In this chapter, we survey several previous studies in WMNs. Chapter 2.1 briefly describes the main ideas of a routing algorithm proposed by Pedro M. Ruiz and Antonio F. Gómez-Skarmeta [10], and some of previous studies of channel assignment in WMNs. Chapter 2.2 defines the network model and interference model used in this thesis.
2.1: Some of the Previous Studies
In this section, we review some of previous routing and channel assignment studies in WMNs.
2.1.1: Minimal Number of Transmissions Multicast Tree
The problem of computing minimal-cost multicast trees in multi-hop wireless mesh networks has been studied elsewhere [10]. The problem of finding a minimum-multicast tree is well-known to be NP-complete, as proven by Karp [11].
Some heuristic algorithms exist for computing minimal-cost multicast trees, such as the MST algorithm [12, 13] and others. The authors of one work [10] claimed that the Steiner tree is not generally the minimal-cost multicast tree in wireless mesh networks and illustrated their claim with an example. The critical point is that the Steiner tree does not take wireless broadcast advantage into account. The authors considered that the cost function, the minimal edge cost, used in preceding works is not relevant in cases that involved wireless mesh networks. Consequently, they proposed a new cost function to compute the minimal-cost multicast tree. The minimal-cost multicast tree
is the tree that connects sources and receivers by issuing a minimum number of transmissions, rather than having a minimal edge cost. They also demonstrated that the problem of minimizing the cost of such a multicast tree in a wireless mesh network is NP-complete. They proposed two heuristic algorithms: one was a greedy-based heuristic algorithm and the other one was a distributed approximation algorithm. The greedy-based heuristic algorithm first establishes a set of nodes that can communicate directly with more than two receivers, and then generates the multicast tree by building a Steiner tree from this set of nodes. The distributed approximation algorithm builds the multicast tree from the destination nodes to the source nodes. The underlying concept is the same as that of the greedy-based algorithm. The algorithm builds paths from the nodes, which can directly communicate with more than two receivers, to the source nodes, until each source node can communicate with each destination node.
2.1.2: Channel Assignment Strategies for Multi-Channel WMNs
The channel assignment problem of multi-channel WMNs is that each node is equipped with multiple NICs, which can be classified into three sub-classes - static, dynamic and hybrid. These three are described below.
(1) Static Assignment. Static channel assignment strategies assign a channel to each NIC permanently, or for a long period. Such assignment is very suitable if interface switching takes a long time. Static channel assignment strategies can be subdivided into identical and non-identical. Identical approaches assign a channel a common set of channels to each node in the network. Draves et al. [14] presented LQSP, a source routing protocol for multi-channel multi-radio network. They developed a new combined path
metric, WCETT, to identify a high-through path from a source to a destination. High-quality routes must be selected. However, the protocol limits the number of NICs to the number of channels in the network. Unlike the identical approach, the non-identical approach can assign a channel to each node in the network, according to the various sets of channels; the number of available NICs can be less than the number of available channels.
Bandwidth allocation and load-balance routing have been developed elsewhere [15] [16]. The main idea is to increase available bandwidth by efficiently separating the interference regions.
(2) Dynamic Assignment. Dynamic channel assignment is more flexible than static channel assignment as the former can switch NICs to any available channel that has the lowest interference in any time slot. The Packing Dynamic Channel Assignment (PDCA) algorithm, which simultaneously performs link channel assignment and scheduling, has been proposed [17].
The main idea that underlies the PDCA algorithm is the packing of the flows in a greedy manner in each period.
(3) Hybrid Assignment. As indicated by the term “hybrid”, this approach combines static and dynamic channel strategies. Some of the NICs in the network apply the static channel strategy and the rest apply dynamic channel strategy. A common channel has been assigned to all nodes communicate control messages to coordinate interfaces dynamically [18].
Each node has one NIC that is assigned a specific channel and other NICs are switchable [19] [20]. The fixed NIC is always listening to a particular channel called the listening channel. Each node in the network must maintain a table that records the listening channel of its neighbor nodes. If node A is to send data to its neighbor node B, then node A will switch one of
its switchable NICs to node B’s listening channel and then perform the transmission.
2.2: Wireless Transmission and Interference Model
The wireless mesh network is assumed herein to be composed of many stationary mesh routers. Each mesh router is equipped with a number of NICs and can aggregate traffic (like an access point). Thus, the mesh routers form a multi-hop wireless backbone to relay traffic from mobile clients in their coverage area. Several mesh routers are equipped with gateway functionality and can connect to the Internet.
Several non-overlapping (orthogonal) available channels thus increase the available bandwidth.
A node can communicate with another node if and only if both are within the communication range of each other and a common channel is assigned to their interfaces. A pair of nodes that use a single channel and are within interference range may interfere with each other’s communication, even if they cannot communicate with each other directly. Node pairs that use different channels can simultaneously transmit data without interference. Each node has been defined as having an interference disk with the node at the center [21]. Consider for example Fig. 3. The circles plotted as broken lines represent the interference disks of nodes A and B. Link (A, B) interferes with link (C, D) because node C is within node B’s interference disk and both links use the same channel. In [22], interference was defined in a manner similar to the definition in [21]: the interference range is defined as RI . Two links, (A, B) and (C, D), do not interfere with each other if and only if all of the four pairs of nodes (A, C), (A, D), (B, C), (B, D) are at least RI apart from each other. Otherwise, the two links interfere with each other.
Figure 3: An example illustrates the interference disk. Link (A, B) interferes with Link (C, D).
RT denotes the transmission range and dis u v( , ) denotes the distance between node u and node v. A link, which connects node u and node v, is said to be in the network if and only if dis u v( , )≤RT and both u and v have an NIC that is assigned a common channel. Accordingly, two nodes, u and v, can communicate with each other if and only if a link exists between them. Simultaneous unicast transmissions from node u to its neighbor nodes are possible if node u is equipped with multiple NICs and all the transmissions are on different orthogonal channels. Moreover, these transmissions can achieve the maximum capacity since the orthogonal channels do not interfere with each other. Nodes in the WMN have two modes of transmission - one is unicast transmission and the other one is broadcast transmission. Nodes select the most suitable method of transmission, according to the number of receivers. For instance, a node would like send a packet to one of its neighbor nodes, and does so by unicast transmission, or a node would like send a packet to some of its neighboring nodes, and does so by broadcast transmission.
RI denotes the interference range. Node u is the interference node of node v if and only if dis u v( , )≤RI . RI usually exceeds RT , and RI =2⋅RT is assumed herein. Link (A, B) is said not to interfere with (C, D) if and only if none of the four,
( , )
dis A C , dis A D( , ), dis B C( , ) and dis B D( , ) is less than or equal to RI . Otherwise, the two links interfere with each other. The interference link set of link (u, v) is composed of those links that interfere with link (u, v).
Many factors influence available capacity of a link; interference has the strongest effect. Given C, the maximum capacity of a link, the available capacity of a link is given by C minus the total load within RT of this link. Figure 4 displays the maximum available capacity of a specific link. All links in Fig. 4 use the same channel. Two constant bit rate (CBR) traffics are present in the network: one is sent from node 1 to node 2 and node 3; the other one is sent from node 7 to node 6 and node 8. The graph also presents corresponding route paths. For the first traffic, node 1 sends data to node 0 and node 2 simultaneously by broadcast transmission; then, node 0 forwards the data received from node 1 to node 3 by unicast transmission. For the second traffic, node 7 sends data by broadcast transmission. Hence, the total load within RT of link (4, 5) is 2+2+2 = 6, contributed to by the two broadcast transmissions and one unicast transmission. Finally, the available capacity of link (4, 5) is max{(C −6), 0}.
Figure 4: An example shows the set of interference nodes, interference links and also illustrates the available capacity of link (4, 5).