Routing method for gateway load balancing in wireless mesh networks. Hiroshi Tokito. Masahiro .... between a mesh node and a gateway node is O(n2). In SPR,.
2009 Eighth International Conference on Networks
Routing method for gateway load balancing in wireless mesh networks Hiroshi Tokito
Masahiro Sasabe Go Hasegawa Hirotaka Nakano Osaka University, Japan {h-tokito@ist, sasabe@comm.eng, hasegawa@cmc, nakano@cmc} .osaka-u.ac.jp Abstract
Wired Internet backbone
Wireless mesh networks have been attracting many users in recent years to achieve a wide-area wireless environment with flexible-configuration and low-cost properties by connecting base stations (mesh nodes) with each other via wireless connections. When the wireless mesh networks are used as an infrastructure for Internet access, all network traffic from mobile nodes go through a gateway node which is directly connected to the wired network. Therefore, we need to distribute the entire traffic load by deploying multiple gateway nodes and each mesh node should select a gateway node to access the Internet according to its traffic load, processing power, and access link capacity. In this paper, we propose a routing method that distributes the traffic load on the gateway nodes. Through several simulations, we show that the proposed method can uniformly distribute the traffic load on gateway nodes, keeping the time complexity and suppressing an increase in the path length at most 15 % compared to the conventional shortest path routing.
Gateway node Mesh node Wireless link Wired link
Figure 1. Mesh network. infrastructures, e.g., countryside, isolated island, etc. In such situations, an access link on the gateway node becomes a bottleneck since all network traffic from mobile nodes goes through the gateway node [8]. Since the gateway node is the single entry point of all traffic between the mesh node and the wired Internet, the capacity of the access link on the gateway node limits the capacity of the mesh network. Therefore, multiple gateway nodes are needed to distribute the entire traffic load. The routing methods for ad hoc networks, which are decentralized wireless networks such as mesh networks, include optimized link state routing (OLSR) [16], ad hoc on-demand distance vector (AODV) [3], and open shortest path first (OSPF) [10]. OSPF is also mainly used in an autonomous system (AS) of the Internet. These routing methods make a mesh node select the closest gateway node in terms of path length between the mesh node and gateway node. As a result, a large amount of traffic may become concentrated in some gateway nodes and congestion occurs. This indicates that only deploying multiple gateway nodes cannot achieve effective load balancing. For better results, each mesh node must select a gateway node to access the Internet according to its traffic load, processing power, and access link capacity. By distributing the traffic load on the gateway node, we can maximize the traffic volume transferred between the mesh network and Internet.
1. Introduction Wireless mesh networks (hereafter, called mesh networks) have been attracting many users in recent years [1, 12]. As shown in Fig. 1, base stations (mesh nodes) connect with each other via wireless connections in mesh networks. An end node (station) connects to one of the mesh nodes located within its communication range and communicates with that connected mesh node. Each mesh node communicates with a mesh node directly connected to the wired network, that is, a gateway node, by a means of multi-hop communication. Consequently, a station can communicate with other nodes in a wired network with the help of mesh and gateway nodes. In addition, mesh networks can achieve a wide-area wireless environment with flexible configuration and low-cost properties by connecting mesh nodes with each other via wireless connections. Mesh networks are expected to become an infrastructure for Internet access at areas with poor wired network 978-0-7695-3552-4/09 $25.00 © 2009 IEEE DOI 10.1109/ICN.2009.21
Station
In this paper, we propose a routing method, called gateway load balanced routing (GLBR) for dispersing the traffic load on gateway nodes in a mesh network constructed 127
of multiple gateway nodes and many mesh nodes. Each mesh node selects a gateway node according to its traffic load. Note that we assume that the processing power and the access link capacity of the gateway nodes are the same. GLBR achieves fair load sharing among gateway nodes while keeping the time complexity and suppressing increases in the path length to, at most, 15 % compared to the conventional shortest path routing. The rest of this paper is organized as follows. In Section 2, we describe related work about load balancing and routing methods in mesh networks. In Section 3, we discuss the network model targeted in this paper. We present the routing methods in Section 4. In Section 5, we show the effectiveness of our proposed method through several simulations. Finally, Section 6 gives conclusions of this paper.
Figure 2. An example of topology of a mesh network.
2. Related Work
pose a simple and effective routing method to distribute the traffic load on the gateway nodes, even if each mesh node uses only one path to the gateway node.
IEEE 802.11s and 802.16 working groups define an architecture and a protocol for mesh networks, respectively [5, 7]. IEEE 802.11s assumes that a mesh network is composed of approximately 30 wireless LAN access points. The default routing method is hybrid wireless mesh protocol (HWMP) [6], which is based on a modified AODV, that is, radio metric AODV (RM-AODV) [15]. If all the access points are located on fixed points and the topology of the mesh network does not change, HWMP applies proactive routing by building a tree. In contrast, IEEE 802.16 standardizes the wireless metropolitan area network (MAN) mesh network. IEEE 802.16 supports two modes: point to multipoint (PMP) mode and mesh mode. We can use the proposed methods on both modes. In the mesh mode, each mesh node communicates with the gateway node through multi-hop communication by relaying its traffic to a mesh node that is randomly chosen among mesh nodes within its communication range. Many researchers have been studying routing methods on IEEE 802.16 mesh networks [14, 9, 18]; however, the focus of these routing methods has been to maximize the throughput of mesh nodes but discount the possibility of congestion on the gateway node. Thus these routing protocols cannot maximize the throughput of mesh networks used as an infrastructure to access the Internet. As a routing method for distributing the load on gateway nodes, Lakshmanan et al. proposed multi-gateway association (MGA) [11]. In MGA, a mesh node determines the path to the gateway node based on the amount of network resources on each link along the path. However, MGA does not consider the processing power and access link capacity of a gateway node. Furthermore, MGA requires large overhead for maintaining the path information since it simultaneously uses multiple paths, each of which leads to one of the available gateway nodes. In this paper, we pro-
3. Network Model In this section, we describe the model of a mesh network. We assume a communication graph G = (V, E), where V = {v1 , . . . , vm , . . . , vn } is the set of mesh nodes (n ≥ m ≥ 1, n is the number of mesh nodes, m is the number of gateway nodes, and mesh nodes from v1 to vm are gateway nodes), and E is the set of links li,j = (vi , vj ). A mesh node has links to the mesh nodes which are within its communication range. The load bi on vi is the amount of traffic from connected stations and the mesh nodes from which vi receives traffic. In addition, stations are uniformly located in the mesh network. Each station connects to the nearest mesh node and the traffic volume from each station is equal. As a result, the amount of traffic on a mesh node generated by connected stations is proportional to the size of the Voronoi area [13] of the mesh node. We denote gi as the ID of the gateway node through which the traffic from mesh node vi passes, and Pi,j ⊆ E as the set of links along the path from vi to vj . Vl is the set of mesh nodes that are leaves of the tree constructed by the shortest path from each mesh node to its nearest gateway node. We illustrate an example of topology of a mesh network in Fig. 2. In this figure, vi is a gateway node and vj and vk are mesh nodes. The dotted line is the link. The area separated by the solid line equals the Voronoi area of each mesh node; li,j is the link between vi and vj , and lj,k is the link between vj and vk . Finally, gj and gk become i and Pi,k = {li,j , lj,k }. In Fig. 2, we can obtain the amount of traffic on vj generated by connected stations by calculating the size of the shaded area. Note that vj also relays the traffic from vk . 128
4. Routing Methods
Algorithm 1 Shortest path routing (SPR). Input: G Output: Pi,gi : m + 1 ≤ i ≤ n 1: for i = 1 to m do 2: for j = m + 1 to n do 3: Calculate the shortest path from vi to vj 4: hi,j =|Pi,j | (|Pi,j |is the path length of Pi,j ) 5: end for 6: end for 7: for j = m + 1 to n do 8: gj = arg min1≤k≤m (hk,j ) 9: end for
In this section, we explain shortest path routing (SPR) as a conventional method and gateway load balanced routing (GLBR) as the proposed method.
4.1. Shortest Path Routing Algorithm 1 shows the algorithm of SPR. In SPR, when there is more than one shortest path from a mesh node to different gateway nodes or to the same gateway node, a mesh node randomly chooses one of them. When SPR uses Dijkstra’s algorithm [4] for calculating the shortest path, the time complexity of obtaining the path between a mesh node and a gateway node is O(n2 ). In SPR, each mesh node repeats this operation m times. It then determines the path to the gateway node within O(n). Therefore, the time complexity of SPR is O(n2 ).
Algorithm 2 Gateway load balanced routing (GLBR). Input: G Output: Pi,gi : m + 1 ≤ i ≤ n 1: Shortest P ath Routing (Algorithm1) 2: For all vi ∈ V , calculate bi . Then calculate the variance value f0 of the load on gateway nodes. 3: for all i such that vi ∈ Vl do 4: d = i, γ = |Pi,gi | 5: repeat 6: for all j such that ld,j ∈ E do 7: Calculate bgj , bgd and the variance value fd of the load on gateway nodes 8: if fd < f0 and |Pi,gi | ≤ γ + h then 9: f0 = fd , Pd,gi = {ld,j } ∪ Pj,gj 10: else 11: Restore the value of bgj and that of bgd 12: end if 13: end for 14: d = s (s is the endpoint of ld,s ∈ Pd,gd and s = d) 15: until d ≤ m and vd has done the above processes 16: end for
4.2. Gateway Load Balanced Routing Algorithm 2 shows the algorithm of GLBR. In GLBR, each mesh node selects the path so that the variance of the load on gateway nodes becomes as small as possible. It is known that the wireless network resource is more consumed when a mesh node selects a longer path than the shortest path. Therefore, GLBR regards the hop count between a mesh node and a gateway node as the path length and suppresses an increase in the hop count caused by changing the path up to hop count h. We show the overview of the GLBR algorithm as follows.
that it has the links to all other mesh nodes), and all mesh nodes except the gateway nodes carry out STEP 2 only one time. Thus STEP 2 can be completed within O(n2 ). Consequently, the time complexity of GLBR is O(n2 ).
STEP 1 For all vi ∈ V (m + 1 ≤ i ≤ n), calculate the shortest path from vi to its nearest gateway node by using Algorithm 1. Next, obtain the load on each gateway node, the variance of the load on gateway nodes, and the path length γi from vi to vgi .
Algorithm 3 shows the algorithm of the exhaustive search based GLBR (ES-GLBR). ES-GLBR is the routing method for distributing the traffic load on gateway nodes, as in GLBR. Whereas a mesh node vi ∈ V only searches for the links directly connected to vi in GLBR, vi exhaustively searches for all possible paths from vi to vgi in ES-GLBR.
STEP 2 For all vj ∈ Vl , repeat the following steps. STEP 2-1 Find a neighboring node vk that satisfies the following conditions: (1) the decrease in the variance of the load on gateway nodes is maximum and (2) the path length from vj to the gateway node is less than γj + h. If vk exists, vj selects vk as the neighboring node to relay its traffic.
The worst-case time complexity of ES-GLBR occurs with a full mesh topology. In this case, each mesh node has m links between the gateway nodes and (n − m − 1) links between the mesh nodes, except the gateway nodes. Therefore, (n − m) mesh nodes search for (m(n − m) + (n − m − 1)!) paths. As a result, the time complexity of ES-GLBR is O((n − m)!) .
STEP 2-2 If vk is not a gateway node and does not finish STEP 2-1, vk starts STEP2-1. Otherwise, the algorithm returns to STEP 2.
In the next section, although we assumed the situation where the processing power and the access link capacity of the gateway nodes are identical due to space limitation, we have also evaluated the effectiveness of the proposed method in the opposite case, in which these are not the same.
The time complexity of STEP 1 is O(n2 ), since the order of calculating the shortest path is O(n2 ) and the other processes can be completed within O(n). In STEP 2, a mesh node needs to repeat STEP 2-1 up to n−1 times (in the case 129
Algorithm 3 Exhaustive search based GLBR (ES-GLBR).
Table 1. Parameter settings.
Input: G Output: Pi,gi : m + 1 ≤ i ≤ n 1: Shortest P ath Routing (Algorithm1) 2: For all vi ∈ V , calculate bi . Then calculate the variance value f0 of the load on gateway nodes. 3: for all i such that vi ∈ Vl do 4: ChangeRoute(vi , 1, |Pi,gi |) 5: end for Procedure: ChangeRoute Input: vi , t, γ Output: Pi,gi 6: for all j such that li,j ∈ E do 7: Pi,gi = {li,j } ∪ Pj,gj 8: if j > m then 9: ChangeRoute(vj , t + 1, γ) 10: else 11: For all vi ∈ V , calculate bi . Then calculate the variance value fi of the load on gateway nodes. 12: if fi ≤ f0 and t ≤ γ + h then 13: f0 = fi 14: else 15: Restore the value of Pi,gi 16: end if 17: end if 18: end for
Number of simulations Area of deployment Number of gateway nodes Number of mesh nodes except gateway nodes Communication range for communication between mesh nodes Communication range for communication between a mesh node and a station Location of gateway nodes Location of mesh nodes Quantization factor α
1000 1×1 2, 4, 8, 16 20, 40, 60, 80, 100 Minimum range establishing at least one path from the mesh node to the gateway node 0.35 (see Figure 3) uniform distribution 100
5. Performance Evaluation ：2
In this section, through several simulations, we demonstrate the effectiveness of the proposed methods in terms of the load on the gateway nodes and the path length. We also evaluate how the proposed methods have an impact on the utilization efficiency of the wireless network resource. For evaluating the utilization efficiency of the wireless network resource, we use the frame resulting from the TDMA link scheduling [17]. Here, the frame length is defined as the number of time slots needed for all links to transmit their traffic according to their traffic demand. The number of time slots assigned to each link is given by its link weight based on its traffic demand. The link weight ωli,j on a link li,j is defined as follows ωli,j = α × bli,j .
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Figure 3. Location of gateway nodes.
5.1. Optimal Threshold Setting GLBR suppresses an increase in the hop count caused by switching the paths up to h. We first investigate the optimal value of h from the viewpoints of both the load on the gateway nodes and the path length. Figure 4 illustrates averages with 95 % confidence intervals of the maximum load on gateway nodes for SPR and GLBR (h = 0, 1, 2, ∞) when the number of mesh nodes varies and the number of gateway nodes is set to 4. Figure 5 depicts the distribution of the path length of GLBR when there are 4 gateway nodes and 60 mesh nodes. As shown in Fig. 4, the load on the gateway nodes does not change if h is over 1. However, the larger h results in making the path length longer, as shown in Fig. 5. The increase of path length can be avoided if h is not more than 1. Since we obtained similar results in other cases with different numbers of gateway nodes, we set h = 1 in the following evaluation.
(1)
Here, α is the quantization factor for suppressing the sum of link weight and bli,j is the traffic demand on li,j . bli,j equals the traffic demand on vi when vj receives traffic from vi . In addition, we define the radio interference between links based on RTS/CTS model [2]. Table 1 and Fig. 3 show the parameter settings used in the evaluation. We set the communication range for communication between a mesh node and a station to 0.35 so that we can cover the area of deployment by more than 99 %, even if there are only 20 mesh nodes. In addition, we deploy the gateway nodes on grids, as shown in Fig. 3. This is because the number of gateway nodes and their locations are carefully determined to maximize the throughput between the mesh network and the Internet.
5.2. Load on Gateway Nodes We evaluate the load on gateway nodes in SPR, GLBR, and ES-GLBR. Figure 6 shows how averages with 95 % confidence intervals of the coefficient of variation of the load on gateway 130
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Figure 7. Average path length. of gateway nodes is large. This is because the size of the Voronoi area decreases with an increase in gateway nodes.
Next, we focus on the transitions of the coefficient of variation according to the number of mesh nodes. The coefficient of variation of GLBR and that of ES-GLBR become low as the number of mesh nodes increases. The larger the number of mesh nodes, the smaller the traffic that one mesh node receives from connected stations. Thus GLBR and ES-GLBR can allocate the load among gateway nodes more uniformly. However, in the case of 16 gateway nodes, the coefficient of variation of SPR does not decrease monotonically. If the number of mesh nodes is small, the main part of the load on the gateway nodes is generated by connected stations, which means there is almost no difference of the load on gateway nodes.
5.3. Path Length Figure 7 depicts how the average path length between a mesh node and a gateway node varies (a) according to the number of gateway nodes when the number of mesh nodes is 60, and (b) according to the number of mesh nodes when the number of gateway nodes is 4. We find the average path length of GLBR and that of ES-GLBR are at most 15 % and 20 % higher, respectively, than that of SPR. Since ESGLBR searches more paths than GLBR, and the number of mesh nodes which change their path is large, the average path length of ES-GLBR is longer than that of GLBR. However, the increase of the path length is not large. This effect is achieved by not only the introduction of h but also by the setting of the communication range for communication between mesh nodes. Since we set the communication range for communication between mesh nodes to the minimum range by establishing at least one path from the mesh node to the gateway node, the number of communica-
Next, we examine the changes of the coefficient of variation according to the number of gateway nodes. When there is a large number of mesh nodes, the coefficients of variation become large with an increase in gateway nodes independently of the method. This is because the ideal load on gateway nodes becomes small, that is, 1/m, where m is the number of gateway nodes. Meanwhile, the coefficient of variation of GLBR and that of ES-GLBR become small when the number of mesh nodes is small and the number
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References
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Figure 8. Ratio of frame length. tion links in a mesh network is suppressed to the minimum. Thus there are not many paths which are longer than the shortest path.
5.4. Utilization Efficiency of Wireless Network Resource Figure 8 shows how averages with 95 % confidence intervals of the ratio of the frame langth of GLBR and that of ES-GLBR to that of SPR change under the same conditions as in Fig. 7. The frame length of GLBR and that of ESGLBR are at most 5 % and 10 % higher, respectively, than that of SPR. This indicates that GLBR and ES-GLBR can uniformly distribute the traffic load on gateway nodes while slightly decreasing the utilization efficiency of wireless network resource. This is because GLBR and ES-GLBR suppresses an increase in the path length.
6. Conclusions and Future Work In this paper, we proposed GLBR and ES-GLBR, routing methods for distributing the traffic load on gateway nodes in a mesh network constructed of multiple gateway nodes and many mesh nodes. We showed that GLBR achieves the same order of time complexity as SPR by making the control mechanism as simple as possible. Through several simulations, we showed that GLBR can uniformly distribute the traffic load on gateway nodes, and can restrict the increase in path length to, at most, 15 % compared to SPR. We also found that GLBR can equalize the load on gateway nodes as well as ES-GLBR with much lower time complexity. Several issues are remaining. We have to design protocols for GLBR in a decentralized manner : exchanging load information among gateway nodes and distributing the load information to mesh nodes. We also plan to improve GLBR to not only distribute the traffic load on gateway nodes but also decrease radio interference as possible.
Acknowledgment This research was supported in part by a Grant-in-Aid for Scientific Research (B) 19360173. 132
