【摘要】 排队网络是一种常见的对供应链、生产线以及交通系统等进行建模的工具,可以被用来分析系统中各资源的利用率,并对系统结构的设计提供指导.相比较于利用仿真进行分析,排队网络可以更快速地得到系统的资源利用率.在实际中,常用闭环Jackson网络来对顾客总数不变的封闭系统进行建模.在本文中,首先利用闭环Jackson网络归一化参数的母函数,得到了网络中各节点利用率的解析表达式.通过对利用率解析表达式的分析,给出了在顾客总数趋于无穷时利用率的极限,并证明了利用率是饱和函数.在这些结论的基础上,进一步计算不同服务时间下达到饱和状态所需的顾客总数.最后将该方法应用于一个实际的自动化码头例子,将其建模为闭环Jackson网络,分析码头的瓶颈所在,计算系统饱和点对应的车辆数,并与仿真实验进行了对比.更多还原

【Abstract】 Queueing networks are widely used in modeling supply chains, assembly lines and transportation systems.The analytical results of queueing networks can help comparing the efficiency of different configurations and providing guidance for system design. Closed Jackson network(CJN) is frequently used to model these systems. In this paper, based on the generating function of the closed Jackson network’s normalized parameters, the utilization’s analytical expression is obtained. It is also proved that the limit of utilization exists when the total number of customers tends to infinity, and utilization is a saturation function. Then the saturation point, which is the total number of customers required to reach saturation state, can be calculated. Finally, this method is applied to a queuing network modeled from an actual automated terminal to analyze the bottleneck and the saturation vehicle number of the terminal. The results from the closed Jackson network are close to the results from simulation experiments. So queueing network is a feasible method to analyze the performance of systems like container terminals.更多还原