Approximating nonstationary two-priority non-preemptive queueing systems

An approximation for analyzing transient and nonstationary two-priority non-preemptive queueing systems is presented. This system has a three-dimensional state space, and through use of state-space partitioning in conjunction with use of conditional surrogate distributions with constant parameters an approximation is designed. Regardless of system capacity K, the approximation requires the numerical solution of only ten differential equations, compared to the K² + K+1 Kolmogorov-forward equations required for the classic solution. Time-dependent approximations of the mean number of entities of type i and of the probability of a type-i entity being in service are obtained. Empirical test results over a wide range of systems indicate the approximation is quite accurate.     

A decision support system for the procurement of military equipment

The use of life-cycle costs in procurement is limited by the accuracy of cost estimates and assessments of availability risks under the conditions generating costs. Critical to these problems are the needs and responses of equipment to maintenance and repair. Using transition probabilities to define the relationships between serviceability and maintenance and repairs, this article develops a comprehensive decision support system for military procurement. It uses a dynamic programming model to determine the least-cost set of maintenance and repair decisions, where adjustments are included for warranty conditions, time value of money, the opportunity costs of equipment failure, and the end-of-cycle salvage values or disposal costs. The system allows users to define working and failed states, create their own rules or indicators of availability from estimates of state probabilities and establish thresholds of risk acceptability.     

An (s,S) inventory system with rest periods to the server

We study the (s,S) inventory system in which the server takes a rest when the level of the inventory is zero. The demands are assumed to occur for one unit at a time. The interoccurrence times between successive demands, the lead times, and the rest times are assumed to follow general distributions which are mutually independent. Using renewal and convolution techniques we obtain the state transition probabilities.     

Visibility probabilities on line segments in three-dimensional spaces subject to random poisson fields of obscuring spheres

The methodology of determining simultaneous visibility probabilities and points on line segments is extended to problems of three-dimensional spaces, with Poisson random fields of obscuring spheres. Required functions are derived analytically and a numerical example is given for a special case of a standard Poisson field, with uniform distribution of sphere diameters.     

An assumption-free convergence analysis for a perturbation of the scaling algorithm for linear programs,with application to the L1 estimation problem

This article is concerned with the scaling variant of Karmarkar's algorithm for linear programming problems. Several researchers have presented convergence analyses for this algorithm under various nondegeneracy types of assumptions, or under assumptions regarding the nature of the sequence of iterates generated by the algorithm. By employing a slight perturbation of the algorithm, which is computationally imperceptible, we are able to prove without using any special assumptions that the algorithm converges finitely to an ε-optimal solution for any chosen ε > 0, from which it can be (polynomically) rounded to an optimum, for ε > 0 small enough. The logarithmic barrier function is used as a construct for this analysis. A rounding scheme which produces an optimal extreme point solution is also suggested. Besides the non-negatively constrained case, we also present a convergence analysis for the case of bounded variables. An application in statistics to the L₁ estimation problem and related computational results are presented.     

A general age replacement model with minimal repair

A general age replacement is introduced which incorporates minimal repair, planned and unplanned replacements, and costs which depend on time. Finite and infinite horizon results are obtained. Various special cases are considered. Furthermore, a shock model with general cost structure is considered.     

A poissonian binomial model with constrained parameters

The article examines ways of computing cumulative probabilities for a constrained Poissonian binomial distribution arising from a model of a weapon defense system.     

Algorithmic and approximation analyses of the shorter queue model

A system of two parallel queues where the arrivals from a single stream of customers join the shorter queue is considered. Arrivals form a homogeneous Poisson stream and the service times in each of the two queues are independent exponential variates. By treating one of the queues as bounded, the steady-state probability vector for the system can be expressed in a modified matrix-geometric form and can be computed efficiently. Computational procedures for the sojourn time distribution and characteristics of the departure stream are developed. Some numerical results are presented, and based on these results an efficient approximation scheme for the model is developed which can be readily extended to systems with more than two parallel queues.     

The orienteering problem

Orienteering is a sport in which start and end points are specified along with other locations. These other locations have associated scores. Competitors seek to visit, in a fixed amount of time, a subset of these locations on the way from the start point to the end point in order to maximize the total score. An effective center-of-gravity heuristic is presented that outperforms heuristics from the literature.