一种轮询系统的一般站平均队列长度

Mean queue length of a general station in a polling system

介绍了排队优先权站点轮询系统的操作原则． 通过对系统运行时的状态分析，嵌入马尔科夫链，构造系统稳态时的平衡方程，将其变换为队列母函数方程． 对其进行拉普拉斯─斯蒂吉尔斯变换，利用代数方法求解出了平衡状态下一般站平均队列长度． 可以看出平均队列长度与服务员走步时间之和成正比，与该队列和中心队列的单位时间内顾客到达个数以及γＢ 和γｋ 相关．

This paper first introduces the principle of the queueing priority station polling system which is widely applied in communication system. By analysis of system course and imbedded Markov chain method,constructing equations of balance state、transfering to generating function of queue length and Laplace-Stieltjes Transform, we obtain at last by the algebra method the general station mean queue length in statistical equilibrium. From the formula the mean queue length is directly proportional to the sum of the walking time and relates the numbers of arrival guests per time of center station and the general station and γ B and γ k .