A special case of real-time systems is represented by the mixed criticality systems (MCSs), where tasks with different criticalities, categorized based on a finite set of criticality levels, share the same hardware [9]. The system is considered to run in a number of criticality modes, each mode giving a certain degree of execution time assurance [9]. While the classical real-time approach implies the construction of a single scheduling table, in MCSs, things become more complex due to the number of criticality modes. The change from one criticality mode to another corresponds to a transition from one precomputed scheduling table to another. Thus, in MCSs, there is one scheduling table per criticality level [10]. MCSs are a suitable variant that can be used with respect to providing a real-time response, while isolating the critical functionalities. If we analyze safety-critical systems in the case of MCSs, there are certain advantages of such table-driven approaches over event-driven scheduling: easier certification, given by the fact that table-driven schedulers are completely deterministic [10]; easier synchronization between tasks [1]; easier power management, as each power-mode corresponds to a criticality level, and each level uses its own table; and easier adaptation of real-time applications from different fields like automotive, avionics, etc., which already use table-driven approaches [11]. In this paper we propose an adaptation of a real-time, table-driven, non-preemptive scheduling method for MCSs which guarantees jitterless execution in a mixed criticality time-triggered environment for both uniprocessor and homogenous multiprocessor systems. We also provide a partitioning heuristic for this scheduling method for multiprocessor systems. The main contributions of this paper are as follows:  
* A mixed criticality scheduling algorithm, FENP_MC (Fixed Execution Non-Preemptive Mixed Criticality), is proposed for jitterless task execution in a time-triggered environment;
* An adaptation of the FENP_MC for homogenous multiprocessor systems, P_FENP_MC, is provided;
* Feasibility tests are proposed for both uniprocessor and homogenous multiprocessor systems;
* The algorithm performance is analyzed using the success ratio against the utilization of the task sets;
* The proposed algorithm performance is compared against a time-triggered and an event-driven scheduling method in a non-preemptive context: Time-Triggered Merge (TT-Merge)/Energy-efficient Time-Triggered Merge (Energy-efficient TT-Merge) [12] and Earliest Deadline First with Virtual Deadlines (EDF-VD) [13], a non-preemptive variant. The rest of this paper is structured as follows: In Section 2 we briefly present the state of the art regarding scheduling in a mixed criticality time-triggered environment. In Section 3, we describe our proposed scheduling algorithm for uniprocessor mixed criticality systems, while in Section 4, we propose an adaptation for homogenous multiprocessor MCSs. In Section 5, we analyze the performance of the proposed algorithm in terms of success ratio and compare it against a popular one, namely, EDF-VD NP (EDF-VD in its non-preemptive form). We conclude our paper in Section 6, where we also propose some future research and development directions.