连续时间完全服务与门限服务两级轮询系统性能研究
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摘要
在信息分组以连续时间规律到达系统的基础上,对于轮询系统中不同优先级的业务问题,提出区分优先级的两级轮询服务模型。首先,在该模型中,低优先级站点采用门限服务,高优先级站点采用完全服务;然后,在高优先级转低优先级时,将传输服务与转移查询并行处理来降低服务器在查询转换期间所耗费的时间,提高轮询系统的效率;最后,运用马尔可夫链和概率母函数的方法建立了系统的数学模型,通过对数学模型精确解析,得到了连续时间两级服务系统每个站点的平均排队队长和平均等待时间的表达式,精确解析出平均排队队长和平均等待时间的值。仿真实验结果表明:理论计算值与实验仿真值近似相等,说明理论分析正确合理。该模型既能保障低优先级站点服务质量,又能为高优先级站点提供优质服务。
For the fact that information groups arrive at the system in a continuous time, a two-level polling service model with different priorities was proposed for the business problems of different priorities in the polling system. Firstly, gated service was used in sites with low priority, and exhaustive service was used in sites with high priority. Then, when high priority turned into low priority, the transmission service and the transfer query were processed in parallel to reduce the time cost of server during query conversion, improving the efficiency of polling system. Finally, the mathematical model of system was established by using Markov chain and probabilistic parent function. By accurately analyzing the mathematical model, the expressions of average queue length and average waiting time of each station of continuous-time two-level service system were obtained. The simulation results show that the theoretical calculation value was approximately equal to the experimental simulation value, indicating that the theoretical analysis is correct and reasonable. The model provides high-quality services for high-priority sites while maintaining the quality of services in low-priority sites.
For the fact that information groups arrive at the system in a continuous time, a two-level polling service model with different priorities was proposed for the business problems of different priorities in the polling system. Firstly, gated service was used in sites with low priority, and exhaustive service was used in sites with high priority. Then, when high priority turned into low priority, the transmission service and the transfer query were processed in parallel to reduce the time cost of server during query conversion, improving the efficiency of polling system. Finally, the mathematical model of system was established by using Markov chain and probabilistic parent function. By accurately analyzing the mathematical model, the expressions of average queue length and average waiting time of each station of continuous-time two-level service system were obtained. The simulation results show that the theoretical calculation value was approximately equal to the experimental simulation value, indicating that the theoretical analysis is correct and reasonable. The model provides high-quality services for high-priority sites while maintaining the quality of services in low-priority sites.
引文
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[2] BOON M A A,VANDERMEI R D,WINANDS E M M.Applications of polling systems[J].Surveys in Operations Research and Management Science,2011,16(2):67-82.
[3] BOXMA O J,KELLA O,KOSINSKI K M.Queue lengths and workloads in polling systems[J].Operations Research Letters,2011,39(6):401-405.
[4] CHU Y Q,LIU Z M.The impact of priority policy in a two-queue Markovian polling system with multi-class priorities[C]// Proceedings of the 12th International Conference on Queueing Theory and Network Applications.Berlin:Springer,2017:282-296.
[5] 孙洋洋,杨志军.无线传感器网络轮询系统分析研究[J].电子测量技术,2018,41(15):100-104.(SUN Y Y,YANG Z J.Analysis and research of wireless sensor network polling system[J].Electronic Measurement Technology,2018,41(15):100-104.)
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[7] 冉文学,余丽艳.普洱茶配送中心订单分拣完全—并行门限二级轮询控制机理研究[J].物流工程与管理,2018,40(7):77-81.(RAN W X,YU L Y.Study on complete-parallel threshold polling control mechanism about order-sorting of Pu'er tea distribution center[J].Logistics Engineering and Management,2018,40(7):77-81.)
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[9] 刘龙军,丁洪伟,柳虔林,等.基于现场可编程门阵列战术数据链中优先级轮询接入控制协议的研究[J].兵工学报,2017,38(2):305-312.(LIU L J,DING H W,LIU Q L,et al.Research on priority polling access control protocol in FPGA-based tactical data link[J].Acta Armamentarii,2017,38(2):305-312.)
[10] 孔维东,王永斌,刘宏波.基于排队论模型的轮询协议数据链系统时延分析[J].火力与指挥控制,2017,42(3):100-103.(KONG W D,WANG Y B,LIU H B.Research on time delay of polling protocol data link based on queuing theory model[J].Fire Control and Command Control,2017,42(3):100-103.)
[11] 杨志军,苏杨,丁洪伟.完全服务和非对称门限服务两级轮询系统特性分析[J].自动化学报,2018,44(12):2228-2237.(YANG Z J,SU Y,DING H W.Analysis of two-level polling system characteristics of exhaustive service and asymmetrically gated service[J].Acta Automatica Sinica,2018,44(12):2228-2237.)
[12] 杨志军,孙洋洋.分忙闲站点的限定(K=2)轮询控制系统分析研究[J].计算机科学,2018,45(11):70-74.(YANG Z J,SUN Y Y.Analysis and study on limited (K=2) polling control system with busy and idle sites[J].Computer Science,2018,45(11):70-74.)
[13] YANG Z J,SUN Y Y,GAN J H.New polling scheme based on busy/idle queues mechanism[J].International Journal of Performability Engineering,2018,14(10):2522-2531.
[14] KIM J,KIM B.Stability of a cyclic polling system with an adaptive mechanism[J].Journal of Industrial and Management Optimization,2015,11(3):763-777.
[15] 官铮,杨志军,何敏,等.依托站点状态的两级轮询控制系统时延特性分析[J].自动化学报,2016,42(8):1207-1214.(GUAN Z,YANG Z J,HE M,et al.Study on the delay performance of station dependent two-level polling systems[J].Acta Automatica Sinica,2016,42(8):1207-1214.)
[16] 木文浩,保利勇,丁洪伟,等.离散时间闸门式多级门限服务的两级优先级轮询排队系统分析[J].电子学报,2018,46(2):276-280.(MU W H,BAO L Y,DING H W,et al.An exact analysis of discrete time two-level priority polling system based on multi-times gated service policy[J].Acta Electronica Sinica,2018,46(2):276-280.)
[17] SIDDIQUI S,GHANI S,KHAN A A.ADP-MAC:an adaptive and dynamic polling-based mac protocol for wireless sensor networks[J].IEEE Sensors Journal,2018,18(2):860-874.
[2] BOON M A A,VANDERMEI R D,WINANDS E M M.Applications of polling systems[J].Surveys in Operations Research and Management Science,2011,16(2):67-82.
[3] BOXMA O J,KELLA O,KOSINSKI K M.Queue lengths and workloads in polling systems[J].Operations Research Letters,2011,39(6):401-405.
[4] CHU Y Q,LIU Z M.The impact of priority policy in a two-queue Markovian polling system with multi-class priorities[C]// Proceedings of the 12th International Conference on Queueing Theory and Network Applications.Berlin:Springer,2017:282-296.
[5] 孙洋洋,杨志军.无线传感器网络轮询系统分析研究[J].电子测量技术,2018,41(15):100-104.(SUN Y Y,YANG Z J.Analysis and research of wireless sensor network polling system[J].Electronic Measurement Technology,2018,41(15):100-104.)
[6] 苏杨,杨志军,丁阳洋,等.无线传感器网络中轮询系统控制的实现[J].电子测量技术,2018,41(4):66-70.(SU Y,YANG Z J,DING Y Y,et al.Implementation of polling system control in wireless sensor networks[J].Electronic Measurement Technology,2018,41(4):66-70.)
[7] 冉文学,余丽艳.普洱茶配送中心订单分拣完全—并行门限二级轮询控制机理研究[J].物流工程与管理,2018,40(7):77-81.(RAN W X,YU L Y.Study on complete-parallel threshold polling control mechanism about order-sorting of Pu'er tea distribution center[J].Logistics Engineering and Management,2018,40(7):77-81.)
[8] 冉文学,刘会娟,余丽艳.连续物料订单分拣完全-并行限定(k=1)轮询控制机理[J].中国管理科学,2018,26(8):86-93.(RAN W X,LIU H J,YU L Y.Continuity material order sorting based on the polling control mechanism of exhaustive parallel limited- 1[J].Chinese Journal of Management Science,2018,26(8):86-93.)
[9] 刘龙军,丁洪伟,柳虔林,等.基于现场可编程门阵列战术数据链中优先级轮询接入控制协议的研究[J].兵工学报,2017,38(2):305-312.(LIU L J,DING H W,LIU Q L,et al.Research on priority polling access control protocol in FPGA-based tactical data link[J].Acta Armamentarii,2017,38(2):305-312.)
[10] 孔维东,王永斌,刘宏波.基于排队论模型的轮询协议数据链系统时延分析[J].火力与指挥控制,2017,42(3):100-103.(KONG W D,WANG Y B,LIU H B.Research on time delay of polling protocol data link based on queuing theory model[J].Fire Control and Command Control,2017,42(3):100-103.)
[11] 杨志军,苏杨,丁洪伟.完全服务和非对称门限服务两级轮询系统特性分析[J].自动化学报,2018,44(12):2228-2237.(YANG Z J,SU Y,DING H W.Analysis of two-level polling system characteristics of exhaustive service and asymmetrically gated service[J].Acta Automatica Sinica,2018,44(12):2228-2237.)
[12] 杨志军,孙洋洋.分忙闲站点的限定(K=2)轮询控制系统分析研究[J].计算机科学,2018,45(11):70-74.(YANG Z J,SUN Y Y.Analysis and study on limited (K=2) polling control system with busy and idle sites[J].Computer Science,2018,45(11):70-74.)
[13] YANG Z J,SUN Y Y,GAN J H.New polling scheme based on busy/idle queues mechanism[J].International Journal of Performability Engineering,2018,14(10):2522-2531.
[14] KIM J,KIM B.Stability of a cyclic polling system with an adaptive mechanism[J].Journal of Industrial and Management Optimization,2015,11(3):763-777.
[15] 官铮,杨志军,何敏,等.依托站点状态的两级轮询控制系统时延特性分析[J].自动化学报,2016,42(8):1207-1214.(GUAN Z,YANG Z J,HE M,et al.Study on the delay performance of station dependent two-level polling systems[J].Acta Automatica Sinica,2016,42(8):1207-1214.)
[16] 木文浩,保利勇,丁洪伟,等.离散时间闸门式多级门限服务的两级优先级轮询排队系统分析[J].电子学报,2018,46(2):276-280.(MU W H,BAO L Y,DING H W,et al.An exact analysis of discrete time two-level priority polling system based on multi-times gated service policy[J].Acta Electronica Sinica,2018,46(2):276-280.)
[17] SIDDIQUI S,GHANI S,KHAN A A.ADP-MAC:an adaptive and dynamic polling-based mac protocol for wireless sensor networks[J].IEEE Sensors Journal,2018,18(2):860-874.