Showing papers on "Concave function published in 1979"

A Dynamic Priority Queue with General Concave Priority Functions

Abstract: This paper analyzes mathematically a queueing model where a single server dispenses service to several, m, non-preemptive priority classes. It is assumed that the arrival process of customers who belong to the k class (k customers) is Poisson, and their service times are independent, identical, arbitrarily distributed random variables. The priority degree of a customer at a certain moment is not only a function of his class, but is also a general concave function of the time he has already spent in the system. (The discipline is termed “dynamic-priority.”) Upon departure the server selects for service, from the customers present, the one with the highest instantaneous priority degree, breaking ties by the FIFO rule. An implicit function as well as upper and lower bounds on the expected waiting time of k customer are found. The effectiveness of the bounds is demonstrated by a numerical example.

An efficient dual approach to the urban road network design problem

Abstract: In this paper we present a computationally efficient technique for determining the optimal design of an urban road network. The procedure involves the assignment of network flows and the determination of improved link parameter values so that congestion is minimized subject to a budget constraint. The resulting problem is a very large nonconvex minimization program. It is shown that by dualizing with respect to a single constraint the resulting dual objective function can be evaluated by solving a traffic assignment problem. Since the dual objective function is a concave function of one variable, effective one-dimensional search techniques based on subgradients can be utilized to solve the dual (and thus the primal network design) problem. Since this network design problem reduces to solving several traffic assignment problems, it should be efficient for realistically large networks. Computational results for several problems with up to 553 constraints and 1,862 variables are reported.

Two Theorems on Generalized Diminishing Returns and their Applications to Economic Analysis

Abstract: Under certain weak assumptions such as free disposal and non-satiety, it is shown that the concavity of utility and of technology implies that the maximum value of the set of all attainable programmes is a concave function of the initial capital stocks. For time-independent problems, this implies that along an optimal path, as a capital stock is accumulated, its shadow price falls. The usefulness of the theorems is demonstrated in a number of examples, including Kemp's cake-eating problem and Forster's pollution-control problem.

A remark on the concavity of entropy

Abstract: We investigate to what extent theorems about quantum mechanical or classical entropy can be generalized to functionals of the type ρ→Tr f(ρ), or ψ→∫f(ψ)dμ, respectively, wheref is an arbitrary concave function.

Convex Sets and Convex Functions

Abstract: Because of their useful properties, the notions of convex sets and convex functions find many uses in the various areas of Applied Mathematics. We begin with the basic definition of a convex set in n-dimensional Euclidean Space (En), where points are ordered n-tuples of real numbers such as x’ = (x1, x2,…, xn) and y’ = (y1, y2,…,yn).