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David Salas

Publications and source records attributed to David Salas.

21 records · Page 2Linked to original sources
arXiv2022

Optimal design of exchange water networks with control inputs in Eco-Industrial Parks

Industrial water conservation is an important adaptation to preserve the environment. Eco-Industrial Parks (EIPs) have been designed to encourage the establishment of water exchange networks between enterprises in order to minimize freshwater consumption and wastewater discharge by maximizing wastewater reuse. This control-input model presents a mathematical programming formulation for designing and optimizing industrial water networks in EIPs, formulating and solving it as a Single- Leader Multi-Follower (SLMF) game problem. Enterprises (followers) aim to minimize their operating costs by reusing wastewater from other enterprises, while the designer (leader) aims to minimize the consumption of natural resources within the ecopark. Moreover, when participating in the ecopark, enterprises can control all their input fluxes and the designer guarantees a minimal relative improvement in comparison with the stand-alone operation of each enterprise. The SLMF game is transformed into a single mixed-integer optimization problem. The obtained results are compared with the results of the blind-input model [D. Salas, Cao Van Kien, D. Aussel, L. Montastruc, Optimal design of exchange networks with blind inputs and its application to Eco-Industrial parks, Computers \& Chemical Engineering 143 (2020)].

math.OC↗
arXiv2021

The Convergence Rates of Blockchain Mining Games: A Markovian Approach

Understanding the strategic behavior of miners in a blockchain is of great importance for its proper operation. A common model for mining games considers an infinite time horizon, with players optimizing asymptotic average objectives. Implicitly, this assumes that the asymptotic behaviors are realized at human-scale times, otherwise invalidating current models. We study the mining game utilizing Markov Decision Processes. Our approach allows us to describe the asymptotic behavior of the game in terms of the stationary distribution of the induced Markov chain. We focus on a model with two players under immediate release, assuming two different objectives: the (asymptotic) average reward per turn and the (asymptotic) percentage of obtained blocks. Using tools from Markov chain analysis, we show the existence of a strategy achieving slow mixing times, exponential in the policy parameters. This result emphasizes the imperative need to understand convergence rates in mining games, validating the standard models. Towards this end, we provide upper bounds for the mixing time of certain meaningful classes of strategies. This result yields criteria for establishing that long-term averaged functions are coherent as payoff functions. Moreover, by studying hitting times, we provide a criterion to validate the common simplification of considering finite states models. For both considered objectives functions, we provide explicit formulae depending on the stationary distribution of the underlying Markov chain. In particular, this shows that both mentioned objectives are not equivalent. Finally, we perform a market share case study in a particular regime of the game. More precisely, we show that an strategic player with a sufficiently large processing power can impose negative revenue on honest players.

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