An Incentive Compatible, Efficient Market for Air Traffic Flow Management

We present a market-based approach to the Air Traffic Flow Management (ATFM) problem. The goods in our market are delays and buyers are airline companies; the latter pay money to the FAA to buy away the desired amount of delay on a per flight basis. We give a notion of equilibrium for this market and an LP whose solution gives an equilibrium allocation of flights to landing slots as well as equilibrium prices for the landing slots. Via a reduction to matching, we show that this equilibrium can be computed combinatorially in strongly polynomial time. Moreover, there is a special set of equilibrium prices, which can be computed easily, that is identical to the VCG solution, and therefore the market is incentive compatible in dominant strategy.Comment: arXiv admin note: substantial text overlap with arXiv:1109.521

Optimal Timer Based Selection Schemes

Timer-based mechanisms are often used to help a given (sink) node select the best helper node among many available nodes. Specifically, a node transmits a packet when its timer expires, and the timer value is a monotone non-increasing function of its local suitability metric. The best node is selected successfully if no other node's timer expires within a 'vulnerability' window after its timer expiry, and so long as the sink can hear the available nodes. In this paper, we show that the optimal metric-to-timer mapping that (i) maximizes the probability of success or (ii) minimizes the average selection time subject to a minimum constraint on the probability of success, maps the metric into a set of discrete timer values. We specify, in closed-form, the optimal scheme as a function of the maximum selection duration, the vulnerability window, and the number of nodes. An asymptotic characterization of the optimal scheme turns out to be elegant and insightful. For any probability distribution function of the metric, the optimal scheme is scalable, distributed, and performs much better than the popular inverse metric timer mapping. It even compares favorably with splitting-based selection, when the latter's feedback overhead is accounted for.Comment: 21 pages, 6 figures, 1 table, submitted to IEEE Transactions on Communications, uses stackrel.st

Causality vs. Ward identity in disordered electron systems

We address the problem of fulfilling consistency conditions in solutions for disordered noninteracting electrons. We prove that if we assume the existence of the diffusion pole in an electron-hole symmetric theory we cannot achieve a solution with a causal self-energy that would fully fit the Ward identity. Since the self-energy must be causal, we conclude that the Ward identity is partly violated in the diffusive transport regime of disordered electrons. We explain this violation in physical terms and discuss its consequences.Comment: 4 pages, REVTeX, 6 EPS figure