A characterization of the wald distribution

Suppose X is a random variable having an absolutely continuous distribution function F(x). We assume that F(x) has the Wald distribution. A relation between the probability density function of X⁻¹ with that of X is used to characterize the Wald distribution.     

Involving the elephant: technical isolation and the role of India in a possible solution to the Iranian nuclear crisis

Apart from North Korea, no state's nuclear program in the twenty-first century has raised more concern to international security than Iran's. While Iran insists that its nuclear program is strictly for civilian purpose in line with Article IV of non-proliferation treaty, the USA and its allies insist that Iran has military intentions and called for sanctions. The failure of sanctions to deter Iran from its nuclear agenda had made many scholars and policy-makers call for a preemptive attack on Iranian nuclear facilities. Situated within this debate, this paper positions itself as an antagonist to the preemptive airstrike option and argues that involving India in a possible nuclear “iron curtain” against Iran – a move known as technical isolation – remains the best option to the current nuclear crises.     

Models for multi-item continuous review inventory policies subject to constraints

Models are formulated for determining continuous review (Q, r) policies for a multiitem inventory subject to constraints. The objective function is the minimization of total time-weighted shortages. The constraints apply to inventory investment and reorder workload. The formulations are thus independent of the normal ordering, holding, and shortage costs. Two models are presented, each representing a convex programming problem. Lagrangian techniques are employed with the first, simplified model in which only the reorder points are optimized. In the second model both the reorder points and the reorder quantities are optimized utilizing penalty function methods. An example problem is solved for each model. The final section deals with the implementation of these models in very large inventory systems.     

An engagement model to optimize defense against a multiple attack assuming perfect kill assessment

We present an air-defense engagement model to counter an attack by multiple antiship missiles, assuming perfect kill assessment. In this model, the probability of shooting down all incoming missiles is maximized. A generating function is employed to produce an algorithm which is used to evaluate the outcomes. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 687–697, 1997     

Analysis of a finite‐buffer bulk‐service queue with discrete‐Markovian arrival process: D‐MAP/Ga,b/1/N

Discrete‐time queues with D‐MAP arrival process are more useful in modeling and performance analysis of telecommunication networks based on the ATM environment. This paper analyzes a finite‐buffer discrete‐time queue with general bulk‐service rule, wherein the arrival process is D‐MAP and service times are arbitrarily and independently distributed. The distributions of buffer contents at various epochs (departure, random, and prearrival) have been obtained using imbedded Markov chain and supplementary variable methods. Finally, some performance measures such as loss probability and average delay are discussed. Numerical results are also presented in some cases. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 345–363, 2003.     

Extrapolation of the mean lifetime of a large population from its preliminary survival history

A large population of independent identical units having finite mean lifetime T is observed. From the history A(y) of cumulative arrivals and the history B(y) of cumulative removals in the interval 0 ≦ y ≦ τ one must predict at time τ the desired T . Two lifetime predictors X(τ) and Y(τ) and related simple predictors obtained from A(y) and B(y) are shown to converge to T with a rate of convergence dependent on the structure of the failure rate function of the units. This dependence is studied theoretically and numerically.     

Stochastic control of queueing systems

Suppose that the state of a queueing system is described by a Markov process { Y_t, t ≥ 0}, and the profit from operating it up to a time t is given by the function f(Y_t). We operate the system up to a time T, where the random variable T is a stopping time for the process Yt. Optimal stochastic control is achieved by choosing the stopping time T that maximizes Ef(Y_T) over a given class of stopping times. In this paper a theory of stochastic control is developed for a single server queue with Poisson arrivals and general service times.     

An infiltration game with time dependent payoff

The problem of assigning patrol boats, subject to resource constraints, to capture or delay an infiltrator with perishable contraband attempting escape across a long, narrow strait is formulated as a two-sided time sequential game. Optimal mixed strategies are derived for the situation of one patrol boat against one smuggler. Procedures for obtaining numerical solutions for R > 1 patrol boats are discussed.     

Minimizing the sum of absolute lateness in single-machine and multimachine scheduling

Kanet addressed the problem of scheduling n jobs on one machine so as to minimize the sum of absolute lateness under a restrictive assumption on their common due date. This article extends the results to the problem of scheduling n jobs on m parallel identical processors in order to minimize the sum of absolute lateness. Also, a heuristic algorithm for a more general version with no restriction on the common due date, for the problem of n-job single-machine scheduling is presented and its performance is reported.     

Sensor placement in active multistatic sonar networks

The idea of deploying noncollocated sources and receivers in multistatic sonar networks (MSNs) has emerged as a promising area of opportunity in sonar systems. This article is one of the first to address point coverage problems in MSNs, where a number of points of interest have to be monitored in order to protect them from hostile underwater assets. We consider discrete “definite range” sensors as well as various diffuse sensor models. We make several new contributions. By showing that the convex hull spanned by the targets is guaranteed to contain optimal sensor positions, we are able to limit the solution space. Under a definite range sensor model, we are able to exclude even more suboptimal solutions. We then formulate a nonlinear program and an integer nonlinear program to express the sensor placement problem. To address the nonconvex single‐source placement problem, we develop the Divide Best Sector (DiBS) algorithm, which quickly provides an optimal source position assuming fixed receivers. Starting with a basic implementation of DiBS, we show how incorporating advanced sector splitting methods and termination conditions further improve the algorithm. We also discuss two ways to use DiBS to find multiple source positions by placing sensors iteratively or simultaneously. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 287–304, 2017