The section presents the numerical results and corresponding discussion to explicate the system performance. The results are built on hypothetical analysis and were validated with extensive simulations. Figure 3.14 shows the average service time under different statistics of the PU channels.
With a high probability of 0.8 (the probability of the state remaining in the OFF/IDLE state), there are likelihood that there will be more time-slots in OFF state than ON state and as such, the average service completion time will reduce as compared to 0.5 and 0.2 respectively, which have relatively higher ON- state probability. It also implies that; SU packet transmission (service) will take more time to complete when fewer slots are OFF/IDLE and when many slots are ON/BUSY. However, a probability of 0.8 showed better performance than 0.5 and 0.2 as the time slot π varies from 1 to 20. Also, different traffic statistics of the primary channels have different performances, but saturate after a point along π. As π increases, the average service time of the SU packet increases and at a point remains constant which confirms the SU harmonization with the PU channel structure as previously indicated in the system model.
.
Figure 3.14 Average Throughput vs time-slot
53
Figure 3.15 SU Throughput vs time-slot
In Figure 3.15, the throughput ππ of the primary users over the secondary channel shows that as π increases, the throughput (number of successful packet transmitted) increases irrespective of the occupancy statistics; though a probability of 0.8 implies that more packets were sent due to more slots being available for the PUs over the secondary channel. Closely followed in performance are 0.5 and 0.2 respectively. Nevertheless, the throughputs over secondary channel ππ get to saturation point as the timeslot further increases.
At a glance, the results presented in Figure 3.15, 3.16 and 3.17 respectively, demonstrates similar behaviours. This is due to emphasis on a metric (throughput) which is discussed in details but in different case study. The result in Figure 3.16 shows that the throughput ππ of the SUs over the primary channel increases irrespective of the occupancy statistics as previously stated. As ππ increases, time slot increases implying that, more time slots are available for more packets to be transmitted. However, a probability of 0.5 has a higher throughput than 0.8 and 0.2 respectively. This is due to the equal number of ON/OFF distribution depicting a relative stability or equal sharing of the time slots among the primary and secondary users respectively.
54
Figure 3.16 SU throughput Tp vs time-slot
Figure 3.17 Total (PU/SU) Throughput vs Time-slot
In Figure 3.17, the result of the total throughput π which is a summation of the throughput of PU over the secondary channel and the SU over the primary channel respectively shows that as π increases, the total throughput (total number of successful packet transmitted) increases irrespective of the occupancy statistics. However, as estimated, a probability of 0.8 implies that more packets were sent due to more
55
slots existing for the primary users over the secondary channel. Just as in Figure 3.15, closely followed in performance are 0.5 and 0.2 respectively due to established statistical facts.
Figure 3.18 Throughputs (π and ππ) vs time-slot
Figure 3.18 is a partial comparison between the total throughputs π and that of the SUs over the PU channel. Since π is the summation of the respective throughputs ππ and ππ respectively, it is expected that the total throughput be higher than each individual throughput. For each of the occupancy statistics, π outperformed the other two (ππ and ππ ). Similarly, the same goes for Figure 3.19 which compares the entire throughputs of the system i.e. π, ππ and ππ . The reason for this comparison is to have a clearer representation of the performance of the respective throughputs and also shows how the occupancy statistics has impacted on the system performance at a glance.
56
Figure 3.19 Throughputs (π, ππ and ππ ) vs Time-slot
Figure 3.20 Time delay vs time-slot
Figure 3.20 shows the delays for each of the occupancy statistics as it transits from one state to another.
From result, the delay increase to a point and after the synchronisation with the channel structure, it
57
begins to reduce as more slots are available for the SU packets. A 0.2, 0.8 and 0.5, 0.5 (20% ON-slot, 80% OFF slot and 50% ON-slot, 50% OFF slot) occupancy statistics indicates that more OFF slots than ON slots are available. This implies that enough window periods exist for a secondary user to transmit its packet before a primary user arrives and as such, blocking/dropping of the secondary userβs packet will be reduced at the same time. On the other hand, a 0.8, 0.2 and 0.2, 0.8 (80% ON-slot, 20% OFF slot and 20% ON-slot, 80% OFF slot) occupancy statistics indicates that, equal number of OFF slots and ON slots exist. However, in comparison, the first case shows lower delay statistics compared to the second occupancy statistics.
Figure 3.21 Packet blocking vs time-slot
Figure 3.21 shows the packet blocking for each of the occupancy statistics. A 0.2, 0.8 (20% ON-slot, 80% OFF slot) occupancy statistics indicates that, more OFF slots than ON slots exist. Therefore, a secondary user would transmit more packets before a primary user arrives and as such, blocking of the secondary userβs packet will be reduced significantly. Conversely, a 0.8, 0.2 (80% ON-slot, 20% OFF slot) occupancy rate indicates that more ON slot that than OFF slots exist while a 0.5, 0.5 (50% ON- slot, 50% OFF slot) occupancy statistics shows that equal number of ON and OFF slots exist. However, the packet blocking reduced as more slots were made available. But by evaluation, 0.2, 0.8 statistics will create more opportunities for SU packet than 0.5, 0.5 and 0.8, 0.2 statistics respectively.
58