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We model systemic risk in an interbank market. Banks face liquidity needs as consumers are uncertain about where they need to consume. Interbank credit lines allow to cope with these liquidity shocks while reducing the cost of maintaining reserves. However, the interbank market exposes the system to a coordination failure (gridlock equilibrium) even if all banks are solvent. When one bank is insolvent, the stability of the banking system is affected in various ways depending on the patterns of payments across locations. We investigate the ability of the banking system to withstand the insolvency of one bank and whether the closure of one bank generates a chain reaction on the rest of the system. We analyze the coordinating role of the Central bank in preventing payments systemic repercussions and we examine the justification of the too-big-to-fail policy.