The problem of bandwidth allocation and routing in Virtual Path (VP) based Asynchronous Transfer Mode (ATM) networks was studied. As an efficient way to facilitate the network management, VP concept has been proposed in the literature. Traffic control and resource management are simplified in VP based networks. However, a priori reservation of resources for VP's also reduces the statistical multiplexing gain, resulting in increased Call Blocking Probability (CBP);The focus of this study is on how to reduce CBP (or equivalently, how to improve the bandwidth utilization for a given CBP requirement) by the effective bandwidth allocation and routing algorithms. Equivalent capacity concept was used to calculate the required bandwidth by the call. Each call was represented as a bursty and heterogeneous multimedia traffic;First, the effect of traffic dispersion was explored to achieve more statistical gain. Through this study, it was discovered how the effect of traffic dispersion varies with different traffic characteristics and the number of paths. An efficient routing algorithm, CED, was designed. Since traffic dispersion requires resequencing and extra signaling to set up multiple VC's, it should be used only when it gives significant benefits. This was the basic idea in our design of CED. The algorithm finds an optimal dispersion factor for a call, where the gain balances the dispersion cost. Simulation study showed that the CBP can be significantly reduced by CED;Next, this study provides analysis of the statistical behavior of the traffic seen by individual VP, as a result of traffic dispersion. This analysis is essential in estimating the required capacity of a VP accurately when both multimedia traffic and traffic dispersion are taken into account. Then analytical models have been formulated. The cost effective design and engineering of VP networks requires accurate and tractable mathematical models which capture the important statistical properties of traffic. This study also revealed that the load distribution estimated by equivalent capacity follows Gaussian distribution which is the sum of two jointly Gaussian random variables. For the analysis of load distribution when CED is used, we simplified multiple paths as identical paths using the idea of Approximation by Single Abstract Path (ASAP), and approximated the characteristics of the traffic seen by individual VP. The developed analytical models and approximations were validated in the sense that they agreed with simulation results.