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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jedc.2008.04.011 Byline: Igor Evstigneev (a), Michael Taksar (b) Abstract: The paper develops a stochastic dynamic model of economic equilibrium with locally interacting agents. The main focus of the study is on the modeling of market interactions - those arising in connection with commodity exchange and regulated by price mechanisms. The mathematical framework is a control theory for random vector fields on directed graphs. The graphs involved serve to describe the spatio-temporal structure of commodity flows in the system. The main results are concerned with the existence, uniqueness and stability of stochastic dynamic equilibria. Author Affiliation: (a) Economics Department, University of Manchester, Oxford Road, Manchester M13 9PL, UK (b) Mathematics Department, University of Missouri, Columbia, MO 65211, USA Article History: Received 25 March 2006; Accepted 9 April 2008

The problem of reducing inventory and backlog costs of a single-product machine is solved by using the diffusion approximation method. A solution is needed when there is nonexponential distribution of the times when the machine works or is idle or when there is stochastic demand. A sequence of systems in heavy traffic is built. The limiting system whose optimal control is denoted by a reflecting barrier z* is also presented.

A control policy for a manufacturing system churning out a single product with a random demand is presented. The system can either produce the product at a fixed rate or stop production. The so-called double band policy is derived from a solution to a problem under heavy traffic conditions, which are present when production capacity approximates average demand. The policy has three parameters and is nearly optimal. This means that only a small difference between the cost under the policy and the optimal cost exists in heavy traffic.

The feasibility of using a regenerative generalized elastic screen process (RGESP) as a heavy traffic limiter in a GI/G/1 queue system with optional interruptions was evaluated. Numerical investigations were conducted on a single server queueing system in which the system is allowed to leave the system for a random amount of time, called vacation or service interruption. The renewal counting process associated with the busy cycles in the system was then analyzed. Results indicate that under appropriate assumptions and normalization, the workload and queueing processes converge weakly to a RGESP.

A study was done to evaluate an individual's optimal consumption and investment decisions. The study assumes that the individual possesses initial wealth and wants to maximize total expected discounted utility of consumption. This consumption and portfolio decision dilemma does not allow consumption to decrease beyond certain subsistence levels while allowing the possibility of bankruptcy.