Conclusions

The contributions of this thesis are concluded in this section as bellow:

 All new proposed analytical models have been used to derive the expressions of essential performance metrics, including utilization, throughput, mean number of packets in the system and buffer, mean response time, queueing delay, packet loss probability and fairness, for the corresponding systems.

 A single-server finite queuing system for the performance evaluation of AQM scheme under the non-bursty Poisson arrival process has been developed. Two continuous-time Markov models have been proposed, respectively, for AQM scheme subject to single class and two classes of traffic. Closed-form expressions for corresponding performance metrics in each system have been derived. Specifically, the marginal steady state probabilities in multi-class system have been obtained.

 The model for single class traffic has been adopted to analyze the effects of mean arrival rate, mean service rate and buffer capacity on AQM performance. It can be

concluded as follows: 1) The rise of mean arrival rate enables all performance metrics to increase; 2) A high mean service rate improves most performance metrics including throughput, mean response time, queueing delay, packet loss probability and mean number of packets in the system and buffer but at the cost of utilization; 3) All performance metrics, except packet loss probability, increase as the buffer capacity enlarges. On the other hand, the model for two classes of traffic has been used to investigate the effects of thresholds on aggregate and marginal performance. Numerous experiments results have shown that a high threshold degrades the marginal performance for traffic not controlled by this threshold. Meanwhile, the varying threshold have same effects on aggregate and marginal performance for traffic controlled by it, such as, low packet loss probility but high throughput and utilization, long response time as well as queueing delay can be achieved with increase in the threshold. Furthermore, it was pointed out that, if keeping the difference between thresholds constant, the smaller values of thresholds is capable of reducing the marginal mean number of packets in the system as well as queueing delay of each class and providing similar throughput as bigger one.

 A two-dimensional Markov model has been introduced for a single-server queueing system with AQM scheme subject to bursty traffic captured by an MMPP-2. Closed-form expressions for aforementioned performance metrics have been derived and accuracy of the developed model has been demonstrated by comparing analytical results with those obtained from simulators developed in JAVA programming language. The effects of the burstiness and correlation of the MMPP-

2 traffic on performance has been investigated to demonstrate the model’s application. Numerical results have demonstrated that high burstiness and correlation can significantly degrade the AQM performance in terms of increasing the mean numbers of packets in the system and buffer, mean response time, mean queueing delay as well as packet loss probability and decreasing utilization and throughput. In particular, it has been observed that high burstiness (or correlation) more remarkably affects the AQM performance if the correlation (or burstiness) is high. Additionally, the effects of burstiness and correlation are also sensitive to the threshold value. For example, a low threshold is capable of degrading the negative effects of high burstiness and correlation on the AQM performance.

 The other two-dimensional Markov model has been further developed for AQM with two individual thresholds subject to two classes of traffic modelled by a Poisson process and MMPP-2. We have adopted this model evaluate the impacts of parameters related to Class-1 traffic, including the average arrival rate, burstiness, correlation and its threshold, on the aggregate and marginal utilization, throughput, mean queueing delay and packet loss probability. It can be found that as the traffic rate grows, the marginal performance metrics for Class-2 are degraded substantially, while all values of the aggregate performance and marginal performance for Class-1 increase. Moreover, analytical results have also clearly demonstrated the detrimental impacts of traffic burstiness and correlation on all performance metrics. Lastly, the uncertainty effects of the threshold assigned to Class-1 traffic on all performance metrics have been analyzed. The analytical model is useful for assisting to find the

best set of parameters settings to suit the type of service required, for instance, real- time services like voice require low delay, while data services require low packet loss.

 A three-dimensional Markovian chains has been developed for AQM scheme with two classes traffic and PR scheduling scheme in a single queue. Two classes of traffic are generated by a non-bursty Poisson process and a bursty two-state MMPP, respectively. Adoption of PR scheme reduces the mean response time and queueing delay for Class-2 as the cost of increasing the corresponding performance metrics for Class-1. Moreover, the marginal mean response time and queueing delay for the high-priority traffic are improved significantly while those for the low-priority traffic are degraded remarkably due to the PR scheduling scheme. The other three- dimensional Markov model has been proposed for a single-server two-queues system with AQM and PR scheme. This model has been adopted to compare priority-based AQM performance with a single queue and multiple class-based systems. The effects of multiple queues capacities on the aggregate and marginal performance including throughput, packet loss probability, mean response time and queueing delay as well as utilization and fairness has been evaluated. By taking specific scenario as an example, we have explained how to seek the best way to allocate the capacity to each queue according to different aggregate and marginal performance requirements for a specific scenario.