A point-to-multipoint communication system that is well operative for transmitting megabytes of information in the form of a signal burst. Each slave unit temporarily stores a signal and measures the amount of the signal information before transmitting the signal. A master unit requests that slave units report the measured amounts of information, and they give reports to the master unit. On the basis of the reports from the slave units, the master unit determines an allowable amount of information for each slave unit and permits the slave units to transmit the stored signals according to the request from the master unit. The interval between the reports from the slave units to the master unit can be varied.