Abstract-This work investigates properties of signal flow graphs (SFGs) over max-plus algebra, which are referred to as synchronous SFGs. New topological methods for evaluating gains of synchronous matrix SFGs are described. These methods are based on the existing theory for matrix SFGs over regular algebra. SFGs are useful in studying complex engineering systems by representing them as interconnection of relatively simple subsystems. In particular, synchronous SFGs can be used to graphically model the timing behavior of deterministic discrete event systems. The paper illustrates an application of synchronous SFGs to modeling and performance evaluation of deterministic manufacturing systems
