Modeling and Simulation of Missile Defense M/M/N Queueing System

doi:10.16182/j.issn1004731x.joss.201804007

Abstract

Abstract: To simulate the process of ballistic missile defense and to study the effectiveness of defense, the M/M/N queueing system of missile defense was modeled and simulated. A queueing modeling framework was given to explain the meaning and distribution of related parameters. The M/M/N/N and M/M/N/C queueing models were proposed for short defense depth and long defense depth respectively, and the single target channel and the multiple target channels were distinguished in each model. How to deal with the different types of missile defense system based on equivalent replacement method were also considered. Simulation examples verified the main functions and the effectiveness of proposed queueing model which is helpful to understand the rules of missile defense process, and to provide optimal configuration suggestions for defense decision-making.

Key words: ballistic missile defense, defense efficiency, M/M/N, queueing model

CLC Number:

E917

Li Longyue, Liu Fuxian, Zhao Huizhen. Modeling and Simulation of Missile Defense M/M/N Queueing System[J]. Journal of System Simulation, 2018, 30(4): 1260-1271.

References

[1] 李龙跃, 刘付显, 赵麟锋. 对多波次目标直接分配到弹的反导火力规划方法[J]. 系统工程与电子技术, 2014, 36(11): 2206-2211.
LI L Y, LIU F X, ZHAO L F.Direct interceptor allocation method in antimissile firepower planning for multiple wave targets[J]. Systems Engineering and Electronics, 2014, 36(11): 2206-2211.
[2] Nunn W R, Glass D V, Ih-Ching Hsu, et al.Analysis of a layered defense model[J]. Operations Research (S0030-364X), 1982, 30(3): 595-599.
[3] 齐玲辉, 张安, 郭凤娟, 等. 战术弹道导弹系统效能评估SEA法的建模与仿真[J]. 系统仿真学报, 2013, 25(4): 795-799.
QI L H, ZHANG A, GUO F J, et al.Modeling and simulation of sea method for effectiveness analysis of tactical ballistic missile system[J]. Journal of System Simulation, 2013, 25(4): 795-799.
[4] Erlang A K.The theory of probabilities and telephone conversations[J]. Nyt Tidsskrift for Matematik B,(S0909-3524), 1909, 20: 33-39.
[5] Pinedo M, Reed J.The “least flexible job first” rule in scheduling and in queueing[J]. Operations Research Letters (S0167-6377), 2013, 41(6): 618-621.
[6] Claus Gwiggner, Sakae Nagaoka.Data and queueing analysis of a Japanese air-traffic flow[J]. European Journal of Operational Research (S0377-2217), 2014, 235(1): 265-275.
[7] Sai Rajesh Mahabhashyam, Natarajan Gautam, Soundar R T Kumara. Resource-sharing queueing systems with fluid-flow traffic[J]. Operations Research (S0030-364X), 2008, 56(3): 728-744.
[8] Hou I-Hong, Kumar P R.Queueing systems with hard delay constraints: a framework for real-time communication over unreliable wireless channels[J]. Queueing Systems (S0257-0130), 2012, 71(1/2): 151-177.
[9] 曹雷, 董强, 彭伟, 等. 基于排队论的导弹防御系统的效能分析[J]. 南京理工大学学报, 2011, 35(4): 470-474.
CAO L, DONG Q, PENG W, et al.Effectiveness evaluation of ballistic missile defense system based on queuing theory[J]. Journal of Nanjing University of Science and Technology, 2011, 35(4): 470-474.
[10] Li L Y, Liu F X, Long G Z, etc. Intercepts allocation for layered defense[J]. Journal of Systems Engineering and Electronics (S004-4132), 2016, 27(3): 602-611.
[11] 赵晨光, 李为民, 聂成, 等. 利用排队论探讨多层拦截巡航导弹的问题[J]. 系统工程与电子技术, 2003, 25(2): 177-178.
ZHAO C G, LI W M, NIE C, et al.Discussing on multiplayer defense cruise missile by use of queuing theory[J]. Systems Engineering and Electronics, 2003, 25(2): 177-188.
[12] Li L Y, Liu F X, Long G Z, et al.Performance analysis and optimal allocation of layered defense m/m/n queueing systems[J]. Mathematical Problems in Engineering (S1024-123X), 2016, (5): 1-21.
[13] Vanberkel P T, Boucherie R J, Hans E W, et al.Optimizing the strategic patient mix combining queueing theory and dynamic programming[J]. Computers and Operations Research (S0305-0548), 2014, 43(3): 271-279.
[14] 刘建永. 运筹学算法与编程实现-Delphi实现[M]. 北京: 清华大学出版社, 2004.
LIU J Y.Algorithm and Programming Implementation of Operational Research-Based on Delphi [M]. Beijing: Tsinghua University Press, 2004.
[15] 来斌, 牛存良, 熊友奇. 防空作战模拟与效能评估[M]. 北京: 军事科学出版社, 2005.
LAI B, NIU C L, XIONG Y Q.Simulation and Effectiveness Evaluation of Air Defense Combat [M]. Beijing: Military Science Press, 2005.
[16] 陈绍顺, 张琳. 不同类型防空武器多层防御部署分析[J]. 情报指挥控制系统与仿真技术, 2005, 27(4): 49-52.
CHEN S S, ZHANG L.Analysis on Multiplayer Defense of the Different Types of Air-Defense Weapons’ Disposition[J]. Information Command Control System & Simulation Technology, 2005, 27(4): 49-52.