A system is disclosed for overload control in a hybrid switching system that separately transports each monomedia stream, such as video, voice and data, of a composite multimedia signal. The overload control is based on the time delay for completion of call establishment of each multimedia session. When the average time delay for completion of call establishment of each multimedia session is below a predefined threshold, the system has sufficient capacity and overload corrective measures are not required. When the average time delay for completion of call establishment of each multimedia session, or a connection for any individual monomedia component within the multimedia session, exceeds a predefined threshold, the switching system is approaching an overload condition, and overload control must be implemented to reduce the number of calls accepted in the next time interval. A decision is made at the beginning of each time interval based on the average call completion time delay over some predefined period of time, to accept a determined number of calls during each time interval.