中文摘要：

借助有效的端到端时延分析可实现大规模网络的QoS控制，运用统计网络演算理论中最小加代数的卷积运算规则计算端到端时延界日益引起人们的重视．随着网络规模的不断扩大，统计端到端时延界应同时具有良好的可扩展性和一定的紧致性，而目前满足这一要求的理论成果还比较少．通过结合最小加代数的卷积运算规则和Doob不等式，并采用矩母函数（Moment Generating Function，MGF）对到达曲线和服务曲线进行描述，文中给出了一种基于指数上鞅的端到端时延界表达式．该时延界不仅可以线性扩展，而且数值分析结果表明，在相同假设条件下，该时延界比现有的线性时延界具有更好的紧致性．

英文摘要：

Effective end-to-end delay evaluation can be used to realize QoS control in large scale networks. The derivation of the statistical end-to-end delay bound using （min, ＋） convolution operation developed in Stochastic Network Calculus has attracted more and more attention. With the unceasing expansion of the network scale, an end-to-end delay bound should have better scal- ability and tightness. However, few theoretical results now meet this requirement. In this paper we describe the arrival curve and the service curve in the [orm of Moment Generating Function （MGF） and present a close-form, exponential supermartingale based end-to-end delay bound ex- pression by combining （rain, q-） convolution operation with Doob＇s maximal inequality. The end- to-end delay bound is not only linearly scalable, but also has better tightness than existing linear delay bound under the same assumptions as illustrated by the numerical results.