*3.2.1. Different network topologies*

In this simulation we created two different network topologies of WMN (grid topology and random topology). Ten random topologies were created and average values of chosen QoS parameters were computed.

Figure 5 shows the average values of end-to-end delay for various numbers of radio interfaces and two different network topologies. From results it is obvious that the highest value of end-to-end delay (0.92 sec) was reached in the grid WMN with one radio interface. The lowest value of delay (0.0097 sec) was achieved in grid WMN with seven radio interfaces. In WMN with random topology, the lowest value of delay (0.049 sec) was achieved in WMN with six radio interfaces. The best values of average delay were achieved in WMN with random topology, but differences between values of random and grid topologies were small

**Figure 5.** Average values of end-to-end delays for various radio interfaces and different network topologies

for higher number of radio interfaces. From results it may be concluded that optimal number of radio interfaces which guarantee the maximum allowable average delay 150 ms (ITU-T, 2003) for both network topologies is five, because more than five interfaces improved value of end-to-end delay only slightly, but the complexity of node is increased considerably.

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

In this section results of experiments are presented. The purpose of simulation was to determine the optimal number of radio interfaces for different WMN topologies, different number of data flows and different number of nodes to achieve the network capacity in-

 *Average End-to-end Delay*: The average time taken for a packet to reach the destination. It includes all possible delays in the source node and in each intermediate host, caused by queuing at the interface queue, transmission at the MAC layer, routing discovery, etc.

*Average Throughput*: The sum of data packets delivered to all nodes in the network in a

*Packet Loss*: Occurs when one or more packets being transmitted across the network fail

In this simulation we created two different network topologies of WMN (grid topology and random topology). Ten random topologies were created and average values of chosen QoS

Figure 5 shows the average values of end-to-end delay for various numbers of radio interfaces and two different network topologies. From results it is obvious that the highest value of end-to-end delay (0.92 sec) was reached in the grid WMN with one radio interface. The lowest value of delay (0.0097 sec) was achieved in grid WMN with seven radio interfaces. In WMN with random topology, the lowest value of delay (0.049 sec) was achieved in WMN with six radio interfaces. The best values of average delay were achieved in WMN with random topology, but differences between values of random and grid topologies were small

**Average End-to-End Delay**

Random Grid

**Figure 5.** Average values of end-to-end delays for various radio interfaces and different network topologies

12345678 **Number of Radio Interfaces**

*Average Jitter*: The delay variations between all received data packets.

**3.2. Simulation results** 

given time unit (second).

to arrive at the destination.

*3.2.1. Different network topologies* 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

**Average Delay (s)**

parameters were computed.

creasing expressed in enhancement of QoS parameters. We chose four QoS parameters for simulation evaluation:

Only successfully delivered packets are counted.

Figure 6 shows the average values of network throughput for various numbers of radio interfaces and two different network topologies. The lowest value of average throughput was achieved in grid WMN, where nodes have used for transmission only one radio interface. In this case, the value of average throughput was 504.28 kbps. In the case where WMN with random topology and one radio interface was used, the lowest value of average throughput (739.3 kbps) was achieved. The highest value of throughput (2019.9 kbps) reaches the grid WMN with seven radio interfaces. The best value of average throughput in random WMN topology (1964.2 kbps) was achieved by WMN with seven radio interfaces. Again, the optimal number of interfaces for both network topologies was chosen as five.

**Figure 6.** Average values of throughput for various radio interfaces and different network topologies

As we can see from Fig.7, the highest value of packet loss (75.1%) was reached in grid WMN with one radio interface. The lowest value of packet loss was achieved in WMN with seven radio interfaces. This value was 3.5% for the random topology and 2.5% for grid topology. As in the previous case, we can conclude the optimal number of radio interfaces as five, where grid topology achieved 9.8% of packet loss and 7.6% for random topology.

Figure 8 shows the average values of time jitter for different types of topologies and various number of radio interfaces. From results it is obvious that the highest value of average jitter was reached in the network with one radio interface. For the random topology this value was 0.7 sec and for grid topology it was 0.8 sec. On the other hand the lowest values of average jitter were achieved in grid WMN with seven interfaces (0.3 sec) and in random WMN with six interfaces (0.05 sec). As an optimal number of radio interfaces, the number of six was selected with average jitter value 0.11 sec for random topology and 0.14 sec for grid topology.

Channel Assignment Schemes Optimization for Multi-Interface Wireless Mesh Networks Based on Link Load 87

5 data flows 10 data flows 15 data flows 20 data flows

> 5 data flows 10 data flows 15 data flows 20 data flows

Average End-to end Delay

**Figure 9.** Average values of end-to-end delay for various radio interfaces and different number of data

12345678 Number of Radio Interfaces

Figure 10 shows the simulation results of average values of network throughput for the 5, 10, 15 and 20 data flows. The lowest value of average throughput was achieved in grid WMN with only one radio interface. From results it is obvious that the highest value of average throughput was reached in the multi-interface WMN with six radio interfaces. In

Average Throughput

**Figure 10.** Average values of throughput for various radio interfaces and different number of data flows

12345678 Number of Radio Interfaces

As we can see from Figure 11, the best value of packet loss was reached in multi-interface WMN with six radio interfaces. The highest value of packet loss was reached in WMN,

Figure 12 shows the average values of jitter for the different number of data flows. The highest values were achieved in WMN, where nodes have used for transmission only one

where nodes used for transmission one radio interface.

0.00E+00 2.00E+05 4.00E+05 6.00E+05 8.00E+05 1.00E+06 1.20E+06 1.40E+06 1.60E+06

Average Throughput (bps)

the WMN with more than six interfaces the network performance is decreasing.

flows

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 End-to end delay (s)

**Figure 7.** Values of packet loss for various radio interfaces and different network topologies

#### *3.2.2. Different number of data flows*

Simulation model consisted of 25 static wireless mesh nodes placed in grid in area 1000x1000 m (Fig.4a). Transmission range for each node was set to 200 m. As traffic transmission, the 5, 10, 15 and 20 CBR flows were simulated and packet size of 512 bytes was used. Data flows were created between random chosen node pairs.

Figure 9 shows the average values of end-to-end delay for different number of data flows. From results it is obvious that the best performance was achieved in multi-interface WMN with six interfaces, when the number of flows changed. The highest value of average end-toend delay (for all data flows) was reached by WMN with one radio interface. For small number of data flows (5), WMN with 5 interfaces reached the best performance, whilst for 10 data flows the best performance was reached by 6 interfaces. For more data flows (15 and 20) the system performance is unsatisfactory regardless of number of interfaces.

**Packet Loss**

Random Grid

Random Grid

**Figure 7.** Values of packet loss for various radio interfaces and different network topologies

12345678 **Number of Radio Interfaces**

**Average Jitter**

**Figure 8.** Average values of jitter for various radio interfaces and different network topologies

was used. Data flows were created between random chosen node pairs.

20) the system performance is unsatisfactory regardless of number of interfaces.

Simulation model consisted of 25 static wireless mesh nodes placed in grid in area 1000x1000 m (Fig.4a). Transmission range for each node was set to 200 m. As traffic transmission, the 5, 10, 15 and 20 CBR flows were simulated and packet size of 512 bytes

12345678 **Number of Radio Interfaces**

Figure 9 shows the average values of end-to-end delay for different number of data flows. From results it is obvious that the best performance was achieved in multi-interface WMN with six interfaces, when the number of flows changed. The highest value of average end-toend delay (for all data flows) was reached by WMN with one radio interface. For small number of data flows (5), WMN with 5 interfaces reached the best performance, whilst for 10 data flows the best performance was reached by 6 interfaces. For more data flows (15 and

*3.2.2. Different number of data flows* 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

**Average Jitter (s)**

**Packet Loss (%)**

**Figure 9.** Average values of end-to-end delay for various radio interfaces and different number of data flows

Figure 10 shows the simulation results of average values of network throughput for the 5, 10, 15 and 20 data flows. The lowest value of average throughput was achieved in grid WMN with only one radio interface. From results it is obvious that the highest value of average throughput was reached in the multi-interface WMN with six radio interfaces. In the WMN with more than six interfaces the network performance is decreasing.

**Figure 10.** Average values of throughput for various radio interfaces and different number of data flows

As we can see from Figure 11, the best value of packet loss was reached in multi-interface WMN with six radio interfaces. The highest value of packet loss was reached in WMN, where nodes used for transmission one radio interface.

Figure 12 shows the average values of jitter for the different number of data flows. The highest values were achieved in WMN, where nodes have used for transmission only one

radio interface. The best value of average jitter for all data flows was achieved in WMN with five or six radio interfaces.

Channel Assignment Schemes Optimization for Multi-Interface Wireless Mesh Networks Based on Link Load 89

Figure 13 shows the average values of end-to-end delay for six radio interfaces and six different network topologies. The best value of average end-to-end delay was reached in multiinterface WMN with 25 nodes (5x5). The highest value of average end-to-end delay was achieved by WMN with 100 nodes (10x10). Results show that increasing number of nodes

End-to-end Delay

**Figure 13.** Average values of end-to-end delay for different number of nodes

**Figure 14.** Average values of network throughput for different number of nodes

lowest value of packet loss was achieved in the WMN with 6x6 nodes.

The highest values of packet loss (Fig. 15) were achieved in WMN with 10x10 nodes. The

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

The lowest value of average throughput (Fig. 14) was achieved in WMN with 100 static nodes. The best values of throughput were reached in configuration 6x6 and 7x7 nodes.

Average Throughput

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

increase value of end to end delay.

0

0

500

1000

1500

2000

2500

3000

Throughput (kbps)

200

400

600

800

1000

1200

Delay (ms)

**Figure 11.** Values of packet loss for various radio interfaces and different number of data flows

**Figure 12.** Average values of jitter for various radio interfaces and different number of data flows

#### *3.2.3. Different number of nodes*

In this simulation the static grid WMN was used (Fig. 4a), but with changing number of nodes. Six different *N*x*N* grid networks were created, where *N* was changed from five to ten. Transmission range for each node was set to 200 meters. For traffic transmission, 15 CBR flows were used and the packet size 512 bytes was set. Data flows were created between random chosen node pairs.

Results from previous sections (3.1.1 and 3.1.2) shows that the best values for almost all QoS parameters were achieved in WMN with six radio interfaces. For this reason the simulation model for different number of nodes only for WMN with six radio interfaces was created. Figure 13 shows the average values of end-to-end delay for six radio interfaces and six different network topologies. The best value of average end-to-end delay was reached in multiinterface WMN with 25 nodes (5x5). The highest value of average end-to-end delay was achieved by WMN with 100 nodes (10x10). Results show that increasing number of nodes increase value of end to end delay.

**Figure 13.** Average values of end-to-end delay for different number of nodes

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

**Figure 11.** Values of packet loss for various radio interfaces and different number of data flows

Average Jitter

Average Jitter (s) 5 data flows

12345678 Number of Radio Interfaces

**Figure 12.** Average values of jitter for various radio interfaces and different number of data flows

In this simulation the static grid WMN was used (Fig. 4a), but with changing number of nodes. Six different *N*x*N* grid networks were created, where *N* was changed from five to ten. Transmission range for each node was set to 200 meters. For traffic transmission, 15 CBR flows were used and the packet size 512 bytes was set. Data flows were created between

12345678 Number of Radio Interfaces

Results from previous sections (3.1.1 and 3.1.2) shows that the best values for almost all QoS parameters were achieved in WMN with six radio interfaces. For this reason the simulation model for different number of nodes only for WMN with six radio interfaces was created.

five or six radio interfaces.

*3.2.3. Different number of nodes* 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

random chosen node pairs.

radio interface. The best value of average jitter for all data flows was achieved in WMN with

Packet Loss

10 data flows 15 data flows 20 data flows

10 data flows 15 data flows 20 data flows

Packet Loss (%) 5 data flows

The lowest value of average throughput (Fig. 14) was achieved in WMN with 100 static nodes. The best values of throughput were reached in configuration 6x6 and 7x7 nodes.

**Figure 14.** Average values of network throughput for different number of nodes

The highest values of packet loss (Fig. 15) were achieved in WMN with 10x10 nodes. The lowest value of packet loss was achieved in the WMN with 6x6 nodes.

Channel Assignment Schemes Optimization for Multi-Interface Wireless Mesh Networks Based on Link Load 91

interfaces it is possible to increase network capacity by enhancing of QoS parameters. For all simulations of WMN with common channel assignment method, the number of six radio interfaces appears as an optimum solution, because further increasing of the number of interfaces improved the capacity of WMN only slightly and using more than seven radio interfaces decreased the network performance. These results can be used as a base to another research channel assignment methods, where using of suitable CA algorithm can addi-

Optimal channel assignment in WMNs is an NP-hard problem (similar to the graph coloring problem). For this reason, before we present the channel assignment problem in WMNs, let

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

us first provide some mathematical background about graph coloring problem.

tionally improve network performance.

(Fig. 17) (Prodan & Mirchandani, 2009).

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

**4. Theoretical background** 

**4.1. Graph coloring** 

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

As we can see from figure 16 the best value of average jitter was achieved WMN with 25 nodes and the highest value was reached in 9x9 grid network.

**Figure 16.** Average values of jitter for different 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 certified by enormous packet loss in networks (over 55 % in the best solution).

#### **3.3. Results summary**

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 interfaces it is possible to increase network capacity by enhancing of QoS parameters. For all simulations of WMN with common channel assignment method, the number of six radio interfaces appears as an optimum solution, because further increasing of the number of interfaces improved the capacity of WMN only slightly and using more than seven radio interfaces decreased the network performance. These results can be used as a base to another research channel assignment methods, where using of suitable CA algorithm can additionally improve network performance.
