He Dayi, Li Ran, Huang Qi, Lei Ping
School of Humanities & Economic Management, Lab of Resources & Environment Management, China University of Geosciences (Beijing), Beijing, P. R. China.
PLoS One. 2014 Sep 10;9(9):e106965. doi: 10.1371/journal.pone.0106965. eCollection 2014.
In related research on queuing systems, in order to determine the system state, there is a widespread practice to assume that the system is stable and that distributions of the customer arrival ratio and service ratio are known information. In this study, the queuing system is looked at as a black box without any assumptions on the distribution of the arrival and service ratios and only keeping the assumption on the stability of the queuing system. By applying the principle of maximum entropy, the performance distribution of queuing systems is derived from some easily accessible indexes, such as the capacity of the system, the mean number of customers in the system, and the mean utilization of the servers. Some special cases are modeled and their performance distributions are derived. Using the chi-square goodness of fit test, the accuracy and generality for practical purposes of the principle of maximum entropy approach is demonstrated.
在排队系统的相关研究中，为了确定系统状态，普遍的做法是假设系统是稳定的，并且客户到达率和服务率的分布是已知信息。在本研究中，排队系统被视为一个黑箱，不对到达率和服务率的分布做任何假设，仅保留排队系统稳定性的假设。通过应用最大熵原理，排队系统的性能分布是从一些易于获取的指标推导出来的，比如系统容量、系统中的平均客户数量以及服务器的平均利用率。对一些特殊情况进行建模并推导其性能分布。使用卡方拟合优度检验，证明了最大熵方法在实际应用中的准确性和通用性。
