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Payment channel networks provide a fast and scalable solution to relay funds, acting as a second layer to slower and less scalable blockchain protocols. In this paper, we present an accessible, low-cost attack in which the attacker paralyzes multiple payment network channels for several days. The attack is based on overloading channels with requests that are kept unresolved until their expiration time. Reaching the maximum allowed unresolved requests (HTLCs) locks the channel for new payments. The attack is in fact inherent to the way off-chain networks are constructed, since limits on the number of unresolved payments are derived from limits on the blockchain. We consider three main versions of the attack: one in which the attacker attempts to block as many high liquidity channels as possible, one in which it disconnects as many pairs of nodes as it can, and one in which it tries to isolate individual nodes from the network. We evaluate the costs of these attacks on Bitcoin's Lightning Network and compare how changes in the network have affected the cost of attack. Specifically, we consider how recent changes to default parameters in each of the main Lightning implementations contribute to the attacks. As we evaluate the attacks, we also look at statistics on parameters in the Lightning Network, which are of independent interest and compare the various implementations of Lightning nodes. Finally, we suggest mitigation techniques that make these attacks much harder to carry out.