A method for operating an ATM communication system for statistical multiplexing of message cells belonging to virtual connections of at least two different traffic classes according to an asynchronous transfer mode, a plurality of upstream interfaces being provided in each case, with an output to which at least one logical queue is connected, at least one multi-stage funnel of switching elements being connected to the plurality of upstream interfaces and at least one downstream interface being connected to a last switching element of the respective funnel, and each of the switching elements comprising a plurality of inputs and at least one output to which a logical queue is associated, and wherein the logical queue of each of the switching elements is common for the different traffic classes, comprising the steps of:
- defining a predetermined threshold for filling of the logical queue of the respective switching element for each of the traffic classes;
- in case of exceeding the threshold for the respective traffic class by receiving a message cell for this traffic class, transmitting a back pressure signal by the respective switching element only to the switching element or upstream interface, respectively, just transmitting this message cell;
- and
- by the switching element or upstream interface, respectively, just receiving the back pressure signal, stopping the transmission of message cells for a predetermined period of time periodically until resetting the back pressure signal.