On the bivariate negative binomial distribution of mitchell and paulson

The bivariate negative binomial distribution of Mitchell and Paulson [17] for the case b = c = 0 is shown to be equivalent to the accident proneness model of Edwards and Gurland [4] and Subrahmaniam [19,20]. The diagonal series expansion of its joint probability function is then derived. Two other formulations of this distribution are also considered: (i) as a mixture model, which showed how it arises as the discrete analogue to the Wicksell-Kibble bivariate gamma distribution, and (ii) as a consequence of the linear birth-and-death process with immigration.     

Transient solution of a finite-capacity M/Ga,b/1 queueing system

In this article we consider a single-server, bulk-service queueing system in which the waiting room is of finite capacity. Arrival process is Poisson and all the arrivals taking place when the waiting room is full are lost. The service times are generally distributed independent random variables and the distribution is depending on the batch size being served. Using renewal theory, we derive the time-dependent solution for the system-size probabilities at arbitrary time points. Also we give expressions for the distribution of virtual waiting time in the queue at any time t.     

Note: A local-search heuristic for large set-covering problems

In this note we describe a local-search heuristic (LSH) for large non-unicost set-covering problems (SCPs). The new heuristic is based on the simulated annealing algorithm and uses an improvement routine designed to provide low-cost solutions within a reasonable amount of CPU time. The solution costs associated with the LSH compared very favorably to the best previously published solution costs for 20 large SCPs taken from the literature. In particular, the LSH yielded new benchmark solutions for 17 of the 20 test problems. We also report that, for SCPs where column cost is correlated with column coverage, the new heuristic provides solution costs competitive with previously published results for comparable problems. © 1995 John Wiley & Sons, Inc.     

Ricochet quantification using a multiple sensor approach

This study investigates the ricochet behaviour of three different small-arms projectile types using a novel ricochet measuring device.The results can be used to estimate the danger potential of ricochets on shooting ranges.A ricochet is the change of direction and velocity of a projectile after impacting an oblique surface.This impact produces strong vibrations on a rigid plate.During this impact,flexural waves travel radially outwards from the point of impact.These waves are used to determine the properties of the impactor with accelerometers situated on the target surface.With the use of two measurement plates,one can produce a ricochet and detect the velocity at the same time.Accelerometers are suitable for accurate momentum measurements of single impacts.However,depending upon strike velocity and the impact angle,a ricochet can separate in multiple fragments after being deflected.From the operational safety perspective,these fragments need to be detected,as well.The approach of a coupled sensor concept was chosen to solve this problem.Thermographic sensors were additionally used to visualise the heat which is produced after pene-trating a rubber layer pasted in front of the steel target plate.With this approach one was able to detect the position of impact.The investigations showed that the measurement system performance is better with a multiple sensor design,which includes accelerometers for the velocity,impact strength and partly the position measurement,while the thermographic sensor was used for the position measurement and partly the momentum measurement.The investigated ammunition showed plausible fragmentation behaviour,and the results can already be used to estimate the danger potential of different ammunition types.Frangible projectiles fragment to small particles already after being deflected under a small angle.However,Full Metal Jacket projectiles with or without a steel core do not fragment under angles which are less than 5°.The objective of the paper is to demonstrate the possibility of measuring the complex ricochet me-chanics of small projectiles using standard accelerometers with the adequate signal processing approach.This measuring system is supported by an off the shelf thermographic camera.     

Optimization of steerable sensor network for threat detection

A Markov chain approach to detecting a threat in a given surveillance zone by a network of steerable sensors is presented. The network has a finite number of predetermined states, and transition from one state to another follows a Markov chain. Under the assumption that the threat avoids detection, two game theoretic problems for finding an optimal Markov chain (two surveillance strategies) are formulated: the first maximizes the probability of threat detection for two consecutive detection periods, whereas the second minimizes the average time of detection for the worst‐case threat's trajectory. Both problems are reduced to linear programming, and special techniques are suggested to solve them. For a dynamic environment with moving noise sources, the optimal Markov chain changes at each detection period, and the rate of convergence of the Markov chain to its stationary distribution is analyzed. Both surveillance strategies are tested in numerical experiments and compared one with another. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011