Abstract When we consider the standard Bellman-Ford algorithm, it uses static values of link cost function and distance function. These static values are stored in sink node so that the sink node requires memory to keep data safe. Therefore the space, message and time complexity of a network and node increases. To overcome this we discover Fast Time Dependent Shortest Path algorithm with message and used in network with β synchronizer. The FTSP algorithm uses dynamic values of link cost function and distance function and to store these values we are using vector compression method so that there is no need to store the data into the sink node. Because of this the message, time and space complexity of node will be decreases. Keywords- Duty cycle, Time dependent, β synchronizer