  Auction has been used to allocate resources or tasks to processes, machines
or other autonomous entities in distributed systems. When different bidders
have different demands and valuations on different types of resources or tasks,
the auction becomes a combinatorial auction (CA), for which finding an optimal
auction result that maximizes total winning bid is NP-hard. Many time-efficient
approximations to this problem work with a bid ranking function (BRF). However,
existing approximations are all centralized and mostly for single-unit
resource. In this paper, we propose the first decentralized CA schemes for
multi-unit resources. It includes a BRF-based winner determination scheme that
enables every agent to locally compute a critical bid value for her to win the
CA and accordingly take her best response to other agent's win declaration. It
also includes a critical-value-based pricing scheme for each winner to locally
compute her payment. We analyze stabilization, correctness, and consistency
properties of the proposed approach. Simulation results confirms that the
proposed approach identifies exactly the same set of winners as the centralized
counterpart regardless of initial bid setting, but at the cost of lower total
winning bid and payment.
