Over the last quarter of a century, the Internet has evolved from being a packet-switched network that provides only data services, such as e-mail and file transfer, to a network that provides a wide range of multimedia services. Switching large application flows associated with multimedia services or high-energy physics experiments by using packet switching at the IP layer requires unacceptable energy consumption levels. Given the potential for orders of magnitude savings in energy per bit by using lower (optical) layers, circuit switching, which has been widely used in telephone networks, is expected to have a renewed and important role in future optical networks. Both static and dynamic traffic will coexist in future optical networks. The classification of connections into long-lived and short-lived has been discussed in various papers. Static circuit-switched connections are likely to have priority over dynamic ones as static connections can be booked well in advance. Thus, the performance of static connections is not affected by the loading of dynamic circuit-switched connections. We consider a circuit-switched network with non-hierarchical alternate routing and trunk reservation that involves two types of connections modeled as long-lived and short-lived calls. Longlived connections can be reserved well in advance, and short-lived connections are provided on demand. Therefore, we assume that long-lived connections have strict priority over the short-lived ones. We develop approximations for the estimation of blocking probability based on the quasi-stationary approach in two ways. One uses Erlang fixed-point approximation (EFPA), and the other uses overflow priority classification approximation (OPCA). We compare the results of the approximations with simulation results and discuss the accuracy of the approximations under different system parameters, such as the ratio of offered load, the number of links per trunk, the maximum allowable number of deflections, and trunk reservation. We also discuss the robustness of quasi-stationary approximation to the ratio of the mean holding times of long-lived and short-lived traffic streams as well as that of EFPA and OPCA to the shape of holding time distribution. Finally, we demonstrate that OPCA can be applied to a large network, such as Coronet. For large circuit-switched networks, previous work has shown that EFPA achieves accurate results for networks that have a large number of channels (circuits) per link. However, a conventional application of EFPA for large networks is computationally prohibitive. In cases where the EFPA solution is unattainable, we propose, in Chapter 3, to use an asymptotic approximation, which we call A-EFPA, for the link blocking probability and demonstrate computation time savings of many orders of magnitude for blocking probability approximation in realistically sized networks with a large number of circuits per link. For NSFNet and Internet2, we demonstrate that blocking probability can be accurately calculated by using simulations, EFPA, and A-EFPA, each of which is used for a different range of parameter values. We also demonstrate the scalability of the approximations by applying them to the 100-node CORONET network. Different rates, holding times, and bandwidth requirements are relevant to future circuit switching applications on the Internet. Bandwidth on demand (BoD) services are provided where fixed capacity is allocated for the service duration and then released by the user. Potential customers are cloud service providers, smaller operators, enterprises, research networks, and even retail customers. Accordingly, we can expect a scenario in which all these BoD service classes compete for the same pool of optical capacity available in the core network that needs to be allocated efficiently. Each class can be characterized according to the arrival rate of its burst, flow, or connection requests; its mean holding time; and its capacity requirement. A network operator that aims to provide such a wide range of BoD services needs a way to efficiently dimension its network to meet QoS requirements. A scalable and accurate method is needed to evaluate the blocking probability for each relevant scenario of network topology, parameter values, and traffic demand. To this end, we consider a circuit-switched multi-service multi-rate network with non-hierarchical deflection routing and trunk reservation in Chapter 4. Based on the fundamental concept of OPCA, we develop two approximations for the estimation of blocking probability, namely, OPCA and service-based OPCA. We also apply classical EFPA for the estimation of blocking probability in the network and propose max(EFPA, service-based OPCA) as an accurate and normally conservative evaluation. We compare the approximations with simulation results and discuss the accuracy of the blocking probabilities of the classes under different system parameter values, such as service rates, bandwidth requirements, number of links per trunk, maximum allowable number of deflections, and trunk reservation. We also discuss the robustness of the approximations to the shape of the holding time distribution and their performances under asymmetrical cases. We also present that the approximations can be applied to large networks such as Coronet. We demonstrate that based on testing over a wide range of parameter values, max(EFPA, service-based OPCA) gives a very accurate and conservative estimation of network blocking probability in a multi-service multi-rate network.