Nowadays, information and communication technologies (ICT) are used in many areas of modern life. User equipment (UE), which uses the capabilities of wireless cellular networks, is becoming an integral part of modern social life. The increase in the number of users and services leads to an exponential growth of generated mobile traffic in the broadband wireless network which conducts radio resources lack problem. This problem is becoming major in the development of modern wireless technologies, mainly because users cannot be serviced with the required quality of service (QoS) level. Leading standardization organizations offer different approaches to solve this problem, for example, the use of network slicing (NS) technology, which allows a mobile network operator (MNO) to effectively share its resources with a mobile virtual network operator (MVNO). This paper proposes one of the possible radio resources allocation scheme models for multi-service wireless networks implementing NS technology, described as a queuing system with a buffer and its retrial group. © Springer Nature Switzerland AG 2019.