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Blockchain technology has attracted a lot of attention as the basis of the decentralized digital currency Bitcoin. Its key advantage is that it enables multiple parties to reach consensus without the need for mutual trust. A well-known tradeoff in blockchain networks arises between their scalability, security, and decentralization; this is usually referred to as the "Blockchain Trilemma," and is due to the coordination and security overhead of the distributed consensus algorithm and its trustless environment. Off-chain payment channels have been proposed as a blockchain scalability solution that enables pairs of nodes to transact without burdening the network. Connected channels form a Payment Channel Network (PCN), over which multihop payments are possible, with fast confirmation, low fees, and safety guaranteed via a cryptographic mechanism.In this dissertation, we investigate certain aspects of the Blockchain Trilemma and of PCN performance through a stochastic modeling, optimization, and control lens. First, we analyze the role of network delay in blockchain scalability and security by introducing stochastic models of blockchain evolution. We derive mathematical expressions that capture the blockchain dynamics in the presence of delay as a function of the network parameters, demonstrate their close agreement with measurements from a wide-area network Ethereum testbed, and also show the adverse impact of delay on the network's vulnerability to attacks even against weak adversaries. Subsequently, we focus on the transaction scheduling problem in PCNs and provide its first formal treatment. We introduce a stochastic model of the dynamics of a payment channel under discrete transaction arrivals, and propose that nodes have the ability to hold incoming transactions in buffers until some deadline in order to enable more elaborate processing decisions. We describe a scheduling policy that maximizes the channel throughput for transactions of fixed amounts, prove its optimality, and propose an extension for the general heterogeneous amounts case, which we show to outperform other heuristics through simulations. Next, we study the optimal channel rebalancing problem. PCN nodes may serve as relays for multihop payments and withhold part of the amount as a fee; this leads to unbalanced channels and the need for a rebalancing operation. We study how a relay node can maximize its profits from fees by using the rebalancing method of submarine swaps: we formulate the optimal channel rebalancing problem for a relay node as a Markov Decision Process, and adapt a Deep Reinforcement Learning (DRL) algorithm to arrive at an approximately optimal policy that outperforms current heuristics during experiments in a custom-built discrete event simulator. Our work is the first to introduce DRL for liquidity management in PCNs. Finally, we discuss future directions related to performance optimization and the long-term viability of blockchain networks.
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