In modern infrastructure, the mobile network operator, the owner of the equipment, leases part of the resources of the base stations. Network slicing allows several virtual network operators to use the resources of one base station. This allows operators and resource owners to provide and manage multiple dedicated logical networks with specific functionality running on top of a shared infrastructure. The key task is to manage resource allocation between slices. In the current work, we develop resource queuing model for the analysis of the network slicing technology. Besides, algorithms are being proposed to optimize the operation of slicing mechanisms. The paper provides a brief overview of resource slicing strategies, describes a simplified mathematical model of network slicing, and analyzes it using an effective recurrent algorithm.