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Mathematical Problems in Engineering
Volume 2016, Article ID 5915918, 21 pages
http://dx.doi.org/10.1155/2016/5915918
Research Article

Performance Analysis and Optimal Allocation of Layered Defense M/M/N Queueing Systems

1Air and Missile Defense College, Air Force Engineering University, Xi’an 710051, China
2Chongqing Nankai Secondary School, Chongqing 400030, China

Received 9 May 2016; Accepted 3 October 2016

Academic Editor: Anna Pandolfi

Copyright © 2016 Longyue Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

One important mission of strategic defense is to develop an integrated layered Ballistic Missile Defense System (BMDS). Motivated by the queueing theory, we presented a work for the representation, modeling, performance simulation, and channels optimal allocation of the layered BMDS M/M/N queueing systems. Firstly, in order to simulate the process of defense and to study the Defense Effectiveness (DE), we modeled and simulated the M/M/N queueing system of layered BMDS. Specifically, we proposed the M/M/N/N and M/M/N/C queueing model for short defense depth and long defense depth, respectively; single target channel and multiple target channels were distinguished in each model. Secondly, we considered the problem of assigning limited target channels to incoming targets, we illustrated how to allocate channels for achieving the best DE, and we also proposed a novel and robust search algorithm for obtaining the minimum channel requirements across a set of neighborhoods. Simultaneously, we presented examples of optimal allocation problems under different constraints. Thirdly, several simulation examples verified the effectiveness of the proposed queueing models. This work may help to understand the rules of queueing process and to provide optimal configuration suggestions for defense decision-making.