Mobile network operators observe a significant disparity of quality of service (QoS) and network performance metrics, such as the mean user throughput, the mean number of users and the cell load, over different network base stations. The principal reason being the fact that real networks are never perfectly hexagonal, base stations are subject to different radio conditions, and may have different engineering parameters. We propose a model that takes into account these network irregularities in a probabilistic manner, in particular assuming Poisson spatial location of base stations, lognormal shadowing and random transmission powers. Performance of base stations is modeled by spatial processor sharing queues, which are made dependent of each other via a system of load equations. In order to validate our approach, we estimate all the model parameters from the data collected in a commercial network, solve it and compare the spatial variability of the QoS and performance metrics in the model to the real network performance metrics. Considering two scenarios: downtown of a big city and a mid-size city, we show that our model predicts well the network performance.