In this thesis a queueing model for the D-channel access protocol recommended by CCITT has been developed, and delays of the signalling and packet messages have been analyzed using the model. For modeling Poisson arrival and general message service time distributions are assumed. In our delay analysis telemetry messages have not been considered separately because their behavior is similar to that of packet messages. The analytical results have been verified by simulation results. The two results agree closely for low-to-medium values of total utilization.