Maximizing Expected Coverage of Flow and Opportunity for Diversion in Networked Systems

Placement of facilities, such as those providing surveillance or assistance functions, is essential for effective and efficient system operation. Planning for where to provide these types of services in a network necessitates addressing different objectives. For instance, notifying users of future network conditions and/or availability of other services requires general exposure to that information at some point during a movement between an origin and destination. Alternatively, the usefulness of services such as the provision of information regarding current network conditions can depend upon where the service is provided relative to opportunities for users to divert from their current path to make use of that service. Regardless of the service to be made available, there is always some uncertainty as to whether or not it will be available and/or observed by users of the system. To address these planning considerations, several new models for optimizing the location of service facilities in a network are described. In particular, the proposed models account for expected coverage of network flows as well as the opportunity that exists for flows to make effective use of a service once it has been provided. While the proposed models involve non-linear objective functions, it is shown that a linearization exists given the topological relationships within a network. The developed optimization models are then integrated into a multi-objective modeling framework and applied to a case study to demonstrate the tradeoffs that exist between the planning objectives.