An important feature of next generation networks is a possibility to provide services with various requirements of quality of service (QoS) to users. In accordance with the 3GPP specifications, two types of services are defined - guaranteed bit rate (GBR) services, i.e. real time gaming, and non-guaranteed bit rate (non-GBR) services, i.e. e-mail, data communication. Different types of non-GBR services differ one from other, first, in a data volume defining data transfer time. The data transfer time also depends on subscriber devices, which not necessarily support LTE. This fact superimposes restrictions on the possible maximum bit rate. We analyze a multi-rate model of a LTE network with two types of non-GBR services. The radio admission control scheme assumes restrictions on the maximum bit rate and adaptive bit rate changes. These changes depend on the cell load. We apply teletraffic and queuing theories to get an approximate method for calculating the blocking probability. © 2015 AIP Publishing LLC.