The authors present a TDM (time division multiplexing) channel access concept based on narrowband and wideband traffic requests which are queued in separated parallel queues. The system may be regarded as a part of a wideband integrated services digital network (ISDN). The channel access strategy follows the premise of allocating that type of customer first into service which fits best (fills out best) the nonoccupied channels. A Poisson arrival process and exponentially distributed service times for both are assumed for both traffic types, but they may have different bit rate requirements. The model involves four characteristic random variables; its joint probability is obtained by means of balance equations. Since it is difficult to determine the solution analytically, the authors develop the transition rate matrix and suggest a procedure for the numerical solution of the balance equations. Several numerical results are presented and discussed.>