| The fair division of scarce resources among agents is a challenging issue across a range of applications, especially when there is competition among agents. One application of resource division is in Air Traffic Management (ATM). During severe weather, when there is a reduction in en-route capacity, a specialist using the TSD (Traffic Situation Display) identifies a problem area by creating a Flow Constrained Area (FCA). The air traffic flow management specialists at the Air Traffic Control System Command Center can enter the capacity of the FCA, expressed as the number of flights that can be managed per hour, and an Airspace Flow Program (AFP) will be run. Thus, affected flights will be delayed or rerouted.;Fair allocation of available resources among airlines is very challenging when there is a reduction in en-route resources. Each airline will typically place a different relative weight on delays, rerouting and cancelation. Whereas some airlines would like to preserve the on-time performance for certain flights and cancel or reroute many other flights, other airlines prefer to have less rerouting and cancelations while tolerating higher total delay. Therefore, fairness concerns as well as the ability to respond to different user priorities have played an important role throughout the development of allocation procedures, and continue to be an essential factor. The notion of fairness in air traffic management is largely left implicit and there is no well-defined set of principles that defines what constitutes a fair distribution of resources.;This dissertation is motivated by the fairness issues that arise in the resource allocation procedures that have been introduced under Collaborative Decision Making (CDM). Fair rationing and allocation of available en-route time slots are two major challenges that we address in this research.;The first challenge, fair rationing, is about how to compute a fair share of available resources among agents, when the available resources fall below the total demand. Since the demand, (flights), are time dependent, we introduce a new rationing method that includes the time dependency of demand. The new procedure gives every flight that is disrupted by an AFP a share of available resources. This is in contrast to Ration-By-Schedule (RBS), the allocation method currently in use, where later scheduled flights do not receive any slots. We will discuss and prove the fairness properties of our novel rationing procedure.;The second challenge, allocation of en-route resources, is about how to allocate resources among competitive agents, (flight operators), when each agent has different preferences over resources, (time slots). We design four randomized procedures for allocating scarce resources when the airlines' preferences are included. These procedures use an exogenous fair share, which can be computed using the method described above, as a fairness standard for the allocation of slots among airlines.;The first two procedures, Preference Based Proportional Random Allocation (PBPRA) and Modified-PBPRA, implicity assume equal weight for each time slot. Compared to RBS, PBPRA and M-PBPRA reduce the total internal cost of airlines and also assign each airline a number of slots close (in expectation) to their fair share. The fairness, efficiency and incentive properties of PBPRA and M-PBPRA are evaluated.;The value (or cost of delay) an airline associates with a particular flight may vary substantially from flight to flight. Airlines who wish to receive priority for certain flights usually are willing to pay more for specific time slots. To address the need to express varying priorities, we propose two procedures, Dual Price Proportional Random Allocation (DP-PRA) and Modified-DP-PRA (MDP-PRA), that assign dual prices to resources, i.e. time slots, in order to capture the airlines' preferences over delays, rerouting and cancelations. We explore the fairness, efficiency and incentive properties of DP-PRA and MDP-PRA. |
