有Bernoulli休假和可选服务的Geo/G/1重试排队

A Discrete-Time Geo/G/1 Retrial Queue with Bernoulli Vacation and Second Optional Service

讨论了有Bernoulli休假策略和可选服务的离散时间Geo/G/1重试排队系统.假定一旦顾客发现服务台忙或在休假就进入重试区域,重试时间服从几何分布.顾客在进行第一阶段服务结束后可以离开系统或进一步要求可选服务.服务台在每次服务完毕后,可以进行休假,或者等待服务下一个顾客.还研究了在此模型下的马尔可夫链,并计算了在稳态条件下的系统的各种性能指标以及给出一些特例和系统的随机分解.

We analyze a discrete-time Geo/G/lretrial queue with Bernoulli vacation where all the arriving customers require a first essential service while only some of them demand a second optional service. If upon arrival, the server is busy or vacation, the customer is obliged to leave the service area and to orbit. Each customer in the orbit forms an independent retrial source and the retrial time follows a geometrical law. Just after completion of a customer＇s service the server may take a vacation of random length or may opt to continue staying in the system to serve the next customer. We study the Markov chain underlying the considered queuing system and some performance measures of the system in steady-state. Further, we give two stochastic decomposition laws and some examples.