Abstract: To address the puzzle in setting the constant input and service rates in the M/M/c model, this paper proposes input probability and service degree. The proposed input probability and service degree will change their values according to the changes in the state of a different system. On the basis of the above input probability and service degree, the dynamic input and service rates are developed by combining the input probability with the average input rate and service degree with the average service rate. Next, a transition process is provided using the dynamic input and service rates for developing an extended M/M/c model under the current system state. Additionally, this paper designs an after-determining method by introducing the real state of the system for solving related parameters of the dynamic input and service rates. The M/M/c model has a broader application scope when implementing dynamic input and service rates, and it provides more accurate results when compared to the general queue model. Finally, a practical example is provided to illustrate the effectiveness and feasibility of the proposed model.

Key words: M/M/c model, dynamic input rate, dynamic service rate, state transition, after-determining method

摘要： 为了解决M/M/c模型中恒定输入率和服务率假设与现实现象不符的问题,本文提出了随系统状态变化的输入概率和服务度,并通过新输入概率与平均输入率以及新服务度与平均服务率的结合分别构造了动态输入率和服务率。基于上述动态输入率和动态服务率,建立了依赖系统当前状态的状态转移过程,从状态转换强度方面优化了排队理论及其度量模型,同时,设计了结合系统实际的后确定法求解动态输入率与服务率的相关参数,从而构建了扩展M/M/c模型。由于输入率和服务率的动态性,扩展M/M/c模型具有比原排队论模型更广的适用范围和精度更高的模拟结果。最后,通过一个生活实例对新模型的有效性和实用性进行验证。

关键词: M/M/c模型, 动态输入率, 动态服务率, 状态转移, 后确定法