Many modern applications are of mixed criticality, where safety-critical tasks have to co-exist with less critical ones that are not subject to hard constraints. Recent research in real-time systems has yielded some promising techniques for meeting the two aspects timing properties and efficiency. Mixed-criticality approach assumes multiple processing time values to be specified for each task depending on the levels of assurance. This simple observation, dealing with tasks executed on processors initiates our idea to use the same mixed-criticality approach while dealing with messages transmitted on TT networks. In this case we deal with non-preemptive scheduling, where the processing time of the message can account for its re-transmission depending on its criticality level.