Abstract: To improve the fitting degree and extend the application fields of the M/M/c model, this paper proposes the progressive input-rate and service-rate depended on the real system states by introducing two new definitions, namely the input probability and service degree. The thresholds of the progressive input-rate and service-rate are set based on the actual operating conditions of the real system states. Moreover, the progressive input-rate and service-rate are divided into two stages and three stages respectively. Then, the progressive M/M/c model is constructed by combining the progressive input-rate and service-rate and the transition process in Queuing Theory. Here, we use the after-determining method to estimate the related parameters in this new model. It is pointed out that the progressive M/M/c model is an extended form of the M/M/c model, and can be use to improve the fitting degree and extend the application fields of the M/M/c model. Finally, a practical example is provided to demonstrate the optimization and practicality of the progressive M/M/c model.

Key words: M/M/cmodel, progressive input rates, progressive service rates, state transition, after determining method

摘要： 为了解决M/M/c模型在实际运用中模拟精度不高及使用范围有限的问题,本文立足系统状态变化与输入率和服务率的关系,通过引入输入概率和服务度,构建依赖系统状态的递进式输入率和服务率。递进式输入率和服务率通过研究系统实际运行状况设定临界值,其中输入率分为两阶段,服务率分为三阶段。此外,结合递进式输入率和服务率及排队论状态转移过程构建了递进式M/M/c模型,并采用后确定法确定模型参数。递进式M/M/c模型是M/M/c模型的扩展形式,提高了M/M/c模型的模拟精度,在一定程度上拓展了模型的应用范围。最后,通过一个生活实例验证了递进式M/M/c模型的优化性和实用性。

关键词: M/M/c模型, 递进式输入率, 递进式服务率, 状态转移, 后确定法