The air transportation system provides an extremely safe mode of transportation. Maintaining adequate separation ensures safety but limits the capacity of the airspace. In addition to the expected growth in commercial flights, the number and diversity of other aircraft types will also increase significantly. A diversity of collision avoidance technologies may also exist together in future architectures of the National Airspace System. This article proposes a dynamic event tree (DET) framework and its evaluation methodologies to assess collision risk in airspace with a variety of aircraft types. Several methods are applied to a DET example, which models a midair collision scenario using the framework, and the performance and limitations of each method are discussed.

The N-k problem is very well known in the power industry and it tries to answer the question whether there exists a set of k lines in a power network with N elements whose removal would cause the failure of the system. In practice, it is common to evaluate a system according to an N-1 criterion, i.e., k = 1. While this problem has traditionally been considered in a deterministic setting, stochastic behavior within the system is important especially in the context of extreme events. A number of stochastic Monte Carlo models have been proposed to estimate the probability of cascading failures. In this paper, we deal with simulation budget allocation of the stochastic N-1 problem. More specifically, we assume that a simulation model is able to provide us an estimate of the system failure rate when any line is tripped. It is not difficult to see how simulation of all configurations to some certain accuracy can become computationally expensive with the growth of N. Under such a setting, we transform the N-1 problem into a stochastic selection process with optimal computing budget allocation (OCBA): given N configurations, we would like to sequentially allocate a certain number of simulation replications in order to answer the question whether the system is reliable or not. We show through theoretical analysis and numerical experiments that the probability of correctly identifying the system reliability state can be increased by applying OCBA allocation rules in the simulation budget allocation process.

This paper presents several models to compare centralized and distributed automated separation assurance concepts in aviation. In a centralized system, safety-related functions are implemented by common equipment on the ground. In a distributed system, safety-related functions are implemented by equipment on each aircraft. Failures of the safety-related functions can increase the risk of near mid-air collisions. Intuitively, failures on the ground are worse than failures in the air because the ground failures simultaneously affect multiple aircraft. This paper evaluates the degree to which this belief is true. Using region-wide models to account for dependencies between aircraft pairs, we derive the region-wide expectation and variance of the number of separation losses for both centralized and distributed concepts. This derivation is done first for a basic scenario involving a single component and function. We show that the variance of the number of separation losses is always higher for the centralized system, holding the expectations equal. However, numerical examples show that the difference is negligible when the events of interest are rare. Results are extended to a hybrid centralized-distributed scenario involving multiple components and functions on the ground and in the air. In this case, the variance of the centralized system may actually be less than that of the distributed system. The overall implication is that the common-cause failure of the ground function does not seriously weaken the overall case for using a centralized concept versus a distributed concept.

This paper considers an M/G/1 queue where the service time for each customer is a discrete random variable taking one of N values. We call this an M/DN/1 queue. There are potential numerical problems inverting Laplace transforms associated with this queue because the service distribution is discontinuous. The purpose of this paper is to investigate the performance of numerical transform-inversion methods in analyzing this queue. We first derive continuity properties of the steady-state distribution of wait in the M/DN/1 queue. Then, we show analytically how continuity properties affect the performance of the Fourier method for inverting transforms. In particular, continuity is not required in all derivatives for best performance of the method. We also present a new inversion method specifically for the M/DN/1 queue. Finally, we give numerical experiments comparing these and four other inversion methods. Although no method clearly dominates, the recursion method performs well in most examples.

This paper generalizes an existing method for deriving probability models of manufacturing quality metrics. We specifically consider the problem of deriving probability models for the inertia tensor of a rotor. The inertia tensor is a 3 /spl times/ 3 matrix that determines various dynamical properties of the rotor as it spins, affecting its reliability. The key contribution of this paper is that the quality metric of interest is a matrix or a second-order tensor, and the various manufacturing imperfections that cause deviations in the inertia tensor may be vectors. Existing methods, by contrast, assume that the quality metric, as well as the manufacturing imperfections, are scalar quantities. By using rotational properties of matrices & vectors, we show that the relationship between the inertia tensor, and the manufacturing errors must have a specific form, when the errors are small. This structure significantly restricts the class of allowable distributions for the inertia tensor. For example, we show that the multivariate s-normal distribution is not a physically appropriate distribution for the inertia tensor. The results in this paper, while applied specifically to the inertia tensor, are general, and depend only on transformational properties of vectors & matrices. Thus, the framework is applicable to modeling other engineering systems involving second-order tensors, such as the stress tensor, or strain tensor.

In many modern applications of queueing theory, the classical assumption of exponentially decaying service distributions does not apply. In particular, Internet and insurance risk problems may involve heavy-tailed distributions. A difficulty with heavy-tailed distributions is that they may not have closed-form, analytic Laplace transforms. This makes numerical methods, which use the Laplace transform, challenging. In this paper, we develop a method for approximating Laplace transforms. Using the approximation, we give algorithms to compute the steady state probability distribution of the waiting time of an M/G/1 queue to a desired accuracy. We give several numerical examples, and we validate the approximation with known results where possible or with simulations otherwise. We also give convergence proofs for the methods.

Mass-calling events can cause significant congestion in the phone network due to the high volume of redial attempts. This paper presents dynamic algorithms which randomly block some calls at their origination points, thus reducing traffic in the network. The algorithms respond to changing congestion levels by observing whether or not previous calls have been answered. The algorithms reduce call attempts by 50% during periods of 80% blocking, with little disruption in blocking levels to the dialing customers (blocking increases by less than 1%). We also derive an improved blocking heuristic which is more effective under periods of heavier congestion.