Aiming at the problem of fast charging queuing of UAV swarming, this paper, for the first time, proposes to use the average queueing length and the average waiting time as the evaluation indicators for UAV swarming charging queuing. Through theoretical analysis and numerical calculation, the charging queuing methods of distributed charging and concentrated charging are compared under the condition of multiple charging platforms. We discover that an intersection appears in the curves corresponding to the evaluation indicators with the increase of service intensity when UAV swarming meets the Poisson condition. Before the intersection of the curves, the service intensity is weak, and the method of concentrated charging is better than distributed charging. After the intersection, with the increase of service intensity, the method of distributed charging gradually becomes better than concentrated charging. This paper provides a fast charging queuing solution which helps UAV swarming complete tasks efficiently.
[1] 王荣巍, 何锋, 周璇, 等. 面向无人机蜂群的航电云多层任务调度模型[J].航空学报, 2019, 40(11):323183. WANG R W, HE F, ZHOU X, et al. Avionics cloud multi-layer task scheduling model for UAV swarm[J].Acta Aeronautica et Astronautica Sinica, 2019, 40(11):323183(in Chinese).
[2] 吕娜, 刘创, 陈柯帆, 等. 一种面向航空集群的集中控制式网络部署方法[J].航空学报, 2018, 39(7):321961. LYU N, LIU C, CHEN K F, et al. A method for centralized control network deployment of aeronautic swarm[J].Acta Aeronautica et Astronautica Sinica, 2018, 39(7):321961(in Chinese).
[3] 陈方舟, 黄靖皓, 赵阳辉. 美军无人"蜂群"作战技术发展分析[J].装备学院学报, 2016, 27(2):34-37. CHEN F Z, HUANG J H, ZHAO Y H. Analysis on unmanned swarm flighting system of U.S. armed forces[J].Journal of Equipment Academy, 2016, 27(2):34-37(in Chinese).
[4] 李如琦, 苏浩益. 基于排队论的电动汽车充电设施优化配置[J].电力系统自动化, 2011, 35(14):58-61. LI R Q, SU H Y. Optimal allocation of charging facilities for electric vehicles based on queuing theory[J].Automation of Electric Power Systems, 2011, 35(14):58-61(in Chinese).
[5] HAFEZ O, BHATTACHARYA K. Queuing analysis based PEV load modeling considering battery charging behavior and their impact on distribution system operation[J].IEEE Transactions on Smart Grid, 2018, 9(1):261-273.
[6] BAE S, KWASINSKI A. Spatial and temporal model of electric vehicle charging demand[J].IEEE Transactions on Smart Grid, 2012, 3(1):394-403.
[7] 张维戈, 陈连福, 黄彧, 等. M/G/k排队模型在电动出租汽车充电站排队系统中的应用[J].电网技术, 2015,39(3):724-729. ZHANG W G, CHEN L F, HUANG Y, et al. Application of M/G/k queuing model in queuing system of electric taxi charging station[J].Power System Technology, 2015, 39(3):724-729(in Chinese).
[8] 冯亮. 电动汽车充电站规划研究[D]. 天津:天津大学, 2013:70-96. FENG L. Electric vehicle charging station planning[D]. Tianjin:Tianjin University, 2013:70-96(in Chinese).
[9] 熊虎, 向铁元, 祝勇刚, 等. 电动汽车公共充电站布局的最优规划[J].电力系统自动化, 2012, 36(23):65-70. XIONG H, XIANG T Y, ZHU Y G, et al. Electric vehicle public charging stations location optimal planning[J].Automation of Electric Power Systems, 2012, 36(23):65-70(in Chinese).
[10] 卢芳. 基于排队论的电动汽车充电站选址定容研究[D]. 北京:北京交通大学, 2015:11-42. LU F. The location-sizing problem of electric vehicle charging station deployment based on queuing theory[D]. Beijing:Beijing Jiaotong University, 2015:11-42(in Chinese).
[11] 葛少云, 冯亮, 刘洪, 等. 考虑车流信息与配电网络容量约束的充电站规划[J].电网技术, 2013, 37(3):582-589. GE S Y, FENG L, LIU H, et al. Planning of charging stations considering traffic flow and capacity constraints of distribution network[J].Power System Technology, 2013, 37(3):582-589(in Chinese).
[12] 赵玉荣, 高超, 方明. M/M/1/m系统算子的本征值特性(m=1,2,3,4)[J].数学的实践与认识, 2010, 40(16):184-187. ZHAO Y R, GAO C, FANG M. The characteristic of eigenvalue of M/M/1/m[J].Mathematics in Practice and Theory, 2010, 40(16):184-187(in Chinese).
[13] 毛云峰. 基于M/M/n/m模型网上报名系统连接池优化研究[D]. 昆明:昆明理工大学, 2017:27-38. MAO Y F. Research on optimization of connection pool of online registration system based on M/M/n/m model[D]. Kunming:Kunming University of Science and Technology, 2017:27-38(in Chinese).
[14] 黄业文, 邝神芬. 非强占有限优先权M/M/n/m排队系统[J].应用概率统计, 2018, 34(4):364-380. HUANG Y W, KUANG S F. M/M/n/m queuing model under nonpreemptive limited-priority[J].Chinese Journal of Applied and Statistics, 2018, 34(4):364-380(in Chinese).
[15] 蔡金兵. 两类服务率可变的M/M/n/m排队模型及应用研究[D]. 重庆:重庆师范大学, 2010:15-23. CAI J B. Two kind of servicing rate invariable M/M/n/m queuing model and applied research[D]. Chongqing:Chongqing Normal University, 2010:15-23(in Chinese).
[16] 唐玉玉. 具有可变输入率且有优先权的M/M/n/m排队模型研究[D]. 重庆:重庆师范大学, 2012:19-47. TANG Y Y. The research of M/M/n/m queuing system with variable input rate and the priority[D]. Chongqing:Chongqing Normal University, 2012:19-47(in Chinese).
[17] 唐加山. 排队论及其应用[M]. 北京:科学出版社, 2016:1-20. TANG J S. Queuing theory and its application[M]. Beijing:Science Press, 2016:1-20(in Chinese).
[18] KENDALL, DAVID G. Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain[J].The Annals of Mathematical Statistics, 1953, 24(3):338-354.
[19] 归敏丹, 蒋毅飞, 张志敏, 等. 多服务员时两种等待队列性能的比较[J].计算机工程与应用, 2008(13):44-46,66. GUI M D, JIANG Y F, ZHANG Z M, et al. Comparison of two queuing models with multiple servers[J].Computer Engineering and Applications, 2008(13):44-46,66(in Chinese).
[20] LITTLE, JOHN D C. A proof for the queuing formula:L=λW[J].Operations Research, 1961, 9(3):383-387.
[21] WHITT W. A review of L=λW and extensions[J].Queueing Systems, 1991, 9(3):235-268.
CJA