Simulation Result and Discussion

In this session, we show the performance of proposed schemes, i.e. Hybrid EQL-QLP scheme and Hybrid LQF-QLP scheme. Both schemes have queue length thresholds, denoted as Q_th, which are the conditions that whether change the mechanism to the other one or not. We define the Q_th by

th Q,

Q =α × (2.25)

where α is ranged from 0 to 1 and the queue size Q is set to 1 Mbytes. If α equals to 0, then only EQL mechanism is used in Hybrid EQL-QLP scheme; and only LQF mechanism is used in Hybrid LQF-QLP scheme. On the contrary, if α equals to 1, then both schemes only use QLP mechanism.

In the following, we first introduce the simulation results of Hybrid LQF-QLP scheme. And then, the performance of Hybrid EQL-QLP scheme is observed. In both schemes, we will check whether the average packet delay of voice service is bounded in delay criterion or not. And we will see the performance of data service. We divide all ONUs into high-loading ONUs and low-loading ONUs.

The mean rate of each class of service in low-loading ONUs remains fixed. In high-loading ONUs, the mean rate of real-time services also remains fixed, but the mean rate of best-effort service will change from low to high. We will see the performance of high-loading ONUs and low-loading ONUs individually. After considering the difference between high-loading ONUs and low-loading ONUs, the fairness of best-effort data among all ONUs can be obtained.

In Figure 2.10, we show the average packet delay of voice service by adopting Hybrid LQF-QLP scheme. We can see that all the cases, with different value of alpha, have average packet delays of voice service bounded in a value, which is lower than the specified delay criterion (1.5ms).

The figure can verify that our system satisfies the basic delay requirement.

Figure 2.10: Average Packet Delay of Voice Service by adopting Hybrid LQF-QLP

Figure 2.11 and Figure 2.12 show the effect of Q_th in packet blocking probability by adopting Hybrid LQF-QLP scheme. In Figure 2.11, we can see that LQF mechanism has better performance in average packet blocking probability than QLP mechanism. The reason is that if LQF mechanism is adopted, high-loading ONUs will be assigned the higher priority than low-loading ONUs. So, most of the resource will be assigned to high-loading ONUs, and the packet blocking probability would be lower in high-loading ONUs. Intuitively, the packet blocking probability of low-loading ONUs would be higher by adopting LQF scheme than by adopting QLP scheme. Consequently, the difference of packet blocking probability between high-loading ONUs and low-loading ONUs would be smaller by adopting LQF scheme than by QLP scheme. Finally, we can see the fairness index of packet blocking probability is better in LQF scheme, as shown in Figure 2.12.

Figure 2.11: Average packet blocking probability (high-loading ONUs) of data service by adopting Hybrid LQF-QLP

Figure 2.12: Packet blocking probability fairness index of data service by adopting Hybrid LQF-QLP

When we adjust Q_th from 0 to 1, the packet blocking probability would be higher in the

beginning of the curves, because the characteristic of Hybrid LQF-QLP scheme will approach to the characteristic of QLP mechanism as Q_th is close to 1. But if the system load approaches to saturate, the LQF scheme will dominate the performance of packet blocking probability. Because under saturation-load condition, the queue occupancy would increase greatly and almost exceed the condition of Q_th more. Thus, there is usually no resource after the first assignment of Hybrid LQF-QLP scheme. As a result, the performance of all cases will approaches to LQF mechanism.

And then, in Figure 2.13 and Figure 2.14, we show the effect of Q_th in average packet delay and it’s fairness index. By adopting QLP, the resource assign to each ONU is proportional to the requested data volume. So, the variance of average packet delay is lower and the fairness of average packet delay would be higher. If we adopt LQF scheme, the high-loading ONUs get most of the resource. The average packet delay of high-loading ONUs would be decreased. But the average packet delay of low-loading ONUs will increase dramatically, even more than the average packet delay of high-loading ONUs. So the packet delay fairness will be lower than the others.

Figure 2.13: Average Packet Delay (high-loading ONUs) of Data Service by adopting Hybrid LQF-QLP

Figure 2.14: Packet delay fairness index of data service by adopting Hybrid LQF-QLP

The result of the overall fairness index F, defined in equation (2.3), is shown in Figure 2.15.

We can see that if we consider fairness of packet delay and fairness of packet blocking probability together, the QLP scheme (Q_th =1) and LQF scheme (Q_th =0) would not be the best choices. In this figure, the hybrid scheme with Q_th =0.7 exhibits the best performance.

Figure 2.15: Overall fairness index of data service by adopting Hybrid LQF-QLP

And then, we show the effect of Q_th by adopting Hybrid EQL-QLP scheme. Similarly, we must guarantee the average packet delay of voice service. The result of average packet delay for voice service is shown in Figure 2.16. We can see that the average packet delay of voice service still bounds in 1.5ms.

Figure 2.16: Average packet delay of voice service by adopting Hybrid EQL-QLP

In Figure 2.17 and Figure 2.18, we show the effect of Q_th in average packet blocking probability and fairness of packet blocking probability. The packet blocking probability of high-loading ONUs is higher in QLP than in EQL. It is also because that the most of the resource is assign to high-loading ONUs by adopting EQL scheme. The effect of Q_th in packet blocking probability is not obvious when the system load is increasing. Because when a system begins to block packets, the queue occupancies increase dramatically with system load. Under this condition, the EQL scheme will always be adopted. In addition, by adopting Hybrid EQL-QLP scheme, the assignment is independent of Q_th when any requested data volume exceeds Q_th. Thus, there is no obvious effect in packet blocking probability and fairness of packet blocking probability if we adjust the Q_th.

Figure 2.17: Average packet blocking probability (high-loading ONUs) of data service by adopting Hybrid EQL-QLP

Figure 2.18: Packet blocking probability fairness index of data service by adopting Hybrid EQL-QLP

We show the result of average packet delay of high-loading ONUs and fairness of average packet delay in Figure 2.19 and Figure 2.20, respectively. Similarly, QLP has better performance in packet delay fairness, because the resource assigned to each user is proportional to the requested data volume. By adopting EQL scheme, the average packet delay of high-loading ONUs is lower, due to fact that most of the resource are assigned to them. But the average packet delay of low-loading ONUs would be increased very much, even exceeds the average packet delay of high-loading ONUs.

So the fairness of packet delay would be worse than QLP. Then we focus the effect of Q_th in these two figures. For Hybrid EQL-QLP scheme, the design of Q_th decides when the algorithm must switch to EQL scheme. If the value of Q_th be set lower, then the probability that the algorithm switches from QLP to EQL is higher. It means that we have more opportunity to use EQL schemes.

Then the performance will achieve the result of EQL scheme.

Finally, we can see the overall fairness index shown in Figure 2.21. The Hybrid EQL-QLP scheme has the best performance when Q_th =0.9.

Figure 2.19: Average Packet Delay (high-loading ONUs) of Data Service by adopting Hybrid EQL-QLP

Figure 2.20: Packet delay fairness index of data service by adopting Hybrid EQL-QLP

Figure 2.21: Overall fairness index of data service by adopting Hybrid EQL-QLP