ORTAP:An Offset-based Response Time Analysis for a Pipelined Communication Resource Model Hany Kashif, Sina Gholamian, Rodolfo Pellizzoni, Hiren D. Patel and Sebastian Fischmeister Dept. of Electrical and Computer Engineering, University of Waterloo, Waterloo, Canada {hkashif, sgholamian, rpellizz, hdpatel, sfischme}@uwaterloo.ca Abstract—This work addresses the challenge of computing worst-case response times of hard real-time applications deployed on multiprocessor systems. In particular, the worst-case response time analysis (WCRTA) focuses on the communication between distributed tasks of hard real-time applications. The proposed WCRTA models the communication as a pipelined communi- cation resource model. This model incorporates the effect of pipelining, and the parallel transmission of data. Applications of such a model include multiprocessor systems that use complex interconnects such as network-on-chips (NoC)s with priorities. In this paper, we present an exponential analysis, and a polynomial analysis, and prove its correctness. As an application, we apply the pipelined communication resource model to priority-aware NoCs, and we compare the proposed analyses against prior anal- ysis techniques. Our experimental evaluation on two instances of 4 × 4 and 8 × 8 NoCs with 512,000 synthetic benchmarks shows 48.3% and 66.7% improvement in schedulability for the two NoC sizes over prior work. I. I NTRODUCTION Hard real-time applications must guarantee that their tem- poral requirements are met at all times. This requires a worst- case response time analysis (WCRTA), which provides a method to compute the upper-bounds on the amount of time it takes tasks of an application to complete execution. Such an analysis is essential in determining whether a hard real-time application meets its application deadlines. If it does, then the application is deemed schedulable; otherwise, unschedulable. The requirement to deliver tight worst-case response time (WCRT) estimates is paramount when developing WCRTA techniques because it improves schedulability. An important challenge in distributing hard real-time sys- tems onto modern computing platforms is in developing WCRTA techniques that combine communication and compu- tation execution latencies. Such WCRTA techniques must con- sider the worst-case latency of data transmissions across the communication medium connecting the processing resources, and its effect on any dependent computation tasks to determine accurate WCRT estimates. To address this challenge, re- searchers proposed various WCRTA techniques aiming to pro- vide tight and accurate WCRTs of such distributed hard real- time systems [1], [2], [3]. These efforts make the fundamental assumption that the communication occurs over a single shared bus interconnect. A shared bus interconnect consists of a single communication resource that only allows mutually exclusive access. This presents a traditional communication resource model, but, it does not apply to computing platforms prevalent today. Nowadays, platforms consist of multi-processor systems with multiple processing resources that are typically connected using communication resources such as a network-on-chip (NoC). Modelling the interconnect as a single shared bus interconnect does not accurately model the communication resources available in such platforms. Furthermore, it does not capture the pipelined nature of the communication resources that allow for parallel transmission of data between process- ing resources across multiple stages of the communication resources. This prohibits accurately predicting the latencies offered by communication resources such as NoCs resulting in gross over-estimates for the WCRTs. We find that an important challenge in distributing hard real-time applications onto modern computing platforms is in devising WCRTA techniques that incorporate a communication resource model representative of modern communication in- terconnects. To this end, we propose a WCRTA technique that uses a pipelined communication resource model. We present the theory behind the WCRTA, which includes two variants of the analysis. The first is an exponential analysis, and the second is a polynomial. In general, the exponential analysis is intractable; however, the polynomial analysis is tractable. We present an application of the pipelined communication resource model by constructing two instances of priority- aware NoCs as presented by Shi and Burns [4], [5], [6]. Our experimental evaluation of this application uses a large suite of synthetic benchmarks varying the utilization on the NoC. We contend that using synthetic benchmarks for the NoC application is the correct method for evaluating the strengths and weaknesses of the proposed WCRTA technique. This is because concrete deployments of software provide a restricted exploration space. With synthetic benchmarks, we are able to stress the analysis techniques by varying parameters such as communication interconnect utilization. We compare the proposed WCRTA technique against known prior works including that of Palencia and Gonzalez [2], and a transactional extension of the work by Shi and Burns [4]. Every approxi- mated analysis technique uses the methodology proposed by Maki and Turja [3]. We show application schedulability, and the execution times of the analysis for both the exponential and polynomial WCRTA techniques. The results indicate that the schedulability of ORTAP is 48.3% and 66.7% higher than the schedulability of OFLA and Palencia, respectively. II. RELATED WORK Tindell and Clark [1] introduce a WCRTA for a transactional task model where multiple tasks within the transaction can be