The importance of reliable information transfer in wireless networks, especially regarding communication delay, is drastically increasing to fulfill safe and high-quality communication in the 5G and post-5G era. However, conventional media access control (MAC) protocol for wireless networks, notably Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA), sometimes yields unexpectedly significant delay due to its complex arbitration mechanism assuming asynchronous communication among terminals. As the delay cannot be strictly bounded by a deterministic value, this causes a vulnerability of systems relying on wireless networks. This paper utilizes precise time synchronization achieved by Wireless Two-way Interferometry (Wi-Wi), enabling all terminals to be time-synchronized via wireless signals.We show that by an appropriate periodic assignment of each terminal's data transmission timing, named Arbitration Point (AP), a simple arbitration algorithm obtains a strictly bounded maximum value for the delay while ensuring equalities among all participants. Furthermore, we demonstrate that the total number of terminals manageable in a star-topology wireless network significantly increases by densely packing AP timings, taking into account the spatial geometry information of terminals, which is another feature delivered by Wi-Wi measurement. In the meantime, we experimentally constructed a star-topology wired network where all terminals are time-synchronized via Wi-Wi to confirm the fundamental properties identified in the proposed arbitration protocol. This study paves a new way for future wireless networks where the delay is strictly bounded and provides the basis for ultra-reliable and high-quality information transfer functionalities by utilizing precise time synchronization and space localization (space-time synchronization).