In this paper an analytical model for GSM/EGPRS is developed. It is based on the performance of M/M/C/∞/N queueing system with FCFS queue discipline. This model is adapted to guarantee GPRS/EGPRS system constraint and Internet traffic (ON/OFF traffic) over a single cell. The interaction of voice calls with GPRS/EGPRS connections is studied. Different performance parameters are calculated as blocking and delay probability, average throughput, average number of waiting users and queueing time. These performance parameters are obtained under different coding schemes(C-Sc) and three main radio resource strategies which are Complete Partitioning(CP), Partial Sharing(PS), and Complete Sharing(CS). The obtained results show that the (CP) strategy is more superior than the (PS) and (CS) strategies.