<FONT face=Verdana>Technologies of end-to-end multi-connection and multi-path transmission have gained a lot of re-searchers’ attention since they can improve throughput and promote security and reliability in data transmission. In the Universal Network

mapping mechanisms are presented from service to connection and from connection to path

so that data transmission with concurrent multi-connection and multi-path is also realized. This paper analyzes the mapping mechanism for the service layer of the Universal Network

and proposes the mathematical models for multi-to-multi mappings from service to connection and from connection to path based on network utility maximization. Mapping from service to path via connection is indeed how to allocate the path capacity to all services so that the aggregated utility of all services is globally optimized. General mapping models are also presented when there are inelastic services as well as elastic services in the network

so that the inelastic services can be guaranteed with certain QoS.