A Weighted Interference Estimation Scheme for Interface Switching Wireless Mesh Networks

Yunxia Feng , Minglu Li, Min-You Wu Department of CSE, Shanghai Jiaotong University, Shanghai, China

{yunxia_feng, li-ml, wu-my}@cs.sjtu.edu.cn

Abstract

Figure 1. Example of WMN architecture

The number of available channels in a specific

wireless network is bounded. Therefore, co-channel interference is inevitable in most wireless networks. The co-channel interference problem in wireless mesh networks is more serious than that in single-hop wireless networks. It is preferable for mesh nodes to dynamically adjust channels to elevate the interference level of networks. In this paper, we introduce the conception of communication constraint to denote the strategies that decide the mode of interface switching. We develop an interference estimation scheme. The proposed scheme uses a weight to represent the effects of loads distribution and relative distance between nodes on the interference level of network. We compare the performance of our solution with the model presented by Gupta and Kumar [14] through both graph-based and NS2 simulations. Extensive results show that our solution achieves better performance than the compared scheme when the number of available channels is small. 1. Introduction

Wireless mesh networks (WMN) [1] have emerged recently to resolve the capacity limitations and improve performance of wireless communications. A WMN is a collection of stationary wireless mesh routers and mobile mesh clients. Wireless mesh routers form the multi-hop WMN backbone without the aid of established wired infrastructure. A few wireless mesh routers, called Gateway nodes, connect directly to the wired networks through wired links. Gateway nodes provide wired network access for mobile users in mesh clients. Mesh clients connect to wireless mesh routers via traditional Ethernet or wireless connections. Through multi-hop wireless relay, mobile users in mesh clients can access the resources that reside on the wired networks. The WMN architecture is shown in Fig. 1.

Today more and more WMNs are equipping nodes with multiple interfaces to improve the network

capacity. By fixing interfaces on different channels, a node can simultaneously communicate on multiple channels. Hence multiple interfaces can achieve higher network capacity than single interface. However, the number of available channels in a specific wireless network is very limited. For example, 802.11b/g only provides 3 non-overlapped channels [3]. Therefore, in most wireless networks, even if each node is equipped with enough interfaces, not all links within each other’s interference range can be assigned different channels. In these scenarios, co-channel interference is inevitable. Recall that a WMN is a multi-hop wireless network, which aggregates a great number of wireless mesh clients. The co-channel interference in WMNs is more serious and complex than that in other wireless networks such as Ad Hoc networks and WLANs. Co-channel interference becomes one of the most important problems that affect the capacity of WMNs.

It is preferable for mesh nodes to adjust channels to maximize the capacity of network. By dynamic channel assignment, communication links can always take the channel that has the least interference level in their neighborhood. However, interface switching brings new challenges for proper estimating the interference level of networks. Although a lot of effort [2, 12 and 14-17] has been spent on modeling the co-channel interference of networks, the efficient and effective method has not yet been developed. Almost all interference estimation strategies developed do not consider the effect of interface switching. They cannot properly model the interference of wireless networks that adopt interface switching.

978-1-4244-1890-9/07/$25.00 ©2007 IEEE

In this paper, we study the interference estimation problem that considers the effect of interface switching mode. We introduce the conception of communication constraint to denote the strategies that decide the switching mode of interfaces on nodes. Considering the effect of communication constraints, we present a novel conflict graph to model the interference relationships of networks. Based on the novel conflict graph, we develop a weighted scheme for WMN nodes to estimate the co-channel interference level in their neighborhoods. The proposed scheme not only takes the loads distribution of WMNs into account, but also considers the effect of relative distance between nodes. The proposed scheme can be easily combined with current channel assignment algorithms to select channels for interfaces.

The rest of this paper is organized as follows. In section II, we provide a brief overview of related work. Section III formulates the interference estimation problem. In section IV, we illustrate the proposed interference estimation scheme in details. Simulations and conclusions are respectively provided in section V and VI. 2. Related Work

Co-channel interference estimation is extensively used in analyzing the network capacity bounds and selecting proper channels for interfaces in channel assignment algorithms. A number of papers have been published on the problem of how to estimate the interference level of wireless networks. Authors of [14-18] studied the impact of co-channel interference on the network capacity. Gupta and Kumar [14] for the first time studied the throughput of wireless network under two models of interference. However, the two models are initially designed for fixed single interface.

Most interference estimation schemes use a conflict graph to estimate the interference relationship between nodes [2, 15]. Conflict graph (CG) is initially designed for single interface/channel. Therefore, CG cannot correctly model the nodes that are equipped with multiple radios. Ramachandran, et al. [12] extended the conflict graph to multi-interface conflict graph (MCG).

In order to efficiently utilize the very limited channel resources, a considerable channel assignment algorithms and protocols [2, 4-15, 19] have been proposed. They present different kinds of co-channel interference estimation schemes. Some protocols [2, 12, and 14] use the number of interference nodes/links that sharing a channel as the interference level on that channel. According [12], the interference level of each channel is estimated by the number of interfering radios on the channel supported by each router. An

interfering radio is defined as a simultaneously operating radio that is visible to a router but external to the mesh.

There are also some extension strategies to the protocol model. Some researchers [11, 15 and 19] propose to assign a weight to the conflict graph to represent the different co-channel interference level on different nodes. K. Jain, et al. [15] regard the weight of a directed edge in the conflict graph as a function of the useful signal strength and noise signal strength received at the receivers. Interference level is modeled by the sum of weights of the edges incident to the vertex in the conflict graph corresponding to a network link. In [19], the channel assignment problem of WLANs is modeled as a weighted graph coloring problem with a certain objective function. In this weighted variant, each vertex corresponds to a distinct AP. A conflict between two APs is represented by an edge, and each edge has a weight associated with it. The weight of an edge indicates the importance of using different colors (channels) for the corresponding vertices (APs) that are connected by that edge.

Some other protocols use the traffic information [6, 7] or other information [4] to model the interference level on each link. They assume that the network loads on each link can be accurately achieved ahead of time. Before assigning channel for a link, these channel assignment algorithms first calculate the loads on all channels that have been assigned to the links within its interference range. And they then choose the channel that has been assigned the least loads. However, JOCAC [4] utilizes congestion price to estimate the interference degree of a channel. Congestion price is defined as a function of transmission powers, relative position between nodes, and et al. 3. Problem Formulation

In this section, we first present assumptions and premises that will be used later in this paper. We then extend the two interference models presented in [14] to multiple interfaces under interface switching environment. 3.1. Assumptions and Premises

This paper assumes that each node is equipped with one or multiple interfaces. The number of interfaces on each node is less than that of available channels. Interfaces on a node can switch among multiple channels. A node can communicate with any node that is within its communication range. Two nodes may have several candidate communication links. The communication links between two nodes can be dynamically established and canceled at any time. For simplicity, we assume that two nodes can only establish one communication link at a time no matter

how many candidate links two nodes have. As described in several protocols [4-13], a node

may adopt different interface switching modes. It may also do not adopt switch interface at all. To study the impacts of interface switching modes, we refer the strategies that decide the interface switching modes of nodes to communication constraints. A communication constraint provides one or several cases. A case defines a link between two nodes within each other’s transmission range. Therefore, the number of cases in a communication constraint decides the maximum number of candidate links between two nodes.

According the number of candidate links between two nodes, we classify the communication links into two types. If there is only one candidate link between two nodes, we refer it to a symmetric link. On the contrary, if there are multiple candidate communication links between two nodes, we refer them to asymmetric links. Most protocols [4-6, 9-19] assume the communication links are symmetric links. There are also some strategies that utilize asymmetric links [2, 7, 8 and 20].

We use a simple example to illustrate the meanings of communication constraint and its possible cases. Suppose every node is equipped with 2c interfaces, and each node is assigned c distinct channels in the channel assignment procedure. For every node, these c channels are different from that of all nodes within its communication range. For ease of explanation, we assume that there are enough channels in the networks. In order to send messages to a receiver, the sender should tune an interface to one of the receiver’s assigned channels.

Suppose the communication constraint consists of 2c cases. Suppose two nodes A and B are within each other’s communication range. The assigned channels of A and B are respectively {a1, a2… ac} and {b1, b2… bc}. According the communication constraint, if node A wants to send packets to node B, they can only use channel bi (1≤i≤c). However, if node B initiates the communication with A, they can only use channel aj (1≤j≤c).

Suppose there are total n (n>1) nodes within the communication range of node A. According above constraint, node A can totally use c(n+1) channels. Apparently, c(n+1) is bigger than 2c. Therefore, some interfaces of node A need interface switching to utilize the c(n+1) channels. How do nodes switch their interfaces to the c(n+1) different channels to

communicate with other nodes is not the aim of this paper.

We use a 2-node example to further illustrate the difference between symmetric links and asymmetric links. The two nodes are also named A and B respectively. Suppose there are two available channels, numbered 1 and 2 respectively. Assume that there are two cases in the constraint of asymmetric links. The two cases are the following. If node A initiates the communication with node B, they utilize the link on channel 1. If node B initiates the communication with A, they should utilize the link on channel 2. Fig. 2 gives the scenarios that node A and B respectively utilizes symmetric links and asymmetric links to communicate. In this figure, we use a line without arrow to denote the symmetric link between node A and B. At the same time, we use two opposite arrow lines to denote the two asymmetric links corresponding to the two cases of the communication constraint between A and B. For ease of explication, we denote by ),( BA the asymmetric link initiated by node A. The number besides each link represents the channel used by the corresponding link.

As shown in Fig. 2, the symmetric link used by two nodes is fixed after the channel assignment. (In this example, nodes A and B can only fix on either channel 1 or 2, which is decided by the channel assignment algorithm). On the contrary, the asymmetric link used by the two nodes is dynamically established according the case that initiates the communication. The asymmetric link that will be used by two nodes cannot be predicted until the communication happens. In this example, they will choose channel 1 when node A initiates the communication. Otherwise, they will establish the link on channel 2. Therefore, channel assignment can decide the only symmetric link for two communication nodes. However, channel assignment can only assign the channels that are used by all candidate asymmetric links of two nodes. Only the case that initiates the communications between two nodes can decide the exact asymmetric link used by them. 3.2. Interference models

Recall that the two models of interference in [14] are initially designed for static single interface. Here we extend them to multiple interfaces environments and consider the effect of interface switching.

We consider a wireless network consists of N nodes, where each node is equipped with m wireless interfaces. Let ni (1≤i≤N) denote the ith node, and let d(i, j) denote the distance between nodes ni and nj. Assume that all nodes have identical communication and interference ranges. We use RT and RI (usually RT

A B1 (2)

A B

2

1

(a) Symmetric links (b) Asymmetric linksFig. 2 Symmetric links vs. asymmetric links

< RI) to denote the communication range and the interference range respectively. Suppose node ni wants to transmit packets to node nj at time t. We denote by c(i, k), which equals to c, the channel used by the kth (1≤k≤m) interface on node ni at that time. 3.2.1. Protocol Model: In the protocol model, the transmission from node ni to nj is successful if all of the following conditions are satisfied at that time:

1. ; ),1( mlkc c(j, l)c(i, k) ≤∀≤==2. d(i, j) ≤ RT ; 3. Any other node np (1≤p≤N) that has one interface

fix on the same channel c at time t does not transmitting. That is, if np satisfies following conditions.

c(p, r)=c (1≤∀ r≤m), and d(p, i) ≤ RI, or d(p, j) ≤ RI

np should not be transmitting at time t. 3.2.2. Physical Model: In the physical model, node nj first checks whether it has one interface fix on channel c at time t. If yes, node nj will calculate the signal strength received from ni on channel c. Let pij(c) be the signal strength received by node nj from ni on channel c, and Pj be the total noise strength at ni on channel c. We refer the term SNRij(c) to the ratio between pij and Pj on channel c. The transmission on channel c is successful if they satisfy the following constraints:

• )11( mlm, kc c(j, l)c(i, k) ≤∀≤≤∀≤== ; • SNRij (c)≥ SNRthresh

where SNRthresh is a constant, which is defined as the minimum signal-to-interference ratio that ensures successful receptions. 4. Our Proposed Estimation Scheme

The interference estimation scheme proposed in this paper is called weighed interference estimation scheme (WIES). WIES uses a new version of conflict graph, called Asymmetric Conflict Graph (ACG), to model the interference relationships of the network.

Recall that the traffic loads in WMNs distribute asymmetrically distribute across the network. WIES should consider the variation of traffic loads on different nodes. The main idea of WIES is that nodes need to support higher traffic loads should be assigned channels that have been assigned the least loads.

We establish WIES in three steps. In the first step, we create the ACG according the given network topology and the corresponding communication constraints. According ACG, we get the set of interference nodes for every node in the network. After that, we define the rules for WIES to assign a weight to each node in the set of interference nodes. At last, we combine WIES with the channel assignment algorithm.

4.1. The Asymmetric Conflict Graph (ACG) Suppose all nodes have the same communication

range (RT) and interference range (RI) respectively. Let k be the ratio between RI and RT. We first model the network topology as a graph G = (Q, E). Q and E is the set of nodes and edges respectively. There is an edge in E between nodes u and v in Q if d(u, v) ≤ RT , where d(u, v) is the distance between nodes u and v. Each node is equipped with m wireless interfaces. There are £ channels in the network.

We first use an example to illustrate how to establish the ACG according a simple communication constraint. We then summarize the general procedures to create the ACG for a network if it utilizes complex communication constraints.

The example communication constraint consists of two cases. There will be two asymmetric links between two nodes within each other’s communication range. We also use two opposite arrow lines to denote them respectively. However, we do not care the exact meaning of each case here. Under this communication constraint, a node may have multiple asymmetric links to and from different nodes within its communication range. For ease of explanation, we refer the asymmetric links pointing to a node to its passive links. In contrast, we refer the asymmetric links that away from a node to its positive links.

Owing to the very limited channel resources, some asymmetric links of a node may be assigned the same channels. For ease of explanation, we assume that all passive links of a node utilize the same channel, whereas the positive links may utilize different channels. One example of such asymmetric links is shown in Fig. 3. In this figure, dashed arrow lines represent the asymmetric links and the number besides a link denotes the assigned channel of this link.

As shown in Fig. 3, an asymmetric link is the passive link of the node it points to, whereas it is the positive link of the node on the other end of it. For example, the asymmetric link ),( AE is the passive link of node A, whereas it is the positive link of node E. In this scenario, the goal of the channel assignment algorithm changes to select the channel that is used by all passive links of each node.

At a first glance, the channel assignment problem in this paper appears to be a vertex coloring problem of

Figure 3. Example of asymmetric links, where all

passive links of a node utilize the same channel

the conflict graph [2, 15] (CG). According the network topology G, CG is established as follows. Nodes in CG are established corresponding to links in G. There is an edge between two nodes in CG if and only if the links in G denoted by the two nodes in CG interfere with each other. Fig. 4(b) shows the corresponding CG for the network topology presented in Fig. 4(a).

Apparently, CG cannot correctly formulate the interference relationship of the asymmetric links. This is because CG cannot manifest the multiple links between nodes. For example, according the CG, there is only one link between nodes A and E. In fact, there are two distinct links,

),( EA

),( EA and ),( AE between A and E. Therefore, a new strategy is needed to model the interference relationship between nodes that utilize asymmetric links.

To create ACG, we first represent each edge of G as two opposite links in G’ (as shown in Figure 4(c)). We then merge all passive links of a node in G’ into a new vertex in ACG. The vertex is named by all nodes compose these passive links, and the first letter denotes which node these passive links belong to. For example, a vertex named in ACG denotes that the

P passive links of node u are Ppppu ,...,, 10

),( upi (0≤i<P). There will be an edge between and

if linksPpppu ,...,, 10

nqqqv ,...,, 10 ),( upi and ),( vq j (0 ≤j< n) in G’

interfere with each other. Figure 4(d) gives the ACG for the network shown in Figure 4(a).

We now present the general procedures to create an ACG according a general communication constraint. Suppose the communication constraint consists of S cases. We first represent each edge of G using S distinct asymmetric links in another topology network, G’. Assume that we know which asymmetric links of a node will utilize the same channel. For every node, we merge all asymmetric links of a node assigned the same channel into a new vertex in ACG. The vertex is named in the same way as that is presented in the example.

Recall that an asymmetric link belongs to the two nodes that it connects. However, an asymmetric link

should not be included in two vertexes in ACG. The merging decisions are made on a node-by-node basis. In this procedure, nodes are associated with priorities on deciding the merging sequence. The procedure always chooses the node that has the maximum number of co-channel asymmetric links at present. Once a link is included by a vertex, we remove it from G’. The above procedure repeats until there is no link in G’. The edges between the vertices in ACG are created in the same way as presented in the sample scenario, and we do not describe them in details here. 4.2. Estimate Interference Level of Network

Supposed there is a node i, and QI(i) is its set of interference nodes gotten from ACG. If another node j is in QI(i), we say j is an interference candidate node of i. Because of the broadcast nature of the wireless medium, the interference level of the channel of i is decided by the amount of multiple access interference.

It is natural to use the number of interference candidate nodes that share a channel with node i as the interference level on i. However, this strategy does not reflect the real interference characteristics of asymmetric links. There are two main reasons. For one thing, asymmetric links are dynamically established to transfer loads. Therefore, the interference possibility of node j on i is greatly influenced by the loads on j. Secondly, the wireless signal power decreases in an exponential function of distance [21]. Hence, the interference degree of node j on i decreases dramatically along with the distance between them increasing.

Based on above observations, we assign a weight, ω(j), to each node j Q∈ I(i) to model its interference level on i if they are assigned the same channel. In ω(j), we respectively use ωt(j) and ωd(j) to denote the influence of traffic loads and distances. ω(j), ωt(j) and ωd(j) is shown in (1):

(1))()()( jjj dt ωωω ×= In practice, both ωt(j) and ωd(j) depend on the

specific network settings, which are difficult to confirm precisely. We thus propose two empirical formulas to decide the value of ωt(j) and ωd(j) respectively. The simulations presented in latter section prove that our method is feasible. 4.2.1. Deciding the value of ωt(j)

(a) G (b) CG (c) G’ (d) ACG

It is impractical to get the exact loads on each node at this time. On the other hand, we know that most of the traffics on a WMN are directed to/from the wired networks. Therefore, each node discovers a path to reach one or multiple gateway nodes. Assume that all traffics in the WMN are directed to/from the wired networks via gateway nodes. Then, each node should discover at least one path to gateway nodes. Recall that Figure 4. Differences between CG and ACG

gateway nodes provide network access for mobile users in mesh clients. It is clear that gateway nodes are assumed to carry heavier traffic. The traffic loads on the other nodes decrease as nodes are apart from the gateway. Roughly, the farther a node is away from a gateway, the lighter traffic loads on the node.

Let h(i) respectively be the length of the shortest path between node i and its nearest gateway node. Based on above observations, we design an empirical function utilizing both h(i) and h(j) to imitate the effects of traffic loads on the interference level. The function is as follows:

)2()(1

)0)()(()(/)()0)(,0)(()(

)(⎪⎩

⎪⎨

⎧

>>=>

=else

jhihjhihjhihih

jtω

As shown in (2), there are three possibilities for the value of ωt(j). If h(j) equals to 0, whereas h(i) is bigger than 0, ωt(j) is set to the square root of h(i). Else if h(i) is bigger than h(j), ωt(j) is set to the square root of h(i)/h(j). Else ωt(j) is set to 1. 4.2.2. Deciding the value of ωd(j)

The empirical formula to decide the value of ωd(j) is the following. Let k be the ratio between the interference range (RI) and transmission range (RT). Assume that RI is bigger than RT. Suppose r is the ratio between d(i,j) and RT, where d(i,j) is the distance between node i and j. And ωd(j) is estimated using (3):

)3()/(1)( τω +−= krjd where τ is a constant, which is computed as following. Suppose δ is the maximum distance between node i and any node in QI(i). τ is computed as following.

)4(/ kRT −= δτ Apparently, δ is always no less than RI. Therefore,

δ/RT is no less than k, accordingly τ is no less than 0. From the definitions, we can see that the value of ωd(j) is between 0 and 1. 4.3. WIES Acts as Channel Selection Criterion

Let £ be the set of available channels. Let Intfi(c) denote the interference level of a channel c £ on node ∈i. Intfi(c) is estimated as following:

∑ ×=∈ )(

)5()()()(iQj

ijiI

jccIntf ωμ

where μj(c) is an binary variable, which default value is 0. If one assigned channel of node j is c, μj(c) is set to 1. QI(i) is the set of interference nodes for node i.

Let Ci denote the channel assigned to node i, then Ci should satisfy the following constraint:

Intfi(Ci)= minr∈£Intfi(r) (6) 5. Performance Evaluation

In this section, we study the performance of WIES using a combination of graph-based simulations and

NS2 [22] simulations. We compare WIES with a strategy that utilizes the protocol model [14]. For ease of explanation, we denote the compared scheme that uses the protocol model by simple interference estimation scheme (SIES). As its definition, SIES uses the number of interfering nodes sharing a channel to estimate the interference level of networks. For fairness of comparison, both WIES and SIES use ACG to get the interference nodes set.

To compare their performance, we apply both WIES and SIES in a simple multi-interface WMN channel assignment algorithm, which is similar to the algorithm proposed in [6]. The algorithm can be summarized as following. Assume that every node has discovered a path to the wired network. Interfaces on a node are classified into UP-NICs and DOWN-NICs. UP-NICs are used to communicate with its parent node, whereas DOWN-NICs are used to communicate with its children nodes. At beginning, the gateway nodes choose channels for their interfaces. Any other node is only responsible for assigning channels to its DOWN-NICs. Each UP-NICs is associated with a unique DOWN-NIC of the parent node and is assigned the same channel as the parent's DOWN-NIC.

As described in previous section, ACG defines the set of interference nodes for every node. Assume that QI(i) is the set of interference nodes for node i. However, not all nodes in QI(i) will interfere communications of node i. Only those that have common channel(s) with node i will interfere its communications. Therefore, when node j∈QI(i) is assigned a common channel with node i, we say node j is the co-channel node of i on that channel.

In the followings simulations, we generate a 36 nodes wireless mesh network, and each node is equipped with two interfaces. Three nodes that distribute uniformly across the network are chosen to be the gateway nodes. 5.1. Graph Based Evaluations

In this part, we evaluate the effects of the number of channels and k to on the maximum number of co-channel nodes and the maximum interference level of the network. For simplicity, we will use the phrase Maximum co-channel nodes to represent the maximum number of co-channel nodes in the following simulations. In executing the channel assignment algorithm, we respectively increase the number of channels from 3 to 12 and increase k from 1 to 3.5. It should be noted that when we vary one factor during the simulations, the other one keeps constant. Fig. 5 presents the results of Maximum co-channel nodes for WIES and SIES.

From the results, we can see that Maximum co-channel nodes increases along with both the number of

channels and the value of k increase. However, their effect extents on Maximum co-channel nodes are different. The effect extent of the number of channels is much more than that of k. For example, the maximum co-channel nodes for 3 channels are proximately three times of that for 12 channels.

According SIES, the interference level of the network is the number of interference candidate nodes that are assigned the same channel. Apparently, for SIES, the meaning of Maximum co-channel nodes equals to that of the maximum interference level. However, for WIES, the meaning of Maximum co-channel nodes is different from that of the maximum interference level. According WIES, the interference level for a node is defined as the sum of weights on the interference nodes that are assigned the same channel. We then evaluate the impact of k and the number of channels on the maximum interference level for WIES. The results are shown in Fig.6.

The results show that the impacts of both k and the number of channels on the maximum interference level of WIES are similar to that of Maximum co-channel nodes. For example, when k is set to 1, the maximum interference levels of the network under different number of channels are similar. The maximum interference levels roughly increase in proportions along with the increase of k. However, the increase proportions under different available channels are different. The smaller the number of available channels is, the bigger the increase proportion of the corresponding curve is. 5.2. NS2 Based Evaluations

The followings are the default settings for the following NS2 simulations. These simulations use a commonly used 802.11 physical layer model, which

bandwidth is set to 11Mbps. During the simulation period, the network randomly generate multiple CBR traffic flows, the data rate of each flow is set to 8Mbps. The communication range (RT) is set to 150m, whereas k is set to 2. We utilize the Dynamic Source Routing (DSR) protocol for route selection.

Figure 5. Maximum co-channel nodes

5.2.1 Aggregated Throughput Comparison We first measured the aggregated throughput

achieved by WIES and SIES respectively. Aggregated throughput is defined as the sum of successful transferred end-to-end packets during the period of simulation. Fig. 7 gives the comparison results.

As shown in Fig.7, WIES achieves higher throughputs when the number of channels is small. Along with the increasing of the number of available channels, the difference between the throughputs of the two schemes decreases gradually. In this case, WIES achieves higher capacity than SIES when the number of channels is less than 6. After that, the throughputs of both schemes are almost identical. 5.2.2. Average Packet Delay of Traffic Flows

In this part, we evaluate the average data delay of different traffic flows. The average packet delay of a flow is defined as following. Suppose the destination node of a flow receives the first data packet from the flow at time t1, and it totally receives m packets from the same flow at time t2. The average packet delay of the flow, Td, is computed as followings.

Td = (t2-t1)/(m-1) (7) Fig. 8 shows the average data delays of 9 traffic

Figure 6. Maximum interference level of WIES

Figure 7. Aggregated throughputs comparison

Figure 8. Average packet delay for traffic flows

flows, where the number of channels is 3 and k is 2. As shown in Fig. 8, the average data delays of most

flows in WIES are much less than that in SIES. The primary reason behind this reduction in data delay is due to the reduced interference (contention) and collisions, in turn leading to lesser channel access delays (including back-offs and retransmission) in the 802.11 MAC and consequently less queuing delays. 6. Conclusions

In this paper, we have studied the interference evaluation problems for multi-interface WMNs. We presented an interference estimation scheme, which uses a weight to represent the interference level of a node on another node within its interference range. We also presented a novel strategy to estimate the interference relationship between nodes that utilize asymmetric links. Extensive simulations prove that the proposed scheme can model the interference level of WMNs more accurate than the compared model. Simulations also show that both the number of channels and the ratio between interference and communication range affect the interference level of the network greatly. The proposed scheme is practicable and can be easily used in channel assignment algorithms.

Acknowledgment

This paper is supported by the National Basic Research Program of China (973 Program) under Grant No. 2006CB303000, National Natural Science Foundation of China under Grant No. 60473092 and No. 90612018.

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