[Truncated abstract] The accelerating pace of convergence of communications from disparate application types onto common packet networks has made quality of service an increasingly important and problematic issue. Applications of different classes have diverse service requirements at distinct levels of importance. Also, these applications offer traffic to the network with widely variant characteristics. Yet a common network is expected at all times to meet the individual communication requirements of each flow from all of these application types. One group of applications that has particularly critical service requirements is the class of real-time applications, such as packet telephony. They require both the reproduction of a specified timing sequence at the destination, and nearly instantaneous interaction between the users at the endpoints. The associated delay limits (in terms of upper bound and variation) must be consistently met; at every point where these are violated, the network transfer becomes worthless, as the data cannot be used at all. In contrast, other types of applications may suffer appreciable deterioration in quality of service as a result of slower transfer, but the goal of the transfer can still largely be met. The goal of this thesis is to evaluate the potential effectiveness of a class of packet scheduling algorithms in meeting the specific service requirements of real-time applications in a converged network environment. Since the proposal of Weighted Fair Queueing, there have been several schedulers suggested to be capable of meeting the divergent service requirements of both real-time and other data applications. ... This simulation study also sheds light on false assumptions that can be made about the isolation produced by start-time and finish-time schedulers based on the deterministic bounds obtained. The key contributions of this work are as follows. We clearly show how the definition of the virtual time function affects both delay bounds and delay distributions for a real-time flow in a converged network, and how optimality is achieved. Despite apparent indications to the contrary from delay bounds, the simulation analysis demonstrates that start-time rate-based schedulers possess useful characteristics for real-time flows that the traditional finish-time schedulers do not. Finally, it is shown that all the virtual time rate-based schedulers considered can produce isolation problems over multiple hops in networks with high loading. It becomes apparent that the benchmark First-Come-First-Served scheduler, with spacing and call admission control at the network ingresses, is a preferred arrangement for real-time flows (although lower priority levels would also need to be implemented for dealing with other data flows).