**6. Simulation results**

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

**Figure 7.** A typical frame (chromosome) with its SSecs (genes) associated with Figure 1

other equal-size genes (e.g., replace the SSec3 with the SSec5 in Figure 7).

max���∑ ∑∑ �������

�

So we define the fitness function (*F.F.*) as follows:

���

higher performance will be reached; hence, Eq. (7) can be explicated as Eq. (16).

� �� ��� ��� �

�� �� � ∑ ∑∑ ������� � �� ��� ��� � ��� � ���

��

scheduling sections are consecutive and non-overlapping.

Each gene is defined as a scheduling section (SSec). A scheduling section is composed of one or more time slots in which a queue and its non-conflicting queues are scheduled to transmit in parallel. The first scheduling section is started at the beginning of the frame. All the

The crossover operator is 0.5-uniform crossover [19]. Each SSec of one chromosome can be exchanged with equal-size SSec of another chromosome, with a constant probability of 0.5. Each scheduling section (gene) is subject to random mutation with a small independent probability. We use permutation encoding; hence each gene replaces with a duplicate of

Finally, we should use some QoS metrics of the network (that we want to optimize) to define the fitness function. It can be seen from the Eq. (7) that we are interested in depletion of all the queues in the scheduling period. On the other hand, when more queues get emptied,

��� �������� � �� � � � (16)

× 100 (17)

In the previous section, the optimization problem which is needed to create a population was formally defined. This population is created by the MBS based on the fact that the MBS gathers queues' statistics of SSHCs through some control messages. Each chromosome of the population is such that every queue gets its service once per frame, so the scheduling overhead could be minimized. Each queue is scheduled as close to the beginning of the frame as possible, so that its transmission does not overlap with transmissions of its conflicting links. The scheduling period is set to two frames, since VBR traffic streams get

**5.2. A GA-based approach for the scheduling problem** 

their services every two frames.

We developed a TDMA-WMN system based on Orthogonal Frequency Division Multiplexing (OFDM) air interface that works in 5GHz frequency band using NS-2 simulator [20]. Basic OFDM parameters are listed in Table 1. OFDM symbol duration is about 14µs. TDMA frame duration (*L*) is set to 20ms. While TDMA-WMN uses BPSK-1/2 modulation technique, the underlying network (WLAN) uses 16QAM-1/2 modulation technique. Different modulation techniques have been used; because interference between MTs of different SSHCs should be avoided (Figure 6).


**Table 1.** Basic OFDM parameters

We define three types of traffic in the system: CBR, VBR, and ABR traffic streams. CBR traffic (e.g., voice over IP without silent suppression (G.711)), has constant packet size with constant packet interval. VBR traffic (e.g., H.263 video), has variable packet size with variable packet interval feature. At last, elastic traffic (e.g., FTP), can adjust its transmission rate gradually.

Voice and video traffic stream specifications are as follows:


Traffic specifications of these two types of traffic are summarized in Table 2. For the sake of simplicity, we assume that elastic flows are generated using CBR traffic sources with packet size of 1000 bytes.


**Table 2.** Traffic specification parameters of traffic types

In order to evaluate the performance of the proposed scheduler and the admission control procedure, the topology of Figure 6 is considered as the scenario. All of the end nodes (SSHCs) are active, while the intermediate nodes (MSSs) pass only the traffic of the end nodes. SSHCs are configured to work in both WLAN and TDMA-WMN modes; while, MSSs work in TDMA-WMN mode. *k* is fixed at 4, since elastic traffic queues are scheduled every four frames. From one hand, this value is not too small that causes some drawbacks on delay sensitive traffic types and on the other hand it's not too large that leads to unfairness.

Application of Genetic Algorithms in Scheduling of TDMA-WMNs 17

Without Admission Control

With Admission Control

> CBR Queue VBR Queue ABR Queue

packets do not receive the opportunity to be scheduled, the VBR queue length increases

**Figure 9.** VBR packet loss versus increased number of VBR connections, while CBR and ABR connec-

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

**VBR Connections**

**Figure 10.** Residual packets in the three queues, while MTs are monotonically increased

3 6 9 12 15 18 21 24 27 30

**MTs**

Eliminating the thresholds causes the queue size of ABR and VBR traffic to increase, while by using these thresholds (Figure 8 and Figure 9) a fair bandwidth allocation can be reached.

In this chapter we considered an important aspect of TDMA-WMNs: Traffic flow requirements on scheduling the links. Moreover, we considered the underlying network which can affect the overall system performance despite previous research. We assumed three types of traffic with different QoS requirements and formulated a model describing the scheduling

monotonically.

tions are fixed at one

**Residual Packets (Byte)**

**VBR Packet Loss (%)**

**7. Conclusion** 

At first, we assume one VBR MT and one ABR MT and a number of CBR MTs which are gradually increased (Figure 8). It can be seen when there is no admission control mechanism, as the number of MTs exceeds 10, packets of the newly added MTs are dropped. The proposed admission control mechanism for this traffic type works well, since none of the packets has been dropped when it is applied.

**Figure 8.** CBR packet loss versus increased number of CBR connection, while VBR and ABR connections are fixed at 1

In the next simulation, the number of CBR MTs and ABR MTs are fixed to one and the number of VBR MTs (Figure 9) is gradually increased. Since the packet size and the arrival time are variable in case of the packets of these traffic types, the number of admitted VBR MTs is less than the number of admitted CBR MTs. In this figure the packet loss is due to the threshold (τ*<sup>1</sup>*) applied to the queue length. Here again the proposed admission control mechanism works well for this type of traffic.

For the last simulation, we removed all of the thresholds to see how many packets will be backlogged in the queues after scheduling the queues. For this purpose we monotonically increase the number of CBR, VBR, and ABR MTs in each SSHC. It can be seen from Figure 10 that the CBR queue is at its normal size, since almost all of its packets are serviced in appropriate time. However, after the second frame, all of the packets of elastic data type are queued, since there is no chance for them to be scheduled. Moreover, since all of the VBR packets do not receive the opportunity to be scheduled, the VBR queue length increases monotonically.

**Figure 9.** VBR packet loss versus increased number of VBR connections, while CBR and ABR connections are fixed at one

**Figure 10.** Residual packets in the three queues, while MTs are monotonically increased

Eliminating the thresholds causes the queue size of ABR and VBR traffic to increase, while by using these thresholds (Figure 8 and Figure 9) a fair bandwidth allocation can be reached.

#### **7. Conclusion**

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

none of the packets has been dropped when it is applied.

tions are fixed at 1

threshold (

τ

mechanism works well for this type of traffic.

**CBR Packet Loss (%)**

In order to evaluate the performance of the proposed scheduler and the admission control procedure, the topology of Figure 6 is considered as the scenario. All of the end nodes (SSHCs) are active, while the intermediate nodes (MSSs) pass only the traffic of the end nodes. SSHCs are configured to work in both WLAN and TDMA-WMN modes; while, MSSs work in TDMA-WMN mode. *k* is fixed at 4, since elastic traffic queues are scheduled every four frames. From one hand, this value is not too small that causes some drawbacks on delay sensitive traffic types and on the other hand it's not too large that leads to unfairness. At first, we assume one VBR MT and one ABR MT and a number of CBR MTs which are gradually increased (Figure 8). It can be seen when there is no admission control mechanism, as the number of MTs exceeds 10, packets of the newly added MTs are dropped. The proposed admission control mechanism for this traffic type works well, since

**Figure 8.** CBR packet loss versus increased number of CBR connection, while VBR and ABR connec-

In the next simulation, the number of CBR MTs and ABR MTs are fixed to one and the number of VBR MTs (Figure 9) is gradually increased. Since the packet size and the arrival time are variable in case of the packets of these traffic types, the number of admitted VBR MTs is less than the number of admitted CBR MTs. In this figure the packet loss is due to the

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Without Admission Control

**CBR Connections**

For the last simulation, we removed all of the thresholds to see how many packets will be backlogged in the queues after scheduling the queues. For this purpose we monotonically increase the number of CBR, VBR, and ABR MTs in each SSHC. It can be seen from Figure 10 that the CBR queue is at its normal size, since almost all of its packets are serviced in appropriate time. However, after the second frame, all of the packets of elastic data type are queued, since there is no chance for them to be scheduled. Moreover, since all of the VBR

*<sup>1</sup>*) applied to the queue length. Here again the proposed admission control

In this chapter we considered an important aspect of TDMA-WMNs: Traffic flow requirements on scheduling the links. Moreover, we considered the underlying network which can affect the overall system performance despite previous research. We assumed three types of traffic with different QoS requirements and formulated a model describing the scheduling

Application of Genetic Algorithms in Scheduling of TDMA-WMNs 19

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optimization problem which is to be solved to minimize queues in the system. We develop a genetic algorithm method to find the optimal schedule for each relaying node. Furthermore to be able to fulfill QoS requirements of established connections, we developed an admission control mechanism. Finally, the performance of the proposed GA algorithm along with the admission control procedure was evaluated by simulating a typical network scenario. Simulation results showed effectiveness of our admission control and scheduling mechanisms. In our next work, we introduce some new mechanisms including MIMO technique to the above-mentioned system and investigate its performance. Meanwhile, application of genetic algorithms in distributed scheduling of WMNs is investigated.
