An Alloy Verification Model for Consensus-Based Auction Protocols

Max Consensus-based Auction (MCA) protocols are an elegant approach to establish conflict-free distributed allocations in a wide range of network utility maximization problems. A set of agents independently bid on a set of items, and exchange their bids with their first hop-neighbors for a distributed (max-consensus) winner determination. MCA protocols have been proposed, e.g, To solve the task allocation problem for a fleet of unmanned aerial vehicles, in smart grids, or in distributed virtual network management applications. Misconfigured or malicious agents participating in a MCAor an incorrect combination of policy instantiations can lead to oscillations of the protocol, causing, e.g, Service Level Agreement (SLA) violations. In this paper we propose a formal, machine-readable, Max-Consensus Auction model encoded in the Alloy light weight modeling language. The model consists of a network of agents applying the MCA mechanisms instantiated with potentially different policies, and a set of predicates to analyze its convergence properties. We were able to verify that even when all agents follow the protocol, MCA is not resilient against rebidding attacks, and that the protocol fails (to achieve a conflict-free resource allocation) for some specific combinations of policies. Our model can be used to verify, with a "push-button" analysis, the convergence of the MCA mechanism to a conflict-free allocation under a wide range of policy instantiations.