具有自相关服务时间的排队系统的工作量

Workload of Queueing Systems with Autocorrelated Service Times.

作者信息

Chydzinski Andrzej

机构信息

Department of Computer Networks and Systems, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland.

出版信息

Entropy (Basel). 2025 Mar 5;27(3):272. doi: 10.3390/e27030272.

DOI:10.3390/e27030272

PMID:40149196

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11941239/

Abstract

The queuing model with autocorrelated service times is studied with respect to workload, i.e., the time needed to serve all the customers in the queue. Specifically, new formulas for the probability density of workload, its tail, the average value, and entropy are derived and illustrated using numerical examples. Both time-dependent and steady-state cases are covered. It is also demonstrated that the average workload may reach surprisingly large values, exceeding several times the product of the average queue size and the average service time.

摘要

针对具有自相关服务时间的排队模型，研究其工作量，即服务队列中所有客户所需的时间。具体而言，推导了工作量概率密度、其尾部、平均值和熵的新公式，并通过数值示例进行说明。涵盖了时间相关情况和稳态情况。还证明了平均工作量可能达到惊人的大值，超过平均队列大小与平均服务时间乘积的几倍。