Mathematical models for studying systems with interacting components.

摘要

This thesis consists of the following three essays: (1) "On the Existence of Threshold-Type Admission Policies in Series Queueing Networks"; (2) "On the Impact of Worker Interactions on How to Divide a Team"; (3) "Mathematical Models for Studying When to Divide a Team."; Within the field of queueing theory, there is a large body of literature known as admission control that studies how dynamic control of customer arrival rates maximizes queueing network revenues, such as in manufacturing plants, vehicular traffic networks, service industries, or telecommunication systems. In simple queueing systems, it has been shown that the optimal admission policy is of the threshold type, namely, that it is optimal to reject less profitable customers whenever the service congestion exceeds a certain threshold level. In Essay 1, it is established that a threshold-type admission policy exists when multiple customer classes seek access to a system of servers arranged in series and customer blocking occurs, resulting from a full queue.; The second and third essays propose models to examine how interaction affects the division of organizational teams. In Essay 2, the complexities of worker interactions and individual performances are shown to influence the decision of how to divide a team in an organization that is evolving over time through replacements. Analytical results and computer simulations provide managerial insights about the immediate impact of different approaches for reassigning workers based on their current performances, interactions with others, and the degree to which the team has evolved.; The question of how to divide a team suggests a related question, that is, when is it desirable to divide a team? Essay 3 investigates when a growing team benefits from being divided and how interactions among workers and management impact this decision. The proposed model has the property that team performance decreases as the size of the team increases. Analytical results and computer simulations show how team size, business environment, worker performance, interaction among employees, relationships between management and labor, and leadership skill affect when a team should be split.