In this thesis we address the problem of providing end-to-end quality of service (QoS) to real-time and data connections in a third generation (3G) cellular network based on the Universal Mobile Telecommunication System (UMTS) standard. Data applications usually use TCP (Transmission Control Protocol) and the QoS is a minimum guaranteed mean throughput. For this one first needs to compute the throughput of a TCP connection sending its traffic through the UMTS network (possibly also through the wired part of the Internet). Thus we obtain closed form expressions for a TCP throughput in a UMTS environment. For downloading data at a mobile terminal, the packets of each TCP connection are stored in separate queues at the base station (node B). These are fragmented into Protocol Data Units (PDU). The link layer uses ARQ (Automatic Repeat Request). Thus there can be significant random transmission/queueing delays of TCP packets at the node B. On the other hand the link may not be fully utilized due to the delays of the TCP packets in the rest of the network. In such a scenario the existing models of TCP may not be sufficient. Thus we provide new approximate models for TCP and also obtain new closed form expressions of mean window size. Using these we obtain the throughput of a TCP connection for the scenario where the queueing delays are non-negligible compared to the overall Round Trip Time (RTT) and also the link utilization is less than one. Our approximate models can be useful not only in the UMTS context but also else where. In the second half of the thesis, we use these approximate models of TCP to provide minimum mean throughput to data connections in UMTS. We also consider real-time applications such as voice and video. These can tolerate a little packet loss (~1%) but require an upper Bound on the delay and delay jitter (≤ 150 ms). Thus if the network provides a constant bandwidth and the received SINR is above a specified threshold ( with a certain probability), QoS for the real-time traffic will be satisfied. The 3G cellular systems are interference limited. Thus wise allocation of power is critical in these systems. Hence we consider the problem of providing end-to-end QoS to different users along with the minimization of the downlink power allocation.