 Research
 Open Access
Interferenceaware multipath routing in wireless mesh network
 Faiza Iqbal^{1}Email author,
 Muhammad Younus Javed^{1} and
 Anjum Naveed^{2}
https://doi.org/10.1186/168714992014140
© Iqbal et al.; licensee Springer. 2014
 Received: 31 October 2013
 Accepted: 23 July 2014
 Published: 25 August 2014
Abstract
The inherent mesh infrastructure of IEEE 802.11based wireless mesh networks provides added support to construct multiple robust paths. However, based on geometric locations of wireless nodes, neighborhood interference and channel contention impose challenges on multipath routing schemes. A large body of research has been carried out to maximize aggregate endtoend throughput using multipath routing; however, interference has not been accurately modeled in majority of the work. Based on the relative location of transmitters and receivers, information asymmetric noncoordinated interference introduces bottleneck links and significantly reduces the aggregate throughput. The impact of this interference is even observed on links several hops away. In this paper, multipath routing is integrated with topology control to manage such multilevel asymmetric interference. An optimization model has been presented with an objective to achieve optimized endtoend throughput using multiple available paths, considering coordinated and asymmetric noncoordinated interference. The goal of this research is to develop a multipath routing strategy which can achieve better endtoend throughput by purging badly affected asymmetric noncoordinated interfering links during path construction procedure. The proposed model and routing strategy have been tested through extensive simulations. The results clearly exhibit the efficacy of the proposed approach, which achieves better aggregate endtoend throughput compared to existing multipath routing schemes.
Keywords
 Wireless mesh networks
 Linear programming
 Multipath routing
1 Introduction
IEEE 802.11based wireless mesh networks (WMN) have emerged as a promising architecture to provide lastmile Internet connectivity to fixed and mobile users. The architecture of WMN usually comprises mesh clients, mesh routers, and gateways. Mesh routers connect mesh clients with gateways using multihop wireless links. Several deployment scenarios of WMN are in practical use including deployment for coverage enhancement, indoor deployment where Internet cabling is difficult, communitywide deployment such as university campuses, and deployment in disasterstruck areas [1, 2].
Despite a number of worldwide WMN deployments and projects with communications based on WMN [3–6], many research challenges exist that, if addressed, can significantly improve the achievable throughput. In particular, given the broadcast nature of the wireless medium, interference has a significant impact on the capacity of wireless links. A combination of accurate interference estimation and interference avoidance/mitigation techniques is mandatory for acceptable network performance. Accurate estimation of interference can lead to interference avoidance by exploiting the inherent redundant infrastructure of WMN through efficient routing and lowinterference path selection.
Over the past decade, a number of unipath and multipath routing schemes and protocols have been proposed [7–22]. Significant body of research has used protocol model [11, 17, 22], physical model [17, 23], or measurementbased models [9, 24–31] for interference estimation. However, none of these models and metrics accurately capture the impact of interference. Consequently, the selected routing paths do not lead to optimal endtoend throughput. The basic reason for inaccuracy is the underlying assumption that all interfering links have similar impact. In practice, this assumption does not hold and the relative location of the interfering links leads to different impacts of interference. Based on relative locations of transmitters and receivers, Garetto et al. [32] have categorized interfering links into four categories.
According to the authors, two links are said to be coordinated interfering links if the transmitters of links are within carrier sensing range of each other. These coordinated transmitters prevent each other from concurrent transmissions, resulting in negligible packet collisions. On the other hand, if transmitters of the two interfering links are not within carrier sensing range of each other, three additional categories of interference  near hidden, far hidden, and information asymmetric  are possible. We collectively refer to the interference caused by these categories as noncoordinated (nonCO) interference. In case of noncoordinated interfering links, the two transmitters cannot sense the transmissions of each other. This results in increased probability of collisions. Particularly, among noncoordinated interference, information asymmetric interference is the most detrimental in terms of unfair channel sharing and endtoend throughput performance [32]. The asymmetry of the channel view of the two information asymmetric interfering links allows one link to achieve its maximum throughput while the other link starves. Consequently, bottleneck links are introduced in the network, leading to reduced endtoend throughput. Therefore, an efficient routing scheme is required, which considers coordinated as well as asymmetric noncoordinated interactions of transmitters and receivers during path construction procedure to avoid such bottleneck links.
Recent studies have considered noncoordinated interactions during routing decisions. Salonidis et al. [33] have proposed a routing metric AVAIL based on the maximum available bandwidth between source and destination. Authors have proposed the use of fraction of busy time and packet loss probability to identify highthroughput paths. Similarly, Razak et al. [34] have proposed a MAC Interaction Aware Routing metric (MIAR), which considers noncoordinated MAC interactions while constructing a route. Both metrics are focused on creating single path for routing flows and ignore the advantage of redundant mesh infrastructure. Furthermore, it is known that information asymmetric interference not only affects links within carrier sensing range but also affects the throughput of links several hops away [35]. To the best of our knowledge, such multilevel impact of information asymmetric interference has not been addressed by existing routing schemes.
The research study in this paper highlights the adverse impact of information asymmetric interference on endtoend throughput in wireless networks. The advantage of selecting a subset of quality paths over all available paths or using single path per flow is also explained using motivational examples (Section 2). The examples show that purging certain links from network topology reduces the number of available alternate paths for the flows; however, the quality of remaining paths is improved, resulting in better endtoend throughput. Primary objective of this research is to show the effectiveness of combining the topology control to mitigate noncoordinated interference with multipath routing in wireless mesh networks to achieve significantly improved aggregate endtoend throughput. Topology control is used to prune the links from the network that can lead to multilevel information asymmetric interference. Consequently, bottleneck links can be avoided in the network. In Section 3, an optimization model has been proposed for joint topology control and multipath routing. The model aims at selecting a subset of quality paths for each flow such that the aggregate endtoend throughput is maximized. Selection of paths is constrained by per link capacity and interference at each link. The effectiveness of the model in accurately predicting the endtoend throughput is shown through simulations.
Adaptive Multipath Routing with Topology Control (AMRTC) scheme has been proposed in Section 4. AMRTC is a twophase centralized scheme. The first phase of AMRTC performs topology control by identifying and pruning the multilevel noncoordinated interfering links. Resultant topology control graph is used in the second phase where maximum available residual capacity paths to satisfy the flow demands are selected. Extensive simulationbased evaluation is carried out to study the effectiveness of the proposed scheme. The results show that AMRTC can effectively mitigate the impact of coordinated as well as noncoordinated interference and can achieve good performance under different scenarios. The results of the evaluation have been presented in Section 5. Section 6 concludes the study.
2 Motivation
2.1 Reducing interference dependencies and bottlenecks using topology control
This section highlights the adverse impact of noncoordinated interference on endtoend throughput. Consider the topology represented by Figure 1a. The nodes are positioned in such a way that directed link l_{1} is observing asymmetric nonCO interference from link l_{2}, while l_{2} is under asymmetric nonCO interference of link l_{3}. The same multilevel interference exists between l_{3} and l_{4}, producing a chain of multilevel interference dependencies.
Figure 1b shows the throughput of singlehop flows operating on the four links of Figure 1a. The graph shows the throughput of four flows when the offered load of flow f_{4} on link l_{4} is gradually increased while the offered load of flows f_{1}, f_{2}, and f_{3} (operating on links l_{1},l_{2}, and l_{3}, respectively) are kept constant. Observe that as the load on l_{4} is increased from 0.212 to 3.232 Mbps, the achievable throughput of link l_{1} (which is outside carrier sensing range of l_{4}) decreases from 2.465 to 0.628 Mbps. This is due to the presence of multilevel information asymmetric nonCO interference, the impact of which is observed on even remote links. Also, observe that the throughput achieved by links l_{1} and l_{3} is significantly lower when link l_{4} operates in a saturated condition. If the path of a particular flow includes links like l_{1} or l_{3}, the endtoend throughput will severely be affected by load on link l_{4}. In this paper, we propose pruning the links causing multilevel noncoordinated interference through topology control. This form of topology control reduces the number of available alternate paths for routing. However, the better quality of remaining paths helps in improving overall aggregate endtoend throughput.
2.2 Impact of number of paths on aggregate throughput
The key consideration in multipath routing is the selection of number of parallel paths per flow. Research shows that using too many paths is not useful [36]. Nasipuri et al. [7] have analytically proved that the performance advantage of using more than two alternate routes is usually minimal. A simple experiment shows the effect of number of paths on throughput of multihop flows.
Consider the multihop topology of Figure 2a. The throughput of flow f_{1}(s_{1},d_{1}) over multiple paths is compared by increasing its offered traffic load from 20 to 1,500 pkts/s (packet size of 512 B). Figure 2b shows the average throughput of flow f_{1} as a function of offered traffic load. The graph shows that under unsaturated conditions, the number of paths does not impact the throughput. However, under saturated traffic load (200 pkts/s), f_{1} achieves the maximum throughput of 0.819 Mbps when routed using two paths. On the other hand, f_{1} achieves a maximum throughput of 0.674, 0.706, 0.379, and 0.376 Mbps when routed using single, three, four and five paths, respectively. Note that not all paths are linkdisjoint in the case of four and five paths. This shows that increasing the number of paths increases interference on the links, which results in reduced aggregate throughput.
We now show that the quality of paths varies because of varying level of coordinated and noncoordinated interferences. Therefore, selecting any pair of alternate paths will not always result in improved throughput.
2.3 Selection of good quality paths
While opting to route on multiple available paths, usually maximal disjoint paths are selected between a sourcedestination pair. Given a directed graph G(V,E), having sourcedestination pair (s_{ i },d_{ i }), a path p_{ i }∈P(f(s_{ i },d_{ i })) is defined as fully node/link disjoint if it does not share node/link with any other path p_{ j } traversed by the flow f(s_{ i },d_{ i }). The path p_{ i } is defined as maximally node/link disjoint if it shares a minimum number of nodes/links with other paths.
Consider again multihop topology of Figure 2a. Threenodedisjoint and linkdisjoint paths (P a t h 1 (l_{1}, l_{2},l_{3},l_{4}), P a t h 2 (l_{5},l_{6},l_{7}) and P a t h 3 (l_{8},l_{9},l_{10})) are available for flow f_{1}(s_{1},d_{1}). A singlehop flow f_{2}(s_{2},d_{2}) operating under saturated traffic load is creating interference on links of P a t h 2 and P a t h 3 of flow f_{1}. Figure 2c shows aggregate throughput of flow f_{1} when different subsets of paths are selected for routing. It is obvious that not all pairs of paths lead to the same throughput. The throughput is significantly lower when P a t h 2 and (or) P a t h 3 is chosen. This is because link l_{9} of P a t h 3 is experiencing noncoordinated interference from flow f_{2}. Similarly, link l_{5} of P a t h 2 is experiencing noncoordinated interference from link l_{9}. Consequently, a chain similar to that of Figure 1a is formed, resulting in a bottleneck link on P a t h 3. Therefore, ignoring l_{9} during link selection phase of path construction procedure can eliminate the chain. This helps in improving effective capacity of l_{5}, causing P a t h 2 to offer more flow capacity to flow f_{1}. Note that link pair l_{4},l_{1} is also noncoordinated pairs; however, this pair belongs to same path and none of the links operates in saturated mode. Therefore, the impact of interference in minimized, resulting in significant opportunities for link l_{1}.
The above examples illustrate that the approach of topology control for reducing noncoordinated interference and resulting in fewer but highquality paths that can be used for multipath routing has merit. This approach can be used to significantly improve the aggregate endtoend throughput.
3 Optimization model
We now present the optimization framework of throughput maximization problem incorporating coordinated and noncoordinated interference constraints in multihop wireless mesh network. The model computes the upper bound on optimal throughput of a network with given traffic load and interference dependencies of neighboring nodes. We begin with a network model describing terminologies and assumptions.
3.1 Network model
List of notations
Symbol  Description 

N  Set of vertices/nodes 
E  Set of directed links 
G  Directed network topology graph 
G ^{ T }  Graph after topology control 
${C}_{{e}_{k}}$  Capacity of link e_{ k }∈E 
f_{ i }(n_{s}>n_{d})  Flow between nodes n_{s},n_{d} 
${f}_{{i}_{l}}$  Subflow of flow f_{ i } 
P(f_{ i })  Set of all links on path for flow f_{ i } 
L_{CO}(e_{ j })  Set of coordinated links of e_{ j } 
L_{nCO}(e_{ j })  Set of noncoordinated links of e_{ j } 
3.2 Interference model
Let e_{ h }(n_{ i },n_{ j }) denote a directed link between n_{ i } and n_{ j }, where n_{ i } represents transmitter and n_{ j } represents receiver, then a directed link e′_{ h }(n′_{ i },n′_{ j }) is an interfering link if d(n_{ i },n′_{ j }),d(n_{ i },n′_{ i }),d(n_{ j },n′_{ j }) or d(n_{ j },n′_{ i })≤R_{CS}. According to Garetto et al. [32], interfering links can be classified into coordinated and noncoordinated interfering links, depending upon the Euclidean distance between (n_{ i },n_{ j }) and (n′_{ i },n′_{ j }). Two links e_{ h }(n_{ i },n_{ j }) and e′_{ h }(n′_{ i },n′_{ j }) are observing coordinated interference if d(n_{ i },n′_{ i })≤R_{CS}, i.e., if the transmitters of the links are within the carrier sensing range of each other. On the contrary, two links e_{ h }(n_{ i },n_{ j }) and e′_{ h }(n′_{ i },n′_{ j }) are said to be noncoordinated interfering links if d(n_{ i },n′_{ i })>R_{CS} and d(n_{ i },n′_{ j })≤R_{CS}, and/or d(n′_{ i },n_{ j })≤R_{CS}, and/or d(n_{ j },n′_{ j })≤R_{CS}. The interference caused by coordinated links is logical (capacity is affected but there is no actual packet collision) as the coordinated transmitters sense the ongoing transmissions around their surroundings and avoid collisions through back off. On the other hand, the interference induced by noncoordinated links is physical because it results in collisions, packet losses, and unfair traffic distribution. In this paper, the interference model of Garetto et al. is used because of its accuracy in predicting the impact of interference.
3.3 Assumptions
The following assumptions have been made in the proposed optimization model and the proposed routing algorithm:

The location of the routers is known to the centralized computation server. This information can be used to compute the coordinated and noncoordinated links for each pair of nodes.

It is assumed that the flow demand of flows is known a priori. Although it is not possible to know the exact demand in advance, the flow demand can easily be estimated as the weighted average of MAC layer queue length and average data transmitted in previous intervals. This procedure has been used by researchers for flow demand estimation.

We assume that a single interface is available per node. Therefore, all links operate on the same channel. It is easy to see that in case of multiradio multichannel WMN, the algorithm or the optimization model will not change. The only change will be in the number of interfering links, which will be selected as those links that physically belong to a set of interfering links and also operate on same channel. Note that dynamic channel assignment can also be accommodated by recomputing the routes. Further note that channel assignment schemes do not ensure interference elimination because of limited channels available. Consequently, all phases of optimization model and routing algorithm will be required as such.
3.4 Linear program formulation
We formulate joint topology control and multipath routing as linear optimization model. In this section, we explain the decision variable, constraints, and objective function of the model.
3.4.1 Routing constraints
3.4.2 Interference and topology constraints
3.4.3 System constraints
3.4.4 Objective function
3.5 Model validation
Optimization models are NPhard and cannot be solved to give generic solution. However, for specific network instances, global optimum can be achieved using numerical solvers. We have used LPSolve and programmed the model using AMPL language. The values of the variables ${T}_{{f}_{i}}\left({e}_{j}\right),\forall {e}_{j}\in E,\forall {f}_{i}$ achieved by the numerical solution provide the routing information. For each flow, the chain of links originating from source with nonzero value of ${T}_{{f}_{i}}\left({e}_{j}\right)$ forms a distinct path to destination. The actual value of the variables is the normalized amount of data to be routed through a particular path.
The second set of experiments is performed to test the effectiveness of model for different levels of coordinated and noncoordinated interference. This is achieved by increasing the number of nodes in the network with (i) constant terrain dimensions (120×120 m ^{2}), which results in increased coordinated interference but relatively constant noncoordinated interference and (ii) proportionately increasing terrain dimensions, which results in increased noncoordinated interference. We have simulated the Manhattan topology with 25, 36, 49, 64, 81, and 100 nodes.In case of constant terrain dimensions, we have generated the aggregate traffic load of 80 Mbps from multiple sources for all scenarios. Increasing the load beyond this value does not result in increased throughput for all cases. Figure 3b compares normalized (against 80 Mbps) aggregate endtoend throughput achieved using the model with the simulations for constant terrain dimensions case. It is observed that the throughput slightly decreases as the number of nodes are increased. This is because of the increased coordinated interference that results in increased transmission losses. It can also be observed that the model predicts the throughput of the network within 90% of the throughput achieved using simulations.In case of variable terrain dimensions, we have used 9, 12, 16, 16, 20, and 24 source nodes for 25, 36, 49, 64, 81, and 100 nodes network, respectively. Each data source generates the traffic load of 2 Mbps, which results in saturated network load for the respective topologies. For every grid size, the experiment has been repeated five times with different randomly selected sourcedestination pairs and the results have been averaged. It is observed that the saturation point for differentsized networks is achieved at different values, unlike the variable node density case where all sized networks are saturated with aggregate input traffic load of 80 Mbps. This is because the network consists of more carrier sensing ranges as the network size increases. The increased carrier sensing ranges can support more traffic load. Figure 3c shows the normalized throughput (normalized against 49 Mbps, which is saturated load for 100 nodes network) of all cases. The throughput increases with the increasing network size, owing to increased number of carrier sensing ranges. The simulations throughput is ≈89% of the throughput achieved using numerical solution to the model. It is obvious that the accuracy of model is not affected by the increase in coordinated or noncoordinated interference. Therefore, we conclude that model can effectively predict endtoend throughput for multihop wireless networks.
4 AMRTC  adaptive multipath routing with topology control
The scheme first performs topology control on the network. The links creating chain dependencies and having low channel utilization are purged from the network topology. Algorithm 1 is used for this purpose. Given the set of nodes and edges and the distance between all nodes, step 1 to step 6 of the algorithm identify noncoordinated interfering links of each link in set E. Step 7 to step 29 are used to purge the links that have limited throughput because of noncoordinated interference. On step 19, the link that experiences noncoordinated interference from any of the links that themselves do not experience noncoordinated interference is removed from the set E^{ t } of links. Removal of such links results in fewer paths for all flows; however, the forwarding capacity of remaining links will reduce negligibly (if at all). Step 23 adds to set X the links that experience noncoordinated interference from the link that is to be purged from topology. Effectively, all links in set X should experience no noncoordinated interference. Finally, step 30 to step 37 are used to compute the sets of coordinated and noncoordinated links for each link in the network topology (set E^{ t }) after topology control.
Topology control is followed by greedy heuristicbased multipath routing algorithm. Algorithm 2 constructs one path at a time for each flow using Dijkstra algorithm [37]. The cost of using each link for Dijkstra algorithm is the inverse of the link capacity. Initially, the link capacity of all links is set to maximum. After every path construction and percentage of flow assignment on that path, the link capacity is updated by subtracting the aggregate data being forwarded by the link and its coordinated interfering links. The process is repeated until predefined maximum number of paths are constructed for each flow. Note that the first path constructed for each flow will be maximum capacity path. In each path iteration, the forwarding capacity of each subsequent path will be lesser than the already constructed paths.
5 Performance evaluations
This section presents the simulationbased evaluation of the proposed algorithm. We have compared the performance of proposed multipath scheme AMRTC with the following three algorithms: (i) Ad hoc onDemand Multipath Distance Vector (AOMDV) [7] (ii) Multipath Dynamic Source Routing (MDSR) [38], and (iii) AVAIL [33]. Results from the optimization model are also compared in all experiments. AOMDV, the multipath variant of wellknown Ad hoc onDemand Distance Vector, is a distancevector routing algorithm which constructs loopfree, disjoint alternate paths in multihop networks. Similarly, MDSR is the multipath extension of DSR which uses IP source routing to construct linkwise disjoint paths from source to destination. AVAIL is a unipath routing scheme. The scheme is a modified version of Dijkstra’s algorithm and discovers comparatively high throughput longer path for each flow while considering interference on links. The comparison demonstrates the effectiveness of proposed AMRTC algorithm which prioritizes quality of paths by ignoring links under severe multilevel interference.
5.1 Experimental setup
Simulation parameters
Parameter  Value 

Simulation time  1,200 s 
Terrain dimensions  500×500 m ^{2} 
Node placement  Regular grid (Manhattan network) 
Radio interface type  IEEE 802.11b 
Radio propagation model  Two ray 
Propagation shadowing model  Constant (mean=4.0) 
Application traffic  CBR 
Packet interarrival time  2 ms 
Packet size  512 B 
The evaluation is performed through four sets of experiments. In the first set, we show the effectiveness of multipath routing over unipath routing. In the second set, the performance of AMRTC is compared with AOMDV, Multipath Dynamic Source Routing (MDSR), and AVAIL in terms of offered traffic load and network throughput. The third set of experiments is conducted to compare the performance of the four algorithms with respect to quantity and length of the selected paths. The last set compares the average perflow throughput achieved when the number of nodes are increased with constant and variable node density. This tests the algorithms under varying level of coordinated and noncoordinated interference.
5.2 Unipath vs. multipath routing
It can be observed that for network load (≈800 pkts/s), performance of unipath and multipath optimization model is same. However, as the offered traffic load increases, multipath optimization model marginally outperforms unipath optimization model. The saturated traffic load that is routed by multipathroutingbased optimization model is 3.21 Mbps while that of unipathroutingbased optimization model is 3.062 Mbps. The reason that multipathroutingbased optimization model can only marginally outperform the unipathroutingbased optimization model is attributed to the fact that even single path optimization model is able to eliminate noncoordinated interfering links. This reduces the possibility of significant number of alternate paths for the flows. On the other hand, AMRTC (saturated throughput 1.61 Mbps), which is multipath routing algorithm, outperforms AODV (saturated throughput 1.23 Mbps) under saturated traffic load. It can be concluded that multipath routing shall be used under all scenarios of saturated as well as unsaturated traffic load. It can also be observed that appropriately addressing the noncoordinated interference while deciding upon the routes results in good performance, even for unipath routing, which is the case for results from unipath optimization model.
5.3 Offered traffic load and endtoend throughput
Next, we compare the performance of different multipath routing algorithms. The experimental setup is same as in previous section with 100 nodes arranged in grid within terrain dimensions of 120×120 m ^{2}. This arrangement of nodes results in 12 neighboring nodes within the transmission range of each node and results in dense deployment of nodes. Figure 5b plots the impact of increasing traffic load on aggregate endtoend throughput when the traffic load is gradually increased from below saturation (i.e., 25 to 100 pkt/s) point to above saturation (i.e., 200 to 1,500 pkt/s). It is evident that AMRTC outperforms the other three schemes by achieving a higher saturated aggregate endtoend throughput with a factor of 1.37, 1.68, and 1.63 with respect to AVAIL, AOMDV, and MDSR. This increase is the result of avoiding badly suffered links due to noncoordinated interference during path selection procedure. AMRTC outperforms AVAIL because it explicitly avoids bottleneck links as well as chain interference dependencies by purging the responsible links. AVAIL is unable to avoid the chain interference dependencies because it selects longer paths. Also note that AVAIL outperforms MDSR and AOMDV because it tries to select quality paths instead of selecting shortest paths. Therefore, chances of avoiding the bottleneck links increases in the case of AVAIL.
5.3.1 Fairness
From above discussion, it can safely be concluded that introducing the notion of fairness into the routing algorithm does not produce desired results, unless admission control algorithm is employed to limit the number of flows and the demand of each flow. Even in the presence of such measures, true fairness might not be achievable. Therefore, the presented algorithm does not attempt to incorporate fairness.
5.4 Length and number of paths
With experimental set of the above sections, we first compare the length of the paths selected by the four algorithms. Subsequently, we compare the average number of paths created by each algorithm. Figure 5d plots the path length against the number of flows having the specified path length for the four algorithms. AMRTC selects paths with average length of 2.09. This shows that although purging a subset of links from the network results in no connectivity for certain flows, it does not significantly affect the path length for remaining flows. Longest paths are selected by AVAIL with average path length of 2.48. This is because AVAIL tries to construct longer paths with higher link diversity and improved path quality. More number of hops per path result in relatively lesser endtoend throughput for AVAIL, compared to AMRTC. Average path length of MDSR and AOMDV is 2.1 and 2.25, respectively. This is because both algorithms are the shortest path algorithms and do not take quality of links into account while constructing paths. The smaller value of average path length for AOMDV and MDSR confirms that link diversity is not achieved using both algorithms, consequently leading to lower endtoend throughput.Figure 5e shows the number of paths created for each flow using four algorithms. The maximum number of paths for any flow constructed by four algorithms is 2 except AVAIL, which is a unipath algorithm with maximum number of paths to be 1 for all flows. The average number of paths constructed by AMRTC, AOMDV, and MDSR is 1.71, 1.42, and 1.5, respectively. AMRTC constructs fewer paths because purging of a subset of links from the network reduces the possibility of constructing multiple paths that can also result in capacity improvement. This justifies the limited improvement of multipath optimization model compared to unipath optimization model in Figure 5a. Note that AVAIL being a unipath algorithm and selecting high throughput links for each path shall have lesser interference on all links and should have achieved better endtoend throughput; however, this is not the case. Relatively lesser throughput for AVAIL, compared to AMRTC, is attributed to the fact that the constructed paths are longer (as shown through Figure 5d). It is known that endtoend throughput exponentially decreases with increasing path length. Also note that AMRTC has constructed more paths compared to AOMDV and MDSR; however, AMRTC has outperformed MDSR and AOMDV because the selected paths have link diversity as well as lowinterference links, resulting in highquality paths. Consequently, AMRTC leads to improved endtoend aggregate throughput because it achieves both objectives of constructing fewer paths and paths with higherquality links.
5.5 Endtoend delay
5.6 Impact of increasing node density
The final set of experiments has been conducted to observe the impact of increasing number of nodes on average throughput using AMRTC, AVAIL, AOMDV, and MDSR. We have simulated and observed the performance of the four algorithms over 25, 36, 49, 64, 81, and 100 nodes network where nodes are arranged in a regular grid. Increasing the nodes while keeping the terrain dimensions constant results in rapid increase in the number of coordinated interfering links and relatively slower increase in number of noncoordinated interfering links. On the other hand, increasing the number of nodes while keeping the node density constant (by proportionally increasing terrain dimensions) results in rapid increase of noncoordinated interference while coordinated interference remains almost constant. For example, 49 nodes network arranged in a terrain area of 120×120 m ^{2} results in 127 coordinated and 127 noncoordinated interference links. Arrangement of 100 nodes (doubling the nodes) in the same terrain area results in 203 (twofold increase) coordinated and 159 noncoordinated links. On the other hand, 100 nodes arranged in 270×270 m ^{2} terrain area result in 203 coordinated and 203 (twofold increase) noncoordinated links. We present the results with increasing number of nodes and same terrain dimensions (variable node density) as well as proportionally increased terrain dimensions (uniform node density).
6 Conclusions
This paper has presented an integrated approach of multipath routing and topology control to achieve throughput maximization by reducing multilevel interference dependencies and noncoordinated interference. The problem is represented as a Linear Programming model where multilevel noncoordinated interference dependencies are eliminated during the process of route selection. The model is followed by AMRTC algorithm for route selection that achieves the same objective. Eliminating noncoordinated interference dependencies also results in fewer paths, each having fewer hops. Consequently, improved endtoend throughput is achieved, compared to the existing multipath routing algorithms as well as unipath routing algorithms that aim at constructing highquality routes.
The shortcoming of the proposed approach is that it does not ensure connectivity for all flows while eliminating multilevel noncoordinated interference. In the future, we plan to address this issue by avoiding link elimination and adjusting the flow rates of links to reduce the impact of multilevel noncoordinated interference.
Declarations
Authors’ Affiliations
References
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