arXiv subjects

Frank Kelly

Publications and source records attributed to Frank Kelly.

4 recordsLinked to original sources

arXiv2018

Collective Effects and Performance of Algorithmic Electric Vehicle Charging Strategies

We combine the power flow model with the proportionally fair optimization criterion to study the control of congestion within a distribution electric grid network. The form of the mathematical optimization problem is a convex second order cone that can be solved by modern non-linear interior point methods and constitutes the core of a dynamic simulation of electric vehicles (EV) joining and leaving the charging network. The preferences of EV drivers, represented by simple algorithmic strategies, are conveyed to the optimizing component by real-time adjustments to user-specific weighting parameters that are then directly incorporated into the objective function. The algorithmic strategies utilize a small number of parameters that characterize the user's budgets, expectations on the availability of vehicles and the charging process. We investigate the collective behaviour emerging from individual strategies and evaluate their performance by means of computer simulation.

math.OC↗

arXiv2017

A Markov model of a limit order book: thresholds, recurrence, and trading strategies

We analyze a tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand. We establish the existence of a limiting distribution for the highest bid, and for the lowest ask, where the limiting distributions are confined between two thresholds. We make extensive use of fluid limits in order to establish recurrence properties of the model. We use the model to analyze various high-frequency trading strategies, and comment on the Nash equilibria that emerge between high-frequency traders when a market in continuous time is replaced by frequent batch auctions.

q-fin.TR↗

arXiv2015

Critical behaviour in charging of electric vehicles

The increasing penetration of electric vehicles over the coming decades, taken together with the high cost to upgrade local distribution networks and consumer demand for home charging, suggest that managing congestion on low voltage networks will be a crucial component of the electric vehicle revolution and the move away from fossil fuels in transportation. Here, we model the max-flow and proportional fairness protocols for the control of congestion caused by a fleet of vehicles charging on two real-world distribution networks. We show that the system undergoes a continuous phase transition to a congested state as a function of the rate of vehicles plugging to the network to charge. We focus on the order parameter and its fluctuations close to the phase transition, and show that the critical point depends on the choice of congestion protocol. Finally, we analyse the inequality in the charging times as the vehicle arrival rate increases, and show that charging times are considerably more equitable in proportional fairness than in max-flow.

math.OC↗

arXiv2014

Efficient Advert Assignment

We develop a framework for the analysis of large-scale Ad-auctions where adverts are assigned over a continuum of search types. For this pay-per-click market, we provide an efficient mechanism that maximizes social welfare. In particular, we show that the social welfare optimization can be solved in separate optimizations conducted on the time-scales relevant to the search platform and advertisers. Here, on each search occurrence, the platform solves an assignment problem and, on a slower time-scale, each advertiser submits a bid which matches its demand for click-throughs with supply. Importantly, knowledge of global parameters, such as the distribution of search terms, is not required when separating the problem in this way. Exploiting the information asymmetry between the platform and advertiser, we describe a simple mechanism which incentivizes truthful bidding and has a unique Nash equilibrium that is socially optimal, and thus implements our decomposition. Further, we consider models where advertisers adapt their bids smoothly over time, and prove convergence to the solution that maximizes social welfare. Finally, we describe several extensions which illustrate the flexibility and tractability of our framework.

cs.GT↗