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首页> 外文期刊>Applied Mathematical Modelling >Algorithmic computation of steady-state probabilities in an almost observable GI/M/c queue with or without vacations under state dependent balking and reneging
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Algorithmic computation of steady-state probabilities in an almost observable GI/M/c queue with or without vacations under state dependent balking and reneging

机译：在状态依赖的拒绝和重新适应情况下，几乎可以观察到的GI / M / c队列中带或不带休假的稳态概率的算法计算

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摘要

We consider an almost observable GI/M/c/N queue with customer impatience with or without multiple synchronous vacations under state-dependent balking. Upon arriving, a customer joins or refuses to join the system based on certain state dependent joining/balking probabilities. Once an arriving customer joins the system and finds all the servers busy, it initiates an exponentially distributed impatience timer with random duration T. An equilibrium balking strategy is discussed for constant balking as a special case of state-dependent balking. In the constant balking case, the waiting time of a customer in a queueing system has been associated with a linear cost-reward structure for estimating the net benefit if a customer chooses to participate in the system. A steady-state system of equations is obtained using the supplementary variable technique. After that, a recursive algorithm is proposed to obtain the stationary system-length distribution at pre-arrival and arbitrary epochs using those steady-state equations, from which the mean system sojourn time, the average reneging rate and the average balking rate are derived. Finally, we produce numerical results relating to system performance and its net benefit when investigated for different model parameters. The proposed model has applications in the modeling of balking and impatient behavior of incoming calls in a call center, multi-core computing, multi-path routing in delay sensitive communications networks.
机译：我们考虑了一个几乎可观察到的GI / M / c / N队列，该队列在依赖状态的限制下带有或不带有多个同步休假的客户不耐烦。到达后，客户根据某些状态相关的加入/拒绝概率加入或拒绝加入系统。一旦到达的客户加入系统并发现所有服务器都忙，它将启动一个指数分布的不耐烦计时器，其持续时间为T。讨论了针对恒定停电的均衡停电策略，这是状态相关停电的特例。在恒定的拒绝情况下，排队系统中客户的等待时间已与线性成本—报酬结构相关联，用于估算如果客户选择参加该系统的净收益。使用补充变量技术可获得方程的稳态系统。此后，提出了一种递归算法，利用这些稳态方程来获得到达前和任意时期的平稳系统长度分布，从中得出平均系统停留时间，平均滞回率和平均停滞率。最后，当研​​究不同的模型参数时，我们得出与系统性能及其净收益有关的数值结果。所提出的模型在呼叫中心的来话呼叫的叫醒和不耐烦行为建模，多核计算，对延迟敏感的通信网络中的多路径路由中具有应用。

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