一般重试时间、伯努利单重休假的离散Geom/G/1重试排队系统

摘要

We consider a discrete-time Geom/G/1 retrial queue with general retrial times, a single vacation under Bernoulli schedule. There is no waiting position in the server,and a new arriving customer finds the server busy or at vacation, he will join the orbit to retry getting the service,or he will accept service at once (No matter there is a retrial customer). After the service,the server either goes for a vacation with probality θ(0≤θ≤1) or may continue to wait the customer with probality (θ),if there is a customer in the orbit at least;Ortherwise,the server may wait the customer too. Applying for Markov chain, we derive the various steady state distributions of this system,and give a stochastic decomposition law of the system size and a application about it. A recursive formular is also built up to facilitate the orbit site distribution. Finally,some numercial examples show the influence of the parameters on the system performance.%考虑一个带有一般重试时间、伯努利单重休假的离散Geom/G/1重试排队系统.服务台前无等待位置,新到达的顾客若发现服务台忙或处于休假,则进入重试区域等待重试;若发现服务台空闲(不管有无顾客重试),就立即接受服务.顾客在完成服务之后,若重试区域中有顾客存在,则服务台以概率θ(0≤θ≤1)进行一次单重休假,以概率-θ(=1-θ)重新等待顾客的到来;若重试区域中无顾客,则服务台也重新等待顾客的到来.利用马尔可夫链法,得到了本模型各个状态的稳态分布,并给出了系统顾客数的随机分解结果及关于其的一个应用.还给出了一个递推公式去计算重试区域顾客数的分布.最后用数值例子说明了一些参数对系统性能的影响.