A Maximum Entropy Analysis of the G/G/1 Queue at Equilibrium
用最大熵原理分析G/G/1队列在均衡状态下的行为，仅需到达和服务时间的前两阶矩，推导出队列长度分布的递归关系，并与经典排队理论和扩散近似对比，数值例子显示分布形式对系统行为的关键影响。
AbstractThe principle of maximum entropy is used to analyse a G/G/1 queue at equilibrium when the constraints involve only the first two moments of the interarrival-time and service-time distributions. Robust recursive relations for the queue-length distribution are determined, and a probability density function analogue is characterized. Furthermore, connections with classical queueing theory and operational analysis are established, and an overall approximation, based on the concept of 'global' maximum entropy, is introduced. Numerical examples provide useful information on how critically system behaviour is affected by the distributional form of the interarrival and service times, and favourable comparisons are made with diffusion and other approximations. Comments on the implication of the work to the analysis of more general queueing systems are included.Keywords: constrained optimizationdiffusion approximationinformation theoryoperational analysisqueueing theory