In this paper we are interested in mixed-criticality applications implemented using distributed heterogenous architectures, composed of processing elements (PEs) interconnected using the TTEthernet protocol. At the PE-level, we use partitioning, such that each application is allowed to run only within predefined time slots, allocated on each processor. At the communication-level, TTEthernet uses the concepts of virtual links for the separation of mixed-criticality messages. TTEthernet integrates three types of traffic: Time-Triggered (TT) messages, transmitted based on schedule tables, Rate Constrained (RC) messages, transmitted if there are no TT messages, and Best Effort (BE) messages. We assume that applications are scheduled using Static Cyclic Scheduling (SCS) or Fixed-Priority Preemptive Scheduling (FPS). We are interested in analysis and optimization methods and tools, which decide the mapping of tasks to PEs, the sequence and length of the time partitions on each PE and the schedule tables of the SCS tasks and TT messages, such that the applications are schedulable and the response times of FPS tasks and RC messages is minimized. We have proposed a Tabu Search-based meta-heuristic to solve this optimization problem, which has been evaluated using several benchmarks.