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This paper describes a straightforward implementation of a modified Newton algorithm which generates the best interval bounding the solution generated using interval Newton methods. This implementation addresses the issues described by Hansen and Greenberg for analyzing problems with data perturbations using interval analysis. It also indicates a new approach of potentially attractive methods for using interval Newton methods. While our focus is on perturbed problems (sensitivity analysis), the results are more generally applicable. The major difference in the point of view of perturbed problems versus the general use of interval methods is that in perturbed problems we are focused on the behavior of the function around an optimal solution. The more general approach seeks to identify all optimal solutions of the function. (Reprinted by permission of the publisher.)

This paper considers the distribution rising out of a sequence of Bernoulli trials that terminates at the mth success or the mth failure, whichever occurs first. A limiting form of the distribution and the approximations to the distribution are discussed. Estimators for the parameter p of the distribution are obtained. (Reprinted by permission of the publisher.)

In this paper, we consider a dynamic routing problem in a store-and-forward computer-communication network which consists of l parallel channels connected between the source and the destination. We prove that if messages arrive at the network in accordance with a Poisson process and all nodes have an exponential service rate, then the routing strategy that minimizes the total expected time in transmitting all message that arrive before T>0 is to route the arriving message to the channel along which the sum of all queue sizes is minimum. Techniques of martingale and dynamic programming are used on obtaining the result. (Reprinted with permission of the publisher)