The merging of telephone and computer networks is introducing multiple resources into networks, and information is becoming increasingly distributed across the network. Related services are being integrated onto a single network rather than being offered on separate uncoordinated networks. In this paper, we focus upon communication networks that integrate multiple services using multiple resources. In particular, we pose resource allocation problems, present a sensitivity analysis, and provide a glimpse of the possible behavior of such networks. The simplest discipline is assumed: a service request is accepted if the necessary resources are available; otherwise it is rejected. Two results are obtained. The first gives the sensitivity of throughput of service requests of type i with respect to offered traffic and service rates of type j. The second result is that the set of vectors of achievable throughput rates is a convex polyhedron given by an explicit set of linear inequalities.