Queues with slow servers and impatient customers
Queues with slow servers and impatient customers
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DOI：
10.1016/j.ejor.2009.02.024
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发表时间：
2010-02
期刊：
影响因子：
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通讯作者：
N. Perel;U. Yechiali
中科院分区：
文献类型：
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作者：
N. Perel;U. Yechiali
我们研究了顾客不耐烦的两阶段(快和慢)马尔可夫随机环境中的M/M/c排队(c=1，1<；c<；∞和c=∞)。系统处于快速阶段(阶段1)，是一个参数为η的指数分布随机时间，到达速率和服务速率分别为λ和μ。慢速阶段(阶段0)的相应参数为γ，λ0和μ0(⩽μ)。当处于缓慢阶段时，客户会变得不耐烦。也就是说，每个客户在到达时激活一个单独的计时器，该计时器按指数分布，参数为ξ。如果系统在客户的计时器到期之前没有将其环境从0更改为1，则客户将放弃队列，再也不会返回。我们专注于推导队列长度分布的解析解。对于c的每一种情况，我们推导出相应的概率母函数，并计算平均队列长度。对几种极端情况进行了研究，给出了数值结果。
We study M/M/c queues (c=1, 1<c<∞ and c=∞) in a 2-phase (fast and slow) Markovian random environment, with impatient customers. The system resides in the fast phase (phase 1) an exponentially distributed random time with parameter η and the arrival and service rates are λ and μ, respectively. The corresponding parameters for the slow phase (phase 0) are γ, λ0, and μ0(⩽μ). When in the slow phase, customers become impatient. That is, each customer, upon arrival, activates an individual timer, exponentially distributed with parameter ξ. If the system does not change its environment from 0 to 1 before the customer’s timer expires, the customer abandons the queue never to return. We concentrate on deriving analytic solutions to the queue-length distributions. We derive, for each case of c, the corresponding probability generating function, and calculate the mean queue size. Several extreme cases are investigated and numerical results are presented.