Economics Insights @ CBS

We consider a general class of queueing systems with multiple job types and a flexible service facility. The arrival times and sizes of incoming jobs are random, and correlations among the sizes of arriving job types are allowed. By choosing among a finite set of configurations, the facility can dynamically control the rates at which it serves the various job types. We define system work at any given time as the minimum time required to process all jobs currently in the backlog.

In this article I begin by discussing the rationale for mandatory convertibles from the point of view of issuers as well as investors. In general, convertibles securities reduce the costs of "information asymmetry" that can make equity offerings especially expensive for some smaller, high-growth companies (or any firm with little additional debt capacity where management is convinced its shares are undervalued).

We develop a simulation algorithm for estimating the prices of American-style securities, i.e., securities with opportunities for early exercise. Our algorithm provides both point estimates and error bounds for the true security price. It generates two estimates, one biased high and one biased low, both asymptotically unbiased and converging to the true price. Combining the two estimators yields a confidence interval for the true price.

We propose and analyze a heuristic that uses region partitioning and an aggregation scheme for customer attributes (load size, time windows, etc.) to create a finite number of customer types. A math program is solved based on these aggregated customer types to generate a feasible solution to the original problem. The problem class we address is quite general and defined by a number of general consistency properties.