Time-Dependent Solution And Optimal Control Of A Bulk Service Queue

We consider the queueing system denoted by M/M(N)/1/N where customers are served in batches of maximum size N. The model is motivated by a traffic application. The time-dependent probability distribution for the number of customers in the system is obtained in closed form. The solution is used to predict the optimal service rates during a finite time horizon

Time-Dependent Solution And Optimal Control Of A Bulk Service Queue

We consider the queueing system denoted by M/M(N)/1/N where customers are served in batches of maximum size N. The model is motivated by a traffic application. The time-dependent probability distribution for the number of customers in the system is obtained in closed form. The solution is used to predict the optimal service rates during a finite time horizon

A GLOBAL ALGORITHM FOR THE FUZZY CLUSTERING PROBLEM

The Fuzzy clustering (FC) problem is a non-convex mathematical program which usually possesses several local minima. The global minimum solution of the problem is found using a simulated annealing-based algorithm. Some preliminary computational experiments are reported and the solution is compared with that generated by the Fuzzy C-means algorithm

Determining Dominant Wind Directions

In this paper we address the problem of selecting a ser of wind directions that could represent the wind regime at a location. This problem is cast in the form of a nonconvex mathematical program. Important properties of the problem are discussed and a convergent solution algorithm is designed. The algorithm could yield local optimal solutions. A case study which involves the construction of a transition probability matrix for the wind at a location is presented

An Algorithm For Computing The Distance Between Two Circular Disks

This paper presents an algorithm for computing the distance between two circular disks in three-dimensional space. A Kurush-Kuhn-Tucker (KKT) approach is used to solve the problem. We show that when the optimal points are not both at the borders of disks, the solutions of the KKT equations can be obtained in closed-form. For the case where the points are at the circumferences, the problem has no analytical solutions [IBM J. Res. Develop. 34 (5) (1990)]. Instead, we propose for the latter case an iterative algorithm based on computing the distance between a fixed point and a circle. We also show that the point-circle distance problem is solvable in closed-form, and the convergence of the numerical algorithm is linear

Collision Computation Of Moving Bodies

In this paper, an explicit mathematical representation of n-dimensional bodies moving in translation along general trajectories is derived. This representation is used to find out if two moving bodies are going to collide. An optimization problem is developed for finding the time and location of collision. We consider the special cases of linear and piecewise linear trajectories. The collision in this case can be obtained by solving a linear program or a sequence of linear programs, respectively. The problem of finding the collision time and location of several moving bodies is cast as an integer programming problem. A comprehensive simulation study shows that this approach requires much lesser computation time when compared with the current approach of finding the collision between all pairs of bodies

An Algorithm For Computing The Distance Between Two Circular Disks

This paper presents an algorithm for computing the distance between two circular disks in three-dimensional space. A Kurush-Kuhn-Tucker (KKT) approach is used to solve the problem. We show that when the optimal points are not both at the borders of disks, the solutions of the KKT equations can be obtained in closed-form. For the case where the points are at the circumferences, the problem has no analytical solutions [IBM J. Res. Develop. 34 (5) (1990)]. Instead, we propose for the latter case an iterative algorithm based on computing the distance between a fixed point and a circle. We also show that the point-circle distance problem is solvable in closed-form, and the convergence of the numerical algorithm is linear