A Study on Performance Evaluation of Quality of Service in ATM Network

（i-1）在MMPPP/D/1队列的重要性抽样（IS）仿真问题中，我们确定了最优的仿真分布，并以较小的计算复杂度获得了小区损失概率小于10^<-10>的估计。（i-2）我们用IS方法评估了带背压控制的ATM交换机的性能。（1 -3）我们用IS方法评估了ATM突发流量的延迟性能。（i-4）我们将盲IS方法应用于随机性质未知的交通，得到了小区损失概率小于10^<-10>的估计。（ii-1）我们得到了细胞损失概率的渐近系数比以往更好的近似值。（ii-2）我们将EM算法应用于MMPP的参数估计，得到的参数估计速度是常规方法的10倍，且精度相似。（2 -3）我们得到了具有突发输入的分组网络中平均延迟时间的一个很好的近似。（3 -1）考虑所有M/D/1排队系统的集合，将其引入几何结构，讨论基于几何结构的大偏差理论。（iii-2）给出了离散分布尾部指数衰减的一个弱充分条件，并将该条件应用于MAP/G/1队列平稳分布尾部问题。

(i) Evaluation of Cell Loss Probability and Delay Performance by Computer Simulation(i-1) In the problem of the Importance Sampling (IS) simulation for MMPPP/D/1 queueing, we determined the optimal simulation distribution and obtained an estimate for cell loss probability less than 10^<-10> with small computational complexity.(i-2) We evaluated the performance of an ATM switch with back-pressure control by IS method.(i-3) We evaluated the delay performance of ATM burst traffic by IS method.(i-4) We applied the blind IS method to the traffic whose stochastic nature is unknown, and obtained an estimation of the cell loss probability less than 10^<-10>.(ii) Evaluation of Cell Loss Probability and Delay Performance by Analytic Methods(ii-1) We obtained a better approximation than ever for the asymptotic coefficient of cell loss probability.(ii-2) We applied the EM algorithm to the parameter estimation of MMPP, and obtained 10 times faster parameter estimations of similar accuracy as conventional method.(ii-3) We obtained a good approximation for the average delay time in a packet network with bursty input.(iii) Study on the Large Deviations Theory(iii-1) We considered the set of all M/D/1 queueing systems and introduced into it the geometric structure and discussed the large deviations theory based on the geometric structure.(iii-2) We gave a weak sufficient condition for the exponential decay of the tail of a discrete distribution and applied the condition to the problem of the tail of the stationary distribution of MAP/G/1 queue.