连续时间完全-限定(K=2)两级轮询系统性能分析

Performance Analysis of Continuous Time Exhaustive-limited(K=2)Two-level Polling System

为了实现区分网络优先级、保证公平性、提高普通站点的性能和效率,在完全-限定(K=1)两级轮询控制系统模型的基础上,提出连续时间完全-限定(K=2)两级轮询控制系统模型。在该模型中,使用限定(K=2)服务和完全服务分别对普通站点和中心站点进行服务。中心站点转换到普通站点进行服务时,使用捎带查询方式。在此基础上,采用马尔可夫链和概率母函数的数学方法建立该轮询系统模型,并推导平均排队队长和时延。利用MATLAB进行仿真实验,结果表明:理论值与仿真值误差较小,验证了理论分析的正确性;与门限-完全服务模型相比,该模型中心站点的队长和时延均小于门限-完全服务中心站点的队长和时延,具有更高的优先级;与一级完全服务和一级限定(K=2)服务模型相比,区分了优先级,性能分别提升11.7%和14.5%,说明两级服务远好于一级服务;与完全-限定(K=1)两级服务模型相比,增加了发送的数据,减少了等待时间,性能提升13.04%左右,进一步优化了普通站点的性能。

To achieve differentiated network priorities,ensure fairness,and improve the performance and efficiency of common sites,a continuous time exhaustive-limited(K=2)two-level polling system is proposed based on the exhaustive-limited(K=1)two-level polling control system model.First,this model uses a limited(K=2)service and an exhaustive service for normal and central sites,respectively.Second,a piggyback inquiry is used when the central site is converted into a common site for service.Finally,the Markov chain and probabilistic generating function establish the polling system model and derive the average queue length and time delay.The simulation experiments are conducted using MATLAB.The experimental results show that the error between the theoretical and simulated values is small and consistent,thereby verifying the correctness of the theoretical analysis.Compared with the gated-exhaustive service model,the length and time delay of the central site of the model are smaller than the length and time delay of the gated-exhaustive service central site,indicating that the model has a higher priority.Additionally,compared with the one-level exhaustive service and the one-level limited(K=2)service models,which differentiate priorities,performance is improved by 11.7%and 14.5%respectively,indicating that the two-level service is far better than the one-level service.Furthermore,compared to the exhaustive-limited(K=1)two-level service model,which increases the data sent,the waiting time is reduced and performance is improved by about 13.04%,optimizing the performance of the common site even more.