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.
Highlights
These years, ballistic missile (BM) technology has spread to more and more countries
Let n be the number of target channels of Ballistic Missile Defense System (BMDS); that is, the number of BMs shot by defense weapons cannot exceed n at the same time; Pf is the detection probability of BMDS radars
Let E(M,n(M)) be the Defense Effectiveness (DE) of the M-layer BMDS; n(M) = (n1, n2, . . . , nM) is the allocation plan, ni is the number of target channels deployed along the ith layer, and let n1 = n2 = ⋅ ⋅ ⋅ = nM
Summary
These years, ballistic missile (BM) technology has spread to more and more countries. (2) Suppose that the BMs are shot in the order of their arrivals; the shooting time for a BM is exponentially distributed at rate μ; its probability density function and distribution function are. Let n be the number of target channels of BMDS; that is, the number of BMs shot by defense weapons cannot exceed n at the same time; Pf is the detection probability of BMDS radars. Sk means k target channels are busy, and the state is transferred from lower state to higher state when new BMs arrive. For different types of defense weapons, the waiting time of BMs, the detection probability of radars, and SSKP may be different.
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