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In a distributed real-time system (DRTS), jobs are often executed on a number of processors and must complete by their end-to-end deadlines. Job deadline requirements may be violated if resource competition among different jobs on a given processor is not considered. This paper introduces a distributed, locally optimal algorithm to assign local deadlines to the jobs on each processor without any restrictions on the mappings of the applications to the processors in the distributed soft real-time system. Improved schedulability results are achieved by the algorithm since disparate workloads among the processors due to competing jobs having different paths are considered. Given its distributed nature, the proposed algorithm is adaptive to dynamic changes of the applications and avoids the overhead of global clock synchronization. In order to make the proposed algorithm more practical, two derivatives of the algorithm are proposed and compared. Simulation results based on randomly generated workloads indicate that the proposed approach outperforms existing work both in terms of the number of feasible jobs (between 51% and 313% on average) and the number of feasible task sets (between 12% and 71% on average).

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Abstract-Systematic coordination between the physical world and computation is critical for Quality of Service in the control system. We propose a novel task model to support synergy between the control and real-time sides in the event-trigger control system under environmental perturbations. I. MOTIVATIONIn cyber-physical system (CPS) design, it is critical to systematically exploit the interplay between the control strategies and the implementation alternatives, such as the intelligent coordination presented in [1], [3], [5]. Negotiation between the two sides could be facilitated through appropriately choosing task models and dynamically managing task execution. Specifically, desired performance of the control plants shape the choices of the parameters for a specific real-time task model, while the tasks based on the task model need be scheduled in the cyber side.In real-time systems, there are three well known task models, i.e., the periodic task model, the sporadic task model, and the aperiodic task model. The models are either too constraining or too general for many cyber-physical systems. For example, consider the control task for a vehicle's anti-lock brake system. Under normal situations, the task is executed periodically with a relatively large period. As soon as the wheels are detected to be locked, the control task needs to be executed much more frequently. However, this frequency can be gradually reduced when the situation improves. It is obvious that the aforementioned task models would either require much higher resource than necessary or cannot offer the desired Quality of Service.The elastic task model [2], [3] may be able to model the above system, because task periods can be any value within a given range. However, the choices of the actual period values are made based on satisfying the timing requirement instead of in response to the physical system's requirement. Furthermore, the elastic task model is fundamentally still a periodic task model except that task periods can be adjusted once in a while. We propose a new task model that aims to connect directly the control system behavior with real-time task modeling. This model assumes that the separation interval (i.e., task period) and the maximum allowed delay (i.e., task deadline) are defined as functions of time and external disturbances to the physical system. In addition, the model may allow the system to trade off task execution times with task periods and deadlines. In this way, the dynamics of the control system can be reflected in the task model and be exploited to improve resource utilization. II. PROPOSED SOLUTIONIn our preliminary work, we have adopted this task model in a networked control system that is similar to WirelessHART [4]. The system contains a gateway (where the control algorithms are evaluated), a set of sensor nodes, a set of actuator nodes, and a set of relay nodes. The gateway and all the nodes maintain an existing schedule for nominal situations. When disturbances demand changes to the timing parameters in the task...