Graph technologies have been widely utilized for building big data analytics systems. Since those systems are typically wrapped as service providers in industry, it is critical to handle concurrent queries at runtime by incorporating a set of parallel processing units. In many cases, such queries result in local subgraph traversals, which essentially require an efficient scheduling scheme to explore the trade off between the workload balance and the task affinity. In this paper, we present an auction based approach for allocating concurrent subgraph traversals onto the processors. A dynamic weighted bipartite graph is built to model the affinity between subgraph traversals and processors, and the workload of processors. In particular, an edge between a task and a processor in the bipartite graph represents that the data needed by this task is likely cached by this processor. The task vertices and edges are dynamically added or removed, and the heavier edge weight represents stronger belief of the affinity. Besides, the edge weight is also governed by the current workload of the corresponding processor. We perform a parallel auction algorithm to figure out a near-optimal assignment of the subgraph traversal tasks onto the processors, which therefore addresses both the workload balance and the task affinity. The auction algorithm is performed incrementally, so as to capture the changes of the bipartite graph structure. Our experiments show the superior performance of the proposed method for various real-world use cases based on concurrent subgraph traversals.