We show that with ATM cells grouping, the random access protocol of HiPeRLAN type 1 shows satisfactoryy performance without the burden of the management of a contentionless centralized access method. We show simulation results with Constant Bit Rate (CBR) traffics and Variable Bit Rate sources which are likely to generate traffic with non-predictable changing rates. The access method of HIPERLAN type 1 is efficient to handle asynchronous time bounded traffics which are also expected in ATM networks, because jitters and packet clustering can frequently arise and damage the quality of service in case of short packet deadlines.