# Schedulability Analysis in Fixed-Priority Real-Time Multicore Systems with Contention
## 2 Related Works
They provided schedulability tests specifically tailored for Deadline Monotonic (DM) scheduling, encompassing implicit, constrained, or arbitrary deadline models. However, none of these tests incorporate shared hardware resources into their definitions. [PERSON] et al. [24] introduced a schedulability condition initially designed for uniprocessor systems, later extending it to derive an upper limit on the number of cores necessary for a periodic, non-preemptive task set. Additionally, they proposed a comprehensive formula to determine valid start time offsets for a new task to collaborate with existing tasks on the same processor. Consequently, offsets and non-preemption are incorporated, which deviates from our temporal model, and the proposed schedulability condition overlooks interference considerations. [PERSON] et al. [25] introduced an asymmetric analysis method for evaluating the response time of task processing and access to shared resources, considering both the execution and suspension intervals of tasks. Their model incorporates an upper limit on the execution time of shared resource access for each task and the maximum count of segments for accessing resources per task, with each segment potentially comprising multiple consecutive data requests to access the shared resource. In contrast, our approach offers greater flexibility by not constraining the amount of interference or the number of access times in the model. [PERSON] et al. [26] proposed a fundamental technique for estimating the WCRT of synchronous dataflow (SDF) applications in multicore systems, accounting for task dependency and execution time variations. Their approach integrates schedule time bound analysis, which accounts for interference between task instances within the same SDF graph, and response time analysis, which addresses interference from other real-time tasks. While both studies consider interference from other real-time tasks in response time analysis, their work focuses on SDFs, whereas ours does not involve dataflows. In [27], the allocation problem and exact computation of WCRT are addressed by using a compositional framework based on time automata. [PERSON] et al. [28] introduced a schedulability test for the fixed-priority preemptive partitioned scheduling of sporadic, constrained-deadline tasks. Their approach accounts for varying the execution times of tasks based on specific co-runners, which are determined through static analysis or measurements. In a similar vein, [PERSON] et al. [29] concentrated on resource-aware partitioning approaches within the context of fixed-priority partitioned scheduling. They proposed an Integer Linear Programming formulation to efficiently assign tasks to cores, assign priorities to the tasks, and select resource protection mechanisms. This work follows the general system model in [4], which introduced a scheduling algorithm that precisely computes total interference and an allocator that aims to minimize this interference. However, in the above work, the authors did not propose any schedulability test to ensure the system's feasibility. For this reason, [9] proposed two schedulability tests for dynamic-priority, real-time systems with contention. Therefore, our work covers the gap of the schedulability test in [4], but it is focused on fixed-priority, real-time systems with contention.