Optimization Models For Planning Wireless Mesh Networks : A Comparative Study D. Benyamina, A. Hafid
M. Gendreau
N. Hallam
NRL, University of Montreal, Canada {benyamid, ahafid}@iro.umontreal.ca
CIRRELT, University of Montreal,
[email protected]
The University of Nottingham
[email protected]
Abstract Recently, we proposed a multi-objective approach to optimize the planning of Wireless Mesh Networks (WMNs). Unlike other approaches where the deployment cost is the pivotal concept to optimize under typical network constraints, this approach tends to simultaneously optimize the two objectives of network deployment cost and network throughput. Optimal WMN planning solutions under this approach are more realistic and much preferred by network planners in that they have to be both cost-effective and efficient (the deployment cost is minimized while the throughput is maximized). While the deployment cost objective is straightforward, the throughput objective can be viewed from different perspectives: either minimizing the aggregation of network interferences or maximizing the culmination of the flows over the entire network. Here, we propose a third perspective that maximizes the throughput by balancing the load over the network channels. We perform a thorough comparative experimental study on these three instance models with different key-parameter settings. Preliminary results presented in this paper show that this new proposed model totally supersedes the flow aggregation based model and should be used as a contender to the interference based model. Key Words: Wireless Mesh Network, Planning problem, Multiobjective optimization, Meta-heuristic search algorithm.
I.
INTRODUCTION
T
he success of the Wireless Mesh Network (WMN)
technology has caused a paradigm shift in providing high bandwidth network coverage to users. The infrastructure of WMNs encompasses fixed nodes (access points, routers/relays , and gateways) for forwarding messages and orthogonal channels using multi-radios interfaces for allowing simultaneous communications. Access point nodes are the main servers to mesh clients. They also interconnect with each other through point-to-point wireless links using relay routers. Gateways are the main interface to the Internet backbone connection and do have extra functionalities which make them more expensive than simple routers. Deploying such technologies requires considerable budgets and therefore any optimization strategy that minimizes the cost while providing Quality of Service (QoS) is very much sought after. In fact, earlier WMNs deployments have been linked with a number of problems such as intermittent connectivity, poor performance and lack of coverage. It must be noted that the QoS is not necessarily better supported when the number of mesh nodes increases. Indeed, it is risky to correlate the increase of the number of mesh nodes to, for example, a better coverage (throughput increase). Merely
increasing the number of mesh nodes usually increases the complexity of the channel assignment problem thus inducing high interference levels that worsen network performance. Major research efforts have focused on developing planning network solutions for cellular networks and WLANs. However, these solutions strongly differ from those of planning WMNs. Essentially, planning a WMN involves choosing carefully the installation locations, wisely selecting the types of network nodes, and deciding on a judicious channel/node interface assignment, while guaranteeing users coverage, wireless connectivity and traffic flows at a minimum cost. The bulk of related work found in the literature focuses on the problem of performance improvement by assuming a priori fixed topologies [2, 3, 4, 5]. Some of the main drawbacks can be found in [6]. Other studies (e.g., [7, 8]), consider topologies where gateways are fixed a priori, while the studies in [9, 10, 19] attempt to optimize the number of gateways given a fixed layout of mesh routers. On the other hand, recent contributions in [1, 11, 12, 19] propose WMN planning schemes where the locations of routers and gateways are not fixed. Some of these schemes [1] opted for exact optimization techniques (CPLEX for instance) to find optimal planning solutions, which make them bounded to medium-sized instance problems. Others [12, 19] use heuristics (based on greedy selection and genetic algorithms respectively) as optimizers. Furthermore, the common thread in these schemes is that they use variants of single-objective optimization model where the total deployment cost is the sole objective to optimize. The study in [19] deviated from this trend where the authors propose a biobjective model; however, they use a (weighted) aggregate objective function. The very trivial shortcoming of the aggregate approach is the subjective choice of the weights. More importantly, it is widely known in the multi-objective community that the aggregate methods are obsolete and suffer from inherent shortcomings, the noteworthy being the inability to find potential solutions when the landscape of the objective function is non-convex [20]. In this regard, we use an innovative approach, proposed in our recent contributions [15, 18]. To the best knowledge of the authors, up to date there has been no attempt to model WMN planning problems using pure multi-objective meta-heuristic optimization approaches where several non-dominated solutions are produced. In multi-objective optimization, the optimality is redefined and interpreted by Pareto nondominance concept, i.e., none of the solutions is better than the rest with respect to all objectives. Moreover, this set of
“trade-off” solutions is very much appreciated by engineers who usually prefer multiple non-dominated solutions where each can be used in a different decision making scenario. From a (network) modeling perspective, our work differ from the above mentioned contributions in that we plan WMN from scratch to meet the QoS requirements, taking into consideration interference aware model in one instance model while meeting the planner’s objectives and satisfying his/her constraints. The quality of the planned network can be constrained by multiple requirements, namely the signal level received by the mesh clients, the performance quality (in terms of network throughput) or the installation cost. In our previous contributions [15, 18], we proposed two instances of WMN planning optimization models that were based on maximizing the overall network link utilization and minimizing the network level interferences respectively. In this study, we extend our work by proposing a new multiobjective WMN planning model that is based on balancing the links loads over the network. We also provide a thorough comparative experimental study by tuning different keyparameter on the three optimization models. All models are solved using an evolutionary population based meta-heuristic. The rest of the paper is organized as follows. Section II describes the mathematical formulation of the three planning optimization models. Experimental numerical results and a comparative analysis are presented in Section III. Finally, we conclude the paper in Section IV. II.
MULTI-OBJECTIVE MODELING APPROACH AND FORMULATION
In this section, we present three theoretical bi-objectives optimization models. The models attempt to simultaneously minimize the deployment cost and maximize the throughput; they differ, however, in modeling the throughput objective. The first and the third models maximize throughput on a sort of “flow-capacity rate usage” basis, whereas the second one attempts to minimize radio interferences. Before going any further, we briefly present the terminology and notations used in describing our modeling approach – a detailed explanation is found in [15,18]. Let I be the set of positions of traffic concentrations in the service area (Traffic Spots: TSs) and L the set of positions where mesh nodes can be installed (Candidate Locations, CLs) The planning problem aims at: •
•
Selecting a subset S ⊆ L of CLs where a mesh node should be installed so that the signal level is high enough to cover the considered TSs. Defining the gateway set by selecting a subset G ⊆ L of CLs where the wireless connectivity is assured.
Maintaining the cardinalities of G and S small enough to satisfy the financial and performance requirements. Given n TSs and m CLs, let I={1,..,n} and L={1,..,m}. In the following, unless otherwise stated, i and j belong to I and L respectively. The cost associated to installing a mesh node j is denoted by cj, while pj is the additional cost required to install a gateway at location j. di is the traffic generated by TS i. ujl is the traffic capacity of the wireless link between CLs j and l. vj •
is the capacity of the radio access interface of CL j. The coverage and connectivity parameters are given respectively by the binary variables aij and bjl. aij takes the value 1 whenever TS i is covered by a mesh node in CL j. The parameter bjl indicates whether CLs j and l can be connected via a wireless link. We define other decision variables (see Fig.1) in our formulation including: xij takes the value 1 if TS i is assigned to CL j while tj (gj) is set to 1 if a router (a gateway) is installed in CL j. Internet
gj
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Access Point
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Fig.1. WMN planning problem
We suppose initially that the mesh nodes operate using the same number of radios R, each with k channels, (k>R) and k ∈ C, where C ={1,..,c} and c can be at most 12 orthogonal channels if IEE802.11a is used. Extra installation variables are added: =1 if a mesh node is installed in CL j and is assigned channel q, q≤ k, =1 if a wireless link from CL j to CL l using channel q, q ≤ k exists. Let Njl be the set of links that cannot be simultaneously active with the link l. Finally, we define the flow variables and Fj. the first variable denotes the traffic flow routed from CL j to CL l using channel q, the second is the traffic flow on the wired link between a gateway j and Internet. A. Load-Balanced Based Model It seems plausible to enhance the quality of service by minimizing contentions and traffic bottlenecks. One way to achieve this is to properly balance the links loads over the whole network. Our first load-balanced optimization model is therefore formulated as follows: ∑
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subject to the same set of constraints as the one defined in the first model but without constraint 6. C. Flow-Capacity Maximization Model In this model, the (second) throughput objective is modeled as maximizing the total throughput by computing the overall flow-capacity ratio (also called link utilization) of the network. The objectives of the flow-capacity capacity based model are given below. The model is subject to the same set of constraints as defined for the load-balanced alanced based model. ∑
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(1)
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In Section IV,, a comparative experimental study is conducted on these three instance models. III.
NUMERICAL EXPERIMENTS XPERIMENT AND ANALYSIS
In this section, we present the preliminary results obtained by experimenting the three models described in the previous section. A. Optimization Technique and Planning Solutions Generation We use MOPSO, Multi-Objective bjective Particle Partic Swarm optimization, as the optimization technique [13, 14] to solve the models. A position in the search space represents a set of assignments that is a solution to the problem. In our case, each (vector) position contains user connectivity (x ( ij), device installation' ), device connectivity vity , gateway existence (gj), link flows ' ),, and gateway/backbone link flows (F ( j). For each particle in the swarm, we assign a Boolean value to the variables xij, , , and gj and a real value to the flow variables ' ). A solution is feasible feas if it satisfies all constraints. During the iterative search process, non-feasible solutions that violate all constraints are discarded, but those that violate only the soft constraint (5) can be included in the population. This way will increases the likelihood of a nonfeasible solution to mutate and provide a feasible one in later generations. More details on how the generic model is solved using MOPSO can be found in [15].. The optimization process in our approach is as follows: First, feasible planning ning solutions are constructed (Fig. 2): i.e., placing, for each particle in the swarm, a subset S1 of APs to cover all TSs, augmenting S1 to construct the connectivity matrix, selecting gateways,, assigning channels as in [16] and assigning flows using Edmond’s ond’s algorithm [17]. [17] Then, the main algorithm loop is invoked that, based on these initial solutions, goes on mutating planning solutions in the swarm from generation to generation, with a bias towards selecting the fit solutions.
(1) (2b)
(a) (b) (c) Fig.2. A Grid Representation: A feasible Initial solution with (a):TSs locations, (b):Coverage, and (c):connectivity/gateway (c):connectivity/ Assignment.
D. Results and Analysis 1 Grid Size (m) Variation Here the number of candidate locations, m, is gradually increased while all other parameters are maintained fixed. Results (Fig. 3 and Fig.4) show that there is consent in all models that a 49-grid is the best in satisfying the Standard Setting SS. A very important remark is that the cardinality and the width of the spectrum of the planning solutions are greater in the load-balanced model than they are in the other two models. This fact makes the first model the best to find cheaper planning solutions. Interference-based model seems to generate more and well spaced solutions than the third model. These observations, drawn from Fig.3, suggest that a network planner with ‘flexible’ requirements would possibly opt for
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For each model, the planning solutions couples (deployment cost against performance) for a given value of each key parameter variation constitute a (Pareto) front of nondominated solutions that is plotted in a (objective space) graph. On the other hand, only the cheapest solution is used for plotting the resource utilization graph. A noteworthy remark is that a rigorous comparison between the models on the cost/ performance plotting is baseless. This is because the magnitude of the interference based throughput is simply different from that of the flow-capacity based ones. However, other important characteristics of the solutions can be derived and are safely comparable. The number of the solutions, the width of the spectrum of the solutions, the uniform-distribution of the solutions, can all prove very important in decision making. In addition, for each scenario we further plot the device utilization graphs in terms of the number of gateways, routers, and links. This makes comparing the three models possible and plausible.
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The positions of the n TSs are randomly generated. A run of our algorithm involves 100 generations each with a population size and an archive size of 50 and 20 particles respectively. It must be noted that in our recent experiments [15], we came to a conclusion that mutating at a rate of 50% of the population leads to the best Pareto front. The algorithm is coded in the Java programming language and all the experiments were carried out on a Pentium M 1.5GHz machine. We study the performance of our algorithm over grid graphs and under many deployment scenarios. For practical reasons, the throughput objective of the flowcapacity based model is rewritten as a minimization of the inverse of the overall network flow-capacity aggregate. Lastly, for each execution scenario (key parameter variation study), results are reported on 10 runs.
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(vj:54Mb/s), (M:128Mb/s), (cj:200), (pj:8*cj), (R:3), (k:11)].
load-balanced model as it offers more and better diverse planning solutions. Load balance x 104
B. Key Parameter Settings Our numerical analysis is based on WMN key parameters, which are as follows: the number of clients (TSs) n, the number of CL m, the client demands di, the gateway factor cost pj, and the number of radio interfaces R. In this regard, we define the Standard Setting (SS) of the WMN key parameters as the following: SS=[(n:150), (m:49), (di:2Mb/s), (ujl:54Mb/s),
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Fig.4. Network Devices Utilization For Three Models with Different Grids. (a) number of MRs, (b) number of APs and MGs
When we turn our attention to resource utilization, it is clear from Fig.4 that the load-balanced model dominates the flow-capacity model since it uses less network mesh nodes in all types of grids. On the other hand, the interference based model requires fewer routers but more gateways for grids larger than 8x8. One can observe that the load-balanced model is more careful in using the gateways (MG) (Fig. 4.b) as it rather adds more routers (MR) (Fig. 4.a) and precisely more access points (AP) as shown in Fig.4.b. Notice that in all models, a higher number of candidate locations leads to an increase in the number of routers and gateways even for the same number of users. The first reason is the fact that increasing the number of CLs increases the probability of an MC (Mesh Client) not being connected to an AP through a multi hop wireless path, which leads to installing more nodes.
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2 Radio Interfaces (R) Variation The number of radio interfaces R is increased from 2 to 5, each with 11 channels. The Pareto fronts illustrated in Fig 5, show that load-balanced model once more, provides better, diverse and greater number of solutions than the other two models. Notice that the best Pareto front is obtained with four radios rather than five radios (Fig. 5 a). The usual scenario is that the more radio interfaces we deploy the more links are established, and the less gateways are needed. This remains true when R shifts from 2 to 3 and from 3 to 4 (Fig. 6). As can be seen from Fig.6.a, the load-balanced model profits from radio gain by decreasing the number of APs, relays, and gateways and increasing the number of links. Notice also that interference model follows the same pattern as load balanced model in reducing the number of resources. On the other hand, all models show a disruption when the number of radios goes from 4 to 5 (see Fig. 6.a,b). This can be caused by the high level of interferences related to the increase in network links. We can then stipulate that no gain can be obtained if we deploy more than four radio interfaces, which stands true for all three models.
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Fig.6. Network Devices Utilization For Three Models with Different Radio Interfaces.(a) Number of MRs-Links, (b) Number of APs- MGs
4 Traffic Spots (n) Variation As with previous scenarios, Fig. 9 shows that more and diverse planning solutions are produced by load-balanced model. Load-balanced and link-flow models require few
gateways, relays, and links to be added when more users are added in, compared to interference model which adds more of these devices (see Fig. 10). On the other side, the loadbalanced model deploys less APs than the other models; this suggests that load-balanced model may be better in handling the scalability issue. A thorough investigation needs to be undertaken in this regard though. n=100
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be achieved in three ways: either maximizing the overall flowcapacity ratio, minimizing network interference or balancing network links’ load. We instantiated three specific WMN planning models, namely flow-capacity based model, interference-based model, and load-balanced based model. We conducted some numerical experiments on all models to study the impacts of some key parameter variations on network performance. In the light of the results shown in Section III, and from a decision making perspective, load-balanced model always generate a broader set of non-dominated solutions, favors cost-effective solutions, and guarantees a diverse and well dispersed set of solutions than the other two models. This makes this model the better of the three to generate cheaper planning solutions. There is also a tendency in using the costly gateways with care in a sense that it usually adds more links and routers than deploying expensive gateways. On the other side, interference model handles better the increase of demands and no more gain can be obtained with more than four radio interfaces.
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(c ) Fig.9. Pareto Fronts of Planning Solutions For different Traffic Spots. (a) Load-Balance model, (b) Interference model, (c) Link-flow model.
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IV
CONCLUDING REMARKS
The bulk of the contributions in planning WMNs assume a fixed topology and are all bounded to medium size instance problems and optimize a single objective, namely the network deployment cost. In this context, we proposed a generic WMN planning model where the two objectives of deployment cost and network throughput are optimized simultaneously. While the deployment cost is trivial, maximizing the throughput can
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