同步多重工作休假排队系统分析

Analysis of queuing system with multiple working vacation

考虑一类带有正负顾客、休假可中止的同步多重工作休假排队模型.服务台在休假期间不是完全停止工作,而是以相对服务期较低的服务率服务顾客,这种半休假策略叫作工作休假.在此模型的基础上,针对现实生活中的排队模型可能出现的干扰因素,提出了带有负顾客的排队模型,负顾客一对一抵消队尾的正顾客(若有),若系统中无正顾客,到达的负顾客自动消失,负顾客不接受服务;同时引入了另一种策略:休假可中止.采用拟生灭过程和矩阵几何解法得到了系统的稳态队长,证明了稳态条件下队长的随机分解,并且得到了附加队长的分布.最后,应用数值例子说明该模型可以较好地解决一些实际问题.

The working vacation queuing system with negative customers and vacation interruption was considered.The server works with low service rate rather than completely stops during vacation period,and this kind of incomplete vacation strategy is called working vacation.Because the real life queuing model might meet many interference factors,a negative customers queuing model was proposed.In the system,customers are either positive or negative.Negative customers remove positive customers one by one only at the end of line if there is positive customer.When a negative customer arrives,if there is no positive customer in system,the negative customer will disappear.Negative customers do not accept service.Another vacation policy of vacation interruption was introduced.By quasi birth and death process and matrix-geometric solution method,the stationary queue length was obtained.The stochastic decomposition of queue length in stationary state was proved to achieve the distributions for additional queue length.According to numerical examples,the proposed model can represent some practical problems reasonably.