Water distribution networks are designed and managed to provide adequate water flow to all users. Unexpected events, such as prolonged dry spells or cyber-physical attacks, can affect this status quo . Under water scarcity conditions, users located in high-pressure zones have a competitive advantage at the expense of the other customers, which, if exercised freely, can reduce the overall social welfare of the network, i.e., the value its customer get by using it. These conditions of supply failure are a challenge for water utilities, which can either provide full supply, but only for a limited time, or let the system uncontrolled, resulting in a substantial loss of social welfare. Here, we tackle the problem by adopting a game theoretic approach and develop a uniform pricing mechanism aimed to ensure an equitable and fair supply to all customers. The mechanism takes as input the users' demand—an information nowadays available through smart metering—and provides a pricing scheme that induces customers located in high-pressure zones to limit their demand, thus protecting the remaining users. Results obtained for a typical single-branch water distribution network show that the pricing mechanism attains good performance guarantees relative to the optimum, yet unattainable, water allocation. Our results also show that the performance of our pricing mechanism is often comparable to the one obtained by imposing flow restrictions to all users—whose implementation would require massive infrastructural upgrades. The opportunities we identify for supplying customers in an equitable and fair manner can extend to more complex topologies.

中文翻译：

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发生供水故障的智能配水管网的经济控制

供水网络的设计和管理旨在为所有用户提供足够的水流量。意外事件（例如长时间的干旱或网络物理攻击）可能会影响此现状 。在缺水条件下，位于高压区的用户具有竞争优势，而其他客户则受到损失，如果自由行使这些特权，则可能会降低网络的整体社会福利，即，客户通过使用该网络所获得的价值。这些供应中断的状况对水务公司来说是一个挑战，水务公司既可以提供充足的水，但只能在有限的时间内提供水，也可以使系统不受控制，从而导致社会福利的大量损失。在这里，我们通过采用博弈论的方法来解决该问题，并开发出统一的定价机制，旨在确保向所有客户公平和公平地供应。该机制将用户的 需求-当今通过智能计量提供的信息-并提供一种定价方案，可以诱使位于高压区域的客户限制其需求，从而保护其余用户。对于典型的单分支供水网络所获得的结果表明，相对于最优的但仍无法实现的水分配，定价机制获得了良好的性能保证。我们的结果还表明，我们的定价机制的性能通常可与通过对所有用户施加流量限制而获得的定价相媲美，而后者的实施将需要大规模的基础设施升级。我们确定以公平和公正的方式为客户提供服务的机会可以扩展到更复杂的拓扑。对于典型的单分支供水网络所获得的结果表明，相对于最优的但仍无法实现的水分配，定价机制获得了良好的性能保证。我们的结果还表明，我们的定价机制的性能通常可与通过对所有用户施加流量限制而获得的定价相媲美，而后者的实施将需要大规模的基础设施升级。我们确定以公平和公正的方式为客户提供服务的机会可以扩展到更复杂的拓扑。对于典型的单分支供水网络所获得的结果表明，相对于最优的但仍无法实现的水分配，定价机制获得了良好的性能保证。我们的结果还表明，我们的定价机制的性能通常可与通过对所有用户施加流量限制而获得的定价相媲美，而后者的实施将需要大规模的基础设施升级。我们确定以公平和公正的方式为客户提供服务的机会可以扩展到更复杂的拓扑。我们的结果还表明，我们的定价机制的性能通常可与通过对所有用户施加流量限制而获得的定价相媲美，而后者的实施将需要大规模的基础设施升级。我们确定以公平和公正的方式为客户提供服务的机会可以扩展到更复杂的拓扑。我们的结果还表明，我们的定价机制的性能通常可与通过对所有用户施加流量限制而获得的定价相媲美，而后者的实施将需要大规模的基础设施升级。我们确定以公平和公正的方式为客户提供服务的机会可以扩展到更复杂的拓扑。