带启动时间和多重休假的非抢占优先权M/M/c排队

Non-Preemptive Priority M/M/c Queue with Set-up Time and Multiple Vacations

以M/M/c排队模型为依据,主要分析研究带有启动时间和多重休假的非抢占优先权M/M/c排队模型.首先,依据模型描述构造三维马尔科夫过程,并求得转移率矩阵.其次,利用拟生灭过程和矩阵几何解的方法,得到系统的平稳分布,进而求解出一些关键的性能指标.然后,运用数值例子刻画出参数变化对系统性能指标的影响.最后,通过建立个人效益函数和社会效益函数,得到使系统状态达到最优的参数值,从而为系统的资源分配提出合理化的建议.

Based on the M/M/c Queuing Model,this paper mainly analyzes the Non-Preemptive Priority M/M/c Queuing Model with set-up time and multiple vacations.First,construct a three dimension Markov process based on the description of the model,and obtain the matrix of transition rate.Secondly,using the method of quasi birth-and-death process and the matrix-geometric solution,the stationary distribution of the system is obtained,then some pivotal performance indicators are solved.Then,applying numerical examples to depict the effect of the different parameters on system performance indexs.Finally,by means of establishing a personal benefit function and a social benefit function,the parameter values that optimize the state of the system are obtained,thus make reasonable suggestion of resource allocation of the system.