Decision Making & Negotiations

We consider a multiserver queueing system in which customers request service from a random number of identical servers. In contrast to batch arrival queues, customers cannot begin service until all required servers are available. Servers assigned to the same customer may free separately. For this model, we derive the steady-state distribution for waiting time, the distribution of busy servers, and other important measures. Sufficient conditions for the existence of a steady-state distribution are also obtained.

This paper establishes a rather complete optimality theory for the average cost semi-Markov decision model with a denumerable state space, compact metric action sets and unbounded one-step costs for the case where the underlying Markov chains have a single ergotic set.

This paper discusses the structural equations, forecasting properties, dynamic characteristics, and economic policy implications of a quarterly econometric model of U.S. livestock and feedgrain markets. Quarterly, semi-annual, and annual endogenous variables are incorporated by allowing individual structural equations to be estimated and to enter into the solution of the model with different periodicities. Commodity prices are determined by market equilibrium conditions rather than by autoregressive and other time-series techniques.

This paper considers undiscounted Markov decision problems. With no restriction (on either the periodicity or chain structure of the problem) we show that the value iteration method for finding maximal gain policies exhibits a geometric rate of convergence, whenever convergence occurs. In addition, we study the behaviour of the value-iteration operator; we give bounds for the number of steps needed for contraction, describe the ultimate behaviour of the convergence factor and give conditions for the existence of a uniform convergence rate.

A survey is given of the present state of the art of value-iteration and related successive approximation methods, as well as of resulting turnpike properties, in both the discounted and undiscounted version of finite state and action Markov Decision Problems.

This paper is concerned with the effects of capital risk on optimal individual savings decisions in a simple two-period setting. We investigate the respective roles played by risk and time preferences in answering the following related questions: Q1: Will savings increase, remain constant or decrease in response to an increase in capital risk? Q2: Is optimal saving in the presence of capital risk greater than, equal to or less than optimal saving in the certainty case where the rate of return equals the mean (uncertain) return?

In this paper we consider a set of denumerable stochastic matrices where the paramter set is a compact metric space. We give a number of simultaneous recurrence conditions on the stochastic matrices and establish equivalences between these conditions. The results obtained generalize corresponding results in Markov chain theory to a considerable extent and have applications in stochastic control problems.

This paper investigates the solutions to the functional equations that arise inter alia in Undiscounted Markov Renewal Programming. We show that the solution set is a connected, though possibly nonconvex set whose members are unique up to the n* constants, characterize n* and show that some of these n* degrees of freedom are locally rather than globally independent.

A global portrait of the phase plane for a fishery model is obtained for any acceptable values of the parameters. Three different structures of the phase plane are recovered. The first predicts an eventual collapse of the fishery. The second predicts an unstable limit cycle and an eventual stability of solutions which start inside the limit cycle. The last structure predicts two possible stable equilibria, one with high catch rate, and the other with no catch. Each structure corresponds to a different domain in the parameter space.