Wireless sensor networks (WSNs) for control and monitoring applications introduce critical constraints on the design of multiple access schemes to guarantee timely data delivery. However, existing WSNs are mainly designed to conserve energy consumption and not to support timely data transmission. In this paper, we present a novel media access method defined as Wireless Arbitration which grants each user in the network with a specific arbitration frequency representing the priority to access the wireless channel. This proposed method will guarantee that messages with high priority will access the channel and deliver within the deterministic deadline. A mathematical formulation of wireless arbitration is presented together with the corresponding performance analysis of the multiple access schemes. It is shown that the proposed multiple access scheme outperforms IEEE 802.15.4.