一类具有排队现象的工作流图的性能分析

Performance analysis of a class of workflow diagrams with queueing

基于极大代数方法,描述一类具有排队现象的工作流图中AND和XOR的时间逻辑关系.AND逻辑表示输出事件当且仅当输入事件都完成时发生,XOR逻辑表示在数个输入事件中按概率只有一个会发生并导致输出事件的发生.以AND和XOR基本模块构建这类工作流图模型,进行系统的性能分析,并给出顾客输出时间间隔下界的估计方法.通过实例仿真验证了建模、分析方法的可行性和有效性.

Based on min-max systems theory,min-max algebra is used to capture both AND and XOR logic in workflow diagrams with queueing.AND logic requires that output event happens only when all the input events happen.XOR logic requires that output event happens only when one of the input events happens according to the probability distribution.The workflow diagrams with AND/XOR logic and queueing are constructed by using elementary building blocks（AND and XOR blocks）.Analyzing the performance,lower bounds on the output rate of customers in this class of workflow diagrams are provided.A simulation example is given to demonstrate the feasibility and effectiveness of the proposed approaches.