor lifetime. FEER achieves its goals b using man algorithms such as: dominating set lie algorithm, min cut algorithm, ma flo algorithm, and routing algorithm. The compleit of FEER is bounded b the compleit of the min cut algorithm hich is O(n EERGY EFFICIET CLUSTERIG WITH FULLY COECTED BACKBOE (EEC-FCB AD ILP FORMULATIO In this section, e define and formulate the energ efficient clustering problem hen the netor has a full connected bacbone (EEC-FCB. We formulate EEC-FCB as an ILP problem, here ever function must be linear, and the solutions of ever variable must be integer. In EEC-FCB, ever variable can be either 0 or and thus the formulation is called binar ILP formulation. 4. EEC-FCB definition Since flat netors have poor scalabilit [, 2], e designed our netor in a hierarchical fashion. To hierarchical levels are used: cluster heads (CHs level and normal nodes level. ormal nodes can onl communicate ith their corresponding CHs, hile CHs communicate ith each other. The EEC-FCB problem is to group a large set of mobile Ad-Hoc nodes into clusters, elect a CH for each cluster, connect cluster nodes to the chosen cluster heads, and full connect CHs ith each other (this condition ill be relaed in section 5 hile maimiing the netor lifetime. The radio model e use follos the most commonl used poer-attenuation model [5]. The signal poer falls as r, here r is the distance beteen the transmitter/receiver nodes and is a real constant dependent on the ireless environment, tpicall beteen 2 and 4. In our case, e set = 2 for communication beteen normal nodes and CHs, and = 3 for communication beteen CHs. The rationale for using more poer consumption beteen CHs ( = 3 is that CHs bare more burden than normal nodes and the are supposed to route all the traffic that is generated from their cluster members. 4.2 EEC-FCB ILP formulation To mae the ILP formulation eas to follo, e start b introducing the notations used in the formulation. The constants/variables and their definitions are presented as follos: : Total number of nodes in the netor predetermined. P: umber of clusters heads predetermined. d i : Euclidean distance beteen nodes i and. K : Ma number of nodes that can be connected to CH predetermined. c i : Cost of connecting a regular node i to CH (proportional to d. 2 i 3 h : Cost of connecting CH to CH (proportional to d. b : Weight associated ith CH. i : Variable. if node i is connected to CH ; 0 otherise. : Variable. CH is connected to CH ; 0 otherise. : Variable. if node is chosen to be a CH; 0 otherise. i : Variable. if i = and = ; 0 otherise. ote that b can be an meaningful eight assigned to a node (an appropriate eight is discussed in [3]. The higher the value of b, the better the node is. Since the obective function is a minimiation function, each value in the b arra is multiplied b -. EEC-FCB can be formulated as a binar ILP problem as follos: 288

3 Min,, ( = c Subect to: i i i i = ( P ( K i = i = = b ( P = = ( ( h c ; ( ; (2 = ( P P( P / 2 ; (3 P ; (4 = ( P ; = = ( P (5 ; (6 = 0 ; (7 ii = ; i; (8 i i ; i; (9 i i ; i; (0 i ; i; ( i i i i ; (2 ( P ( ; (3 {0,} ; i; (4 i {0,} ; ; (5 {0,} ; (6 ote that variables i,, and are beteen and. The obective function is divided into three parts. The first part calculates the cost of connecting normal nodes to CHs. The second part calculates the cost of electing CHs. The third part calculates the cost of connecting CHs ith each other. B minimiing the obective function, the poer consumption rate is optimied and the lifetime is maimied. Constraint indicates that if node is chosen to be a CH, it needs to support at least (P- other CHs. Constraint 2 indicates that if node is chosen to be a CH, it should be connected to at most (P- CHs and K regular nodes. Constraints and 2 also indicate that if node is a normal node, it should be connected to onl one CH. Constraint 3 indicates that the total number of interconnections is equal to the number of connections beteen regular nodes and CHs plus the number of connections that full connect the CHs. Constraint 4 indicates that the total number of CHs is P. Constraints 5 and 6 mae sure that matri (bacbone contains onl the connections that interconnect CHs. Constraints 7 and 8 indicate that matri is smmetric and its diagonal is 0. Constrains 9, 0, and indicate that i = onl if both i = and =, 0 other ise. i is used to simulate i. Constraints 2 and 3 ensure that if a node is chosen to be a regular node, it should be connected to onl one CH and not to another regular node. Constraints 4, 5, and 6 indicate that the variables have binar values. Figure shos the outcome of EEC-FCB on a netor of 9 nodes. odes, 2, and 3 are elected as CHs. odes 4 and 5 oin CH. odes 6 and 7 oin CH 2. odes 8 and 9 oin CH 3. In the net section, e etend EEC-FCB such that the bacbone connections are reduced. Figure : EEC-FCB for a netor of 9 nodes. 5. EERGY EFFICIET CLUSTERIG WITH COECTED BACKBOE (EEC-CB AD ILP FORMULATIO EEC-FCB (section 4 assumes that the bacbone netor is full connected. To mae the netor more practical, e rela this constraint and reduce the bacbone connections hile ensuring the netor connectivit. One a to ensure the bacbone connectivit is to connect one CH ith all the other CHs. We call such a CH the main cluster head (MCH. ote that, if a node is a MCH, then it is definitel a CH. If a node is a CH, then it might or might not be a MCH. If a node is a normal node, then it is neither a CH nor a MCH. We introduce a ne variable called M, here M = if node is a MCH; 0 otherise. Some of the constraints discussed in section 4 remain the same, hile others are added. EEC-CB is presented b the folloing binar ILP problem: Min,, Subect to: ( = c i M ; M {0,} ; i = b = = (7 (8 h 289

4 M = = ; (9 ( P 2 M ; i i = i (20 ( P P( P / 2 ; (2 ( P 2 = M ( P ; ; (22 (23 = ; ; (24 Constraints 2, 4, and 7 through 6 are also needed to formulate EEC-CB. Constraints 7 and 8 indicate that if a node is chosen as a MCH (M =, then it must be a CH ( = but the inverse is not true (discussed above. Constraint 9 indicates that there should be one MCH in the netor. This condition ensures the connectivit of the bacbone. Constraint 20 indicates that if a node as chosen as a MCH, then it must be connected to at least (P- other CH. Otherise, the node is ust a normal node or a CH. If it as a normal node (M = 0, it should be connected to eactl one CH. If it as a CH, it should be connected to at least one other CH. Constraint 2 is the same as constraint 3, but ith the equal sign changed to less than or equal. In this case, the bacbone netor is not full connected. Constraints 22 and 23 ensure that the MCH is connected to all other CHs, hile normal CH can be connected to a minimum of one other CH. Constraint 24 indicates that the matri (bacbone is smmetric; Figures 2 and 3 displa to sample eecutions of EEC-CB. Figure 3: EEC-CB for a netor of 8 nodes. 6. PERFORMACE EVALUATIO In this section e evaluate the performance of EEC-FCB and EEC-CB. etors of different sies and considered. For each netor, n nodes are uniforml distributed in a unit space. The average of K runs is calculated for each netor. Because EEC-FCB and EEC-CB taes lots of time to eecute (Pcomplete, e onl considered netors ith less than ten nodes. Figure 4 shos the results. EEC-FCB and EEC-CB produce netors ith close costs. But, EEC-CB has a loer cost because it designs a netor ith relaed bacbone i.e. less connections beteen CHs hich translates to less netor cost. ote that EEC-FCB and EEC-CB tend to choose as CHs nodes that are close to each other. As the distance beteen CHs increases, the obective function increases and thus the netor cost increases. Cost 4.E06 3.E06 2.E06.E06 0.E00 Performance Evaluation EEC-FCB EEC-CB umber of odes Figure 4: Costs of ILP, and ILP Etension. Figure 2: EEC-CB for the same netor presented in Figure. 7. EERGY EFFICIET CLUSTERIG WITH A RELIABLE BACKBOE (EEC-R AD ILP FORMULATIO In this section, e further etend EEC-FCB discussed in section IV so that each cluster ill be provided b a bacup cluster head (BCH. Having a BCH is ver useful in man situations such as: ( CH s energ becomes scarce and it can not handle the cluster demand. (2 CH is not able to cover all the nodes in its cluster because of mobilit. (3 Connectivit beteen CHs is broen also because of mobilit. (4 CH fails. 290

5 7. EEC-R definition EEC-R is to group a large set of nodes into clusters, elect each CH, elect each BCH, connect nodes to the chosen CHs and to the chosen BCHs, and full connect CHs and BCHs hile minimiing the poer consumption rate and maimiing the netor lifetime. ote that the bacbone connections can be reduced using the same technique used in section EEC-R ILP formulation The constants/variables notations given in section 4 are still the same ith i removed and three ne variables added. The ne variables are presented as follos: : Variable. if node is chosen to be a BCH, 0 otherise. t i : Variable. if both i = and =, 0 otherise. v i : Variable. if i = and =, 0 otherise. The obective function presented in section 4 is still the same. EEC-R can be formulated as the folloing binar ILP problem: Min,, ( = c i i = b = = ( h c Subect to: ; (25 0; 0 ; (26 Constraints 25 and 26 mae sure that if a node is chosen to be a CH, then it can not be a BCH. And if a node is chosen to be a BCH, then it can not be a CH. i (2P ( (2P ( (2( ; (27, constraint 27 puts a loer bound on the number of connections that node can mae ith other nodes. If node as elected as a CH ( = or as a BCH ( =, then node should be connected to at least all the other CHs and BCHs (2P- connections. If node as a normal node, then it should be connected to its CH and its BCH (2 connections. i ( K 2P ( ( ( 2P K 2 (2( ; (28, constraint 28 puts an upper bound on the number of connections that node can mae ith other nodes. The same reasoning applied in constraint 27 applies also in this constraint. i = i = ( P ( 2P 2P( P ; (29 Constraint 29 sums up the connections made beteen normal nodes and their associated CHs/BCHs plus the connections that full interconnects the CHs/BCHs. = = P ; (30 Constraint 30 indicates that the number of BCH is equal to the number of CHs. = 2( P 2( P ; (3 = = 2( P 2( P ; (32 Constraints 3 and 32 mae sure that matri contains onl the connections that interconnect CHs and BCH (bacbone netor. t ; i; (33 i i t ; i; (34 i t ; i; (35 i i Constraints 33, 34, and 35 mae sure that t i = onl if i = and =, 0 otherise. t i simulates i. t ; t i i ( P (36 ( ; (37 Constraints 36 and 37 are used to ensure that if a node is chosen to be a regular node, then it should be connected to one CH and not to another regular node. v ; i; (38 i i v ; i; (39 i v ; i; (40 i i Constraints 38, 39, and 40 mae sure that v i = onl if i = and =, 0 otherise. v i simulates i. v ; v i i ( P (4 ( ; (42 Constraints 4 and 42 ensure that if a node is chosen to be a regular node, then it should be connected to one BCH and not to another regular node. {0,} ; (43 t {0,} ; ; (44 v {0,} ; ; (45 Constraints 43, 44, and 45 are used to indicate that the variables are binar values. Figure 5 shos the output of EEC-R on a netor of 7 nodes. odes and 4 are elected as CHs. odes 2 and 3 are elected as BCHs for CHs and 4 respectivel. odes 5 and 6 are connected to CH and BCH 2. ode 7 is connected to CH 4 and BCH 3. The bacbone, composed of CHs and BCHs, is full connected. And the normal nodes are connected to both CHs and BCHs. 29

6 Figure 5: EEC-R for a netor of 7 nodes. 8. COCLUSIO AD FUTURE WORK Due to the vast number of useful applications in MAETs, designing an energ efficient routing protocol for such netors is becoming more and more important. Energ efficienc can be translated into the problem of maimiing the netor lifetime. Previousl, e proposed a hierarchical protocol (FEER that aims to maimie netor lifetime. In this paper, e describe the optimal solution to the energ efficient clustering problem (EEC b formulating it as an ILP problem. Three variations of EEC ere formulated. EEC-FCB designs a netor ith a full connected bacbone. EEC-CB reduces the bacbone connections hile ensuring netor connectivit. EEC-R designs a reliable netor b introducing a bacup cluster head for each cluster. We are no in the process of designing a distributed netor design and a distributed routing protocol that achieves the same goals. 9. REFERECE [] Gupta, P. and Kumar, P. R. The Capacit of Wireless etors. IEEE Transactions on Information Theor, IT- 46, 2 (March 2000, [2] Gupta, P., Gra, R., and Kumar, P. R. An Eperimental Scaling La for Ad Hoc etors. (Ma 6, 200, [3] El-Ha, W., Kountanis, D., Al-Fuqaha, A., and Guiani, M. A Fu-Based Hierarchical Energ Efficient Routing Protocol for Large Scale Mobile Ad Hoc etors (FEER. IEEE International Conference on Communication (ICC 06, (Istanbul, Ture, June-5, [4] Chang, J.-H. and Tassiulas, L. Routing for maimum sstem lifetime in ireless ad-hoc netors. In Proc. of 37th Annual Allerton Conference on Communication, Control, and Computing, (September 999. [5] Chang, J.-H. and Tassiulas, L. Energ conserving routing in ireless ad-hoc netors. In Proc. of IEEE IFOCOM, (March 2000, [6] Chang, J.-H. and Tassiulas, L. Fast approimation algorithms for maimum lifetime routing in ireless adhoc netors. In Lecture otes in Computer Science: etoring 2000, 85, (Ma 2000, [7] Garg,. and Koenemann, J. Faster and simpler algorithms for multicommodit flo and other fractional pacing problems. In Proc. of the 39 th Annual Smposium on Foundations of Computer Science, (ovember 998, [8] Sanar, A. and Liu, Z. Maimum lifetime routing in ireless ad-hoc netors. In Proc. of IEEE IFOCOM, (2004. [9] Lin, CR and Gerla, M. Adaptive Clustering for Mobile Wireless etors. IEEE JSAC, 5, (September 997, [0] Amis, D. and Praash, R. Load-Balancing Clusters in Wireless Ad Hoc etors. Proc. of the 3rd IEEE ASSET 00, (March 2000, [] Ru, J.-H., Song, S., and Cho, D.-H. e Clustering Schemes for Energ Conservation in To-Tiered Mobile Ad-Hoc etors. IEEE International Conference on Communication (ICC 0, 3, (June 200, [2] Wu, J. On Calculating Poer-Aare Connected Dominating Sets for Efficient Routing in Ad Hoc Wireless etors. Journal of Communication and etors, 4,, (March 2002, [3] Yu, J. Y. and Chong, P. H. J. 3hBAC (3-hop beteen Adacent Clusterheads: a ovel on-overlapping Clustering Algorithm for Mobile Ad Hoc etors. In Proc. of IEEE Pacrim 03,, (August 2003, [4] Kaadia, V. and Kumar, P. R. Poer control and clustering in ad hoc netors. In Proc. of IEEE IFOCOM, (2003. [5] Rappaport, T.S. Wireless Communications: Principles and Practices. Prentice Hall,