We propose a novel channel access scheme that exploits the application-specific characteristics of sensor networks to meet their power, real-time deadline, fairness, and congestion control requirements. The primary characteristic of the sensor network is that the destination of all the data packets in the network is a central data collector. This central data collector, which is usually denoted as an access point, has unlimited power, whereas sensor nodes have one-battery power for remaining alive for several years. Our protocol PEDAMACS uses the access point to directly synchronize and schedule all the nodes in the network by increasing its transmission power. After learning the topology information, which includes the neighbor and the next hop to reach the access point, of all the nodes in the network in topology learning and topology collection phases, the access point explicitly schedules the node transmissions and announces this schedule to all the nodes. Assuming that the nodes generate packets periodically at the same rate, we described the goal of the scheduling algorithm to be minimizing the time necessary for all the packets to reach an access point where each node has exactly one packet at the beginning. After proving the NP-completeness of the problem, we developed a polynomial time algorithm that can guarantee an upper bound on the maximum delay experienced by the packets, which is proportional to the number of the nodes in the network. Simulations performed in TOSSIM, which is a simulation environment for TinyOS, show the efficiency of the proposed scheme compared to the conventional random access scheme in terms of power and delay.