Using a birth‐and‐death process to estimate the steady‐state distribution of a periodic queue

If the number of customers in a queueing system as a function of time has a proper limiting steady‐state distribution, then that steady‐state distribution can be estimated from system data by fitting a general stationary birth‐and‐death (BD) process model to the data and solving for its steady‐state distribution using the familiar local‐balance steady‐state equation for BD processes, even if the actual process is not a BD process. We show that this indirect way to estimate the steady‐state distribution can be effective for periodic queues, because the fitted birth and death rates often have special structure allowing them to be estimated efficiently by fitting parametric functions with only a few parameters, for example, 2. We focus on the multiserver M_t/GI/s queue with a nonhomogeneous Poisson arrival process having a periodic time‐varying rate function. We establish properties of its steady‐state distribution and fitted BD rates. We also show that the fitted BD rates can be a useful diagnostic tool to see if an M_t/GI/s model is appropriate for a complex queueing system. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 664–685, 2015     

FORECASTING SERIES CONTAINING OFFSETTING BREAKS: OLD SCHOOL AND NEW SCHOOL METHODS OF FORECASTING TRANSNATIONAL TERRORISM

Transnational terrorism data are difficult to forecast because they contain an unknown number of structural breaks of unknown functional form. The rise of religious fundamentalism, the demise of the Soviet Union, and the rise of al Qaeda have changed the nature of transnational terrorism. ‘Old School’ forecasting methods simply smooth or difference the data. ‘New School’ methods use estimated break dates to control for regime shifts when forecasting. We compare the various forecasting methods using a Monte Carlo study with data containing different types of breaks. The study's results are used to forecast various types of transnational terrorist incidents.     

The impact of defense and non‐defense public spending on growth in Asia and Latin America∗

For a three‐sector Feder‐Ram framework, we present time‐series, cross‐sectional estimates for two cohorts, consisting of Asian and Latin American countries. The estimates indicate that private investment, and defense and non‐defense public spending are growth promoting for alternative error components representations. For the best error components representation, greater growth enhancement is associated with the two forms of public spending in Asia than in Latin America, while the opposite comparison characterizes private investment. Although defense is growth promoting, an opportunity cost exists insofar as non‐defense spending, financed by defense spending, appears to give a small net boost to growth in Latin America.     

Joint pricing,assortment, and inventory decisions for a retailer's product line

Consider a set of product variants that are differentiated by some secondary attributes such as flavor, color, or size. The retailer's problem is to jointly determine the set of variants to include in her product line (“assortment”), together with their prices and inventory levels, so as to maximize her expected profit. We model the consumer choice process using a multinomial logit choice model and consider a newsvendor type inventory setting. We derive the structure of the optimal assortment for some important special cases, including the case of horizontally differentiated items, and propose a dominance relationship for the general case that simplifies the search for an optimal assortment. We also discuss structural properties of the optimal prices. Finally, motivated by our analytical results, we propose a heuristic solution procedure, which is shown to be quite effective through a numerical study. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Bayesian inference for a Lanchester type combat model

We undertake inference for a stochastic form of the Lanchester combat model. In particular, given battle data, we assess the type of battle that occurred and whether or not it makes any difference to the number of casualties if an army is attacking or defending. Our approach is Bayesian and we use modern computational techniques to fit the model. We illustrate our method using data from the Ardennes campaign. We compare our results with previous analyses of these data by Bracken and Fricker. Our conclusions are somewhat different to those of Bracken. Where he suggests that a linear law is appropriate, we show that the logarithmic or linear‐logarithmic laws fit better. We note however that the basic Lanchester modeling assumptions do not hold for the Ardennes data. Using Fricker's modified data, we show that although his “super‐logarithmic” law fits best, the linear, linear‐logarithmic, and logarithmic laws cannot be ruled out. We suggest that Bayesian methods can be used to make inference for battles in progress. We point out a number of advantages: Prior information from experts or previous battles can be incorporated; predictions of future casualties are easily made; more complex models can be analysed using stochastic simulation techniques. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 541–558, 2000     

Economic design of a two-stage control chart based on both performance and surrogate variables

The traditional approach to economic design of control charts is based on the assumption that a process is monitored using only a performance variable. If, however, the performance variable is costly to measure and a less expensive surrogate variable is available, the process may be more efficiently controlled by using both performance and surrogate variables. In this article we propose a model for economic design of a two-stage control chart which uses a highly correlated surrogate variable together with a performance variable. The process is assumed to be monitored by the surrogate variable until it signals out-of-control behavior, then by the performance variable until it signals out-of-control behavior or maintains in-control signals for a prespecified amount of time, and the two variables are used in alternating fashion. An algorithm based on the direct search method of Hooke and Jeeves [6] is used to find the optimum values of design parameters. The proposed model is applied to the end-closure welding process for nuclear fuel to compute the amount of reduction in cost compared with the current control procedure. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 958–977, 1999     

Interdiction models for delaying adversarial attacks against critical information technology infrastructure

Information technology (IT) infrastructure relies on a globalized supply chain that is vulnerable to numerous risks from adversarial attacks. It is important to protect IT infrastructure from these dynamic, persistent risks by delaying adversarial exploits. In this paper, we propose max‐min interdiction models for critical infrastructure protection that prioritizes cost‐effective security mitigations to maximally delay adversarial attacks. We consider attacks originating from multiple adversaries, each of which aims to find a “critical path” through the attack surface to complete the corresponding attack as soon as possible. Decision‐makers can deploy mitigations to delay attack exploits, however, mitigation effectiveness is sometimes uncertain. We propose a stochastic model variant to address this uncertainty by incorporating random delay times. The proposed models can be reformulated as a nested max‐max problem using dualization. We propose a Lagrangian heuristic approach that decomposes the max‐max problem into a number of smaller subproblems, and updates upper and lower bounds to the original problem via subgradient optimization. We evaluate the perfect information solution value as an alternative method for updating the upper bound. Computational results demonstrate that the Lagrangian heuristic identifies near‐optimal solutions efficiently, which outperforms a general purpose mixed‐integer programming solver on medium and large instances.     

Fire truck relocation during major incidents

The effectiveness of a fire department is largely determined by its ability to respond to incidents in a timely manner. To do so, fire departments typically have fire stations spread evenly across the region, and dispatch the closest truck(s) whenever a new incident occurs. However, large gaps in coverage may arise in the case of a major incident that requires many nearby fire trucks over a long period of time, substantially increasing response times for emergencies that occur subsequently. We propose a heuristic for relocating idle trucks during a major incident in order to retain good coverage. This is done by solving a mathematical program that takes into account the location of the available fire trucks and the historic spatial distribution of incidents. This heuristic allows the user to balance the coverage and the number of truck movements. Using extensive simulation experiments we test the heuristic for the operations of the Fire Department of Amsterdam‐Amstelland, and compare it against three other benchmark strategies in a simulation fitted using 10 years of historical data. We demonstrate substantial improvement over the current relocation policy, and show that not relocating during major incidents may lead to a significant decrease in performance.     

多平台多目标运动建模与仿真

针对现代战场环境下多平台多目标运动的特点,建立了各种机动、非机动目标运动模型,主要有蛇形机动、转弯和导弹比例导引等几种常见运动模型,并运用Matlab软件分别对其进行了计算机仿真。仿真结果表明,建立的数学模型与实际的目标运动基本是吻合的,可以用来描述目标的运动。     

基于Kullback-Leibler距离离散度的加权代理模型

复杂系统的仿真通常具有高维度、高计算量等特点，代理模型因其明晰的数学表达和良好的计算特性可用于逼近真实系统。加权模型对比单个代理模型来说，其稳定性和适应性更广。不同的代理模型其性能不一，根据特定指标，可以构造最优加权代理模型。基于代理模型预测分布以及Kullback-Leibler距离构造各子代理模型之间的离散度，并提出一种新的权函数构造方法。算例表明，该方法与最优子模型的精度相当，同时能提高对真实响应分布的逼近。