Preference Based Fair Allocation of Limitted Resources

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). 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

Optimization of Permutation Key for Pi-Rotation LDPC Codes

The original low-density parity-check (LDPC) codes were developed by Robert Gallager in early 1960 and are based on a random parity-check matrix construction. In the mid 1990's it was discovered that LDPC codes could be modified slightly to provide the more powerful error correction. These newer LDPC codes, based on an irregular column weight in the underlying check matrix, were still defined with random construction techniques. The Pi-rotation LDPC codes discovered by Echard are a family of LDPC codes completely defined by a small set of integers and have several symmetrical features that are exploited to build efficient encoding and decoding designs. The Pi-rotation codes can be extended to include irregular matrix patterns to obtain the highest performance. In this dissertation we develop a heuristic algorithm to find the best parity-check matrix for Pi-rotation LDPC codes