A payment channel network is a blockchain-based overlay mechanism that allows parties to transact more efficiently than directly using the blockchain. These networks are composed of payment channels that carry transactions between pairs of users. Due to its design, a payment channel cannot sustain a net flow of money in either direction indefinitely. Therefore, a payment channel network cannot serve transaction requests arbitrarily over a long period of time. We introduce DEBT control, a joint routing and flow-control protocol that guides a payment channel network towards an optimal operating state for any steady-state demand. In this protocol, each channel sets a price for routing transactions through it. Transacting users make flow-control and routing decisions by responding to these prices. A channel updates its price based on the net flow of money through it. The protocol is developed by formulating a network utility maximization problem and solving its dual through gradient descent. We provide convergence guarantees for the protocol and also illustrate its behavior through simulations.

翻译：支付通道网络是一种基于区块链的覆盖机制，允许参与方以比直接使用区块链更高的效率进行交易。这些网络由在用户对之间承载交易的支付通道构成。由于其设计特性，支付通道无法在任一方向上无限维持资金的净流动。因此，支付通道网络无法在长期内任意满足交易请求。本文提出DEBT控制协议，这是一种联合路由与流量控制协议，能够引导支付通道网络针对任何稳态需求达到最优运行状态。在该协议中，每个通道为通过其路由的交易设定价格。交易用户通过响应这些价格做出流量控制与路由决策。通道根据通过其的资金净流向来更新价格。该协议通过构建网络效用最大化问题并采用梯度下降法求解其对偶问题而设计。我们为该协议提供了收敛性保证，并通过仿真展示了其行为特性。