Exact Expressions for the First Two Moments of Job Flow Time in a Job Shop
本文推导了作业车间中作业流程时间矩的解析表达式，基于Jackson分解原理，通过计算随机个随机变量的矩得到精确结果，并展示了与拉普拉斯变换方法的等价性。
This paper presents analytical expressions for the moments of job flow time in a job shop by computing the moments of a random number of random variables assuming that the job shop satisfies the sufficient conditions of the Jackson decomposition principle. The mathematical equivalence of the proposed method to the Laplace transform method is shown and then demonstrated in a simple example. Then, expressions for the moments of job flow time in more realistic (and more complex) job shop settings are derived by computing the moments of a random number of random variables, provided that expressions for the moments of job flow time are available for the corresponding single stage shop. It is shown that the analytical expressions developed are exact as long as the assumptions of the Jackson decomposition principle hold. Any violation of these assumptions makes the derived expressions approximations, and their accuracy should be tested by simulation.