In order to support a large number of mobile stations (MSs) with statistical multiplexing in cellular networks, a random access scheme is widely used for uplink (UL) bandwidth request (BR). In the design of a random access based BR scheme, there are two important requirements: short connection delay and diverse Quality of Services (QoSs) support. Such requirements are crucial for IMT-Advanced systems like IEEE 802.16m to provide various types of fourth generation (4G) data services. IEEE 802.16m provides advanced UL BR schemes for non-real time polling service (nrtPS) and best-effort (BE) service to meet the requirements of short connection time and multiple QoS level support. In order to provide short connection time and multiple QoS support, three-step and differentiated BR procedures are adopted. In this paper, a novel modelling of IEEE 802.16m contention based BR scheme is proposed that uses a 2-dimensional discrete time Markov chain. Both the short access delay three-step BR procedures and normal five-step BR procedure are considered in the model. Our proposed model also incorporates the IEEE 802.16m differentiated BR procedure. With the proposed model, we extensively evaluate the performance of IEEE 802.16m BR for two different service classes by changing QoS parameters, such as backoff window size and BR timer. Computer simulations are performed to corroborate the accuracy of the proposed model for various operation scenarios. With the proposed model, accurate QoS parameter values can be derived for the IEEE 802.16m contention-based BR scheme.