**4.1. Graph coloring**

90 Wireless Mesh Networks – Efficient Link Scheduling, Channel Assignment and Network Planning Strategies

Packet Loss

As we can see from figure 16 the best value of average jitter was achieved WMN with 25

Average Jitter

5x5 6x6 7x7 8x8 9x9 10x10 Number of Nodes

These simulations showed unacceptable values for almost all simulated QoS parameters. Average delay combined with average jitter achieved in all networks (from 25 to 100 nodes) doesn't allow using several CBR services running simultaneously. This conclusion is certi-

5x5 6x6 7x7 8x8 9x9 10x10 Number of Nodes

The results show the benefits of using multiple radio interfaces per node. This solution can improve the capacity of WMN. Simulation results show that by increasing the number of

**Figure 15.** Values of packet loss for different number of nodes

0.0000 10.0000 20.0000 30.0000 40.0000 50.0000 60.0000 70.0000 80.0000

Jitter (ms)

Packet Loss (%)

nodes and the highest value was reached in 9x9 grid network.

**Figure 16.** Average values of jitter for different number of nodes

**3.3. Results summary** 

fied by enormous packet loss in networks (over 55 % in the best solution).

The graph coloring theory is used as a base for the theoretical modeling of channel assignment problem. At the beginning we must define two related terms: *communication range* and *interference range*. Communication range is the range in which a reliable communication between two nodes is possible. The interference range is the range in which transmission from one node can affect the transmission from other nodes on the same or partially overlapping channels. The interference range is always larger than the communication range (Fig. 17) (Prodan & Mirchandani, 2009).

**Figure 17.** Communication range and interference range

Consider an undirected graph G(V, E) that models the communication network. A graph G, is defined as a set of vertices V and a set of edges E. Each vertex in graph represents a mesh router and each edge between two vertices represents a wireless link between two mesh routers. The color of each vertex represents a non-overlapping channel and the goal of the channel assignment is to cover all vertices with the minimum number of colors such that no two adjacent vertices use the same channel (Husnain Mansoor Ali et al., 2009).

Channel Assignment Schemes Optimization for Multi-Interface Wireless Mesh Networks Based on Link Load 93

**Figure 18.** Connectivity graph, interfering edges and conflict graph

As has been already mentioned, CA in a multi-interface WMN consists of assigning channels to the radio interfaces in order to achieve efficient channel utilization for minimizing interference and to guarantee an adequate level of connectivity. Nowadays, there exist many approaches to solve the channel assignment problem. These approaches can be divided into

1. *Fixed (static) channel assignment approaches* – channels are statically assigned to different radio interfaces. The main concern includes the enhancement of efficiency and guaran-

2. *Dynamic channel assignment approaches* – a radio interfaces are allowed to operate on multiple channels, implying that a radio interfaces can be switched from one channel to another one. This switching depends on channel conditions, such as the value of interfer-

ence. The basic issues are the switching delay and the switching synchronization. 3. *Hybrid channel assignment approaches* – in this approach the radio interfaces are divided into two groups, the first is fixed for certain channels and the second is switchable dy-

In this section several channel assignment approaches are compared by QoS parameters

**5. Channel assignment algorithms for WMN** 

three main categories (Conti et al., 2007):

teeing of the network connectivity.

namically while deploying the channels.

mentioned in the previous section.
