There is a high degree of uncertainty regarding the nature of traffic on future integrated service networks. This uncertainty motivates the use of adaptive resource allocation policies that can take advantage of the statistical fluctuations in the traffic demands. The adaptive control mechanisms must be 'lightweight', in terms of their overheads, and scale to potentially large networks with many traffic flows. Adaptive routing is one form of adaptive resource allocation, and this thesis considers the application of Stochastic Learning Automata (SLA) for distributed, lightweight adaptive routing in future integrated service communication networks. The thesis begins with a broad critical review of the use of Artificial Intelligence (AI) techniques applied to the control of communication networks. Detailed simulation models of integrated service networks are then constructed, and learning automata based routing is compared with traditional techniques on large scale networks. Learning automata are examined for the 'Quality-of-Service' (QoS) routing problem in realistic network topologies, where flows may be routed in the network subject to multiple QoS metrics, such as bandwidth and delay. It is found that learning automata based routing gives considerable blocking probability improvements over shortest path routing, despite only using local connectivity information and a simple probabilistic updating strategy. Furthermore, automata are considered for routing in more complex environments spanning issues such as multi-rate traffic, trunk reservation, routing over multiple domains, routing in high bandwidth-delay product networks and the use of learning automata as a background learning process. Automata are also examined for routing of both 'real-time' and 'non-real-time' traffics in an integrated traffic environment, where the non-real-time traffic has access to the bandwidth 'left over' by the real-time traffic. It is found that adopting learning automata for the routing of the real-time traffic may improve the performance to both real and non-real-time traffics under certain conditions. In addition, it is found that one set of learning automata may route both traffic types satisfactorily. Automata are considered for the routing of multicast connections in receiver-oriented, dynamic environments, where receivers may join and leave the multicast sessions dynamically. Automata are shown to be able to minimise the average delay or the total cost of the resulting trees using the appropriate feedback from the environment. Automata provide a distributed solution to the dynamic multicast problem, requiring purely local connectivity information and a simple updating strategy. Finally, automata are considered for the routing of multicast connections that require QoS guarantees, again in receiver-oriented dynamic environments. It is found that the distributed application of learning automata leads to considerably lower blocking probabilities than a shortest path tree approach, due to a combination of load balancing and minimum cost behaviour.