Recently, most of the mobile network providers start to introduce General Packet Radio Service (GPRS) in their existing GSM networks. GPRS is the technology that will enable more efficient Internet applications to run on mobile networks even before the installation of 3G systems. However, it is not yet clearly understood, how the new data services will affect the overall network performance. This paper provides a framework for analytical performance evaluation of a single GSM/GPRS cell based on a multidimensional Markov chain model. Important performance measures like new call and handover blocking probabilities, moments of the blocking period distributions, achievable average data rates and resource utilization are determined. Introducing a new connection admission control algorithm, different partitioning strategies between GSM and GPRS resources are investigated. Finally, the influence of typical GPRS applications like Internet browsing on traditional GSM services has been studied.