An Upper Bound to the Lateness of Soft Real-time Tasks Scheduled by EDF on Multiprocessors ∗ Paolo Valente Scuola Superiore S. Anna, Italy pv@gandalf.sssup.it Giuseppe Lipari Scuola Superiore S. Anna, Italy lipari@sssup.it Abstract Multiprocessors are now commonplace for efficiently achieving high computational power, even in embedded sys- tems. A considerable research effort is being addressed to schedulability analysis of global scheduling in Symmetric Multiprocessor Platforms (SMP), where there is a global queue of ready tasks, and preemption and migration are al- lowed. In many soft real-time applications (as e.g. multimedia and telecommunication) a bounded lateness is often tol- erated. Unfortunately, when considering priority-driven scheduling of periodic/sporadic tasks, previous results only focused on guaranteeing all deadlines, and provided worst- case utilization bounds that are lower than the maximum available computational power. In particular, until now, the existence of an upper bound on the lateness of soft real-time tasks for a fully utilized SMP was still an open problem. In this paper we do solve this problem by providing an up- per bound to the lateness of periodic/sporadic tasks – with relative deadlines equal to periods/minimum inter-arrival times – scheduled by EDF on a SMP, under the only assump- tion that the total utilization is no higher than the total system capacity. 1. Introduction Multiprocessors are now commonplace in general- purpose as well as in embedded systems. They provide a cost-effective solution to achieve high computational power. Besides, due to technological and physical constraints, in- creasing the speed of single processors is becoming more and more difficult. Hence multiprocessor platforms seem to be the only option for the most computationally demanding ap- plications. In the last year a large number of multi-core chips as well as multiprocessor architectures have been launched in the market. For example, to meet the requirements of demanding embedded real-time applications, ARM proposes MPCore, a * This work has been supported in part by the European Commission un- der contract IST 2001-34820 (ARTIST project). synthesizable multiprocessor core, while Motorola proposes its PowerPMC-280 SMP platform. In the high-end general purpose processor market, both Intel, with its Pentium D brand, and AMD, with e.g. the Opteron dual-core processor, envision multi-core processors as the architecture of choice for high performance applications. In this paper we consider soft real-time tasks to be ex- ecuted on a Symmetric Multi Processor (SMP) platforms, comprised of M identical processors with constant speed. Unfortunately, multiprocessor platforms pose greater diffi- culties than single processor ones when applications have time requirements. Many negative results are known on the scheduling of real-time applications on multiprocessors, in- cluding SMPs [1, 2, 4, 8, 3, 7, 6, 12]. The results presented in this paper are related to the class of soft real-time applications that can be modeled as a set of periodic/sporadic tasks, i.e. sequences of jobs to execute, where each job is associated with a relative completion dead- line equal to the period/minimum inter-arrival time. In soft real-time applications, deadlines are not critical, but it is im- portant to respect some Quality of Service (QoS) require- ments. Examples of such QoS constraints are: limited num- ber of deadline misses, limited deadline miss percentage, and so on. In this paper we are interested in soft real-time applica- tions that can tolerate a bounded lateness with respect to the desired deadline. This kind of constraint matches a large class of applications, like multimedia, telecommunication, and financial ones. As an example, consider a video player: a given frame-rate must be guaranteed, but a jitter of few mil- liseconds in the frame-time does not significantly affect the quality of the video. In contrast, audio quality is extremely sensitive to silence gaps. However, audio samples are typi- cally buffered and played back at the desired rate by the au- dio device. A bounded lateness in providing new samples to the device can be easily compensated using a pre-buffering strategy. 1.1. Related work Research on real-time multiprocessor scheduling has been mainly focused on guaranteeing strict deadline obser- vance. The two main approaches are partitioning and global Proceedings of the 26th IEEE International Real-Time Systems Symposium (RTSS05) 0-7695-2490-7/05 $20.00 ' 2005 IEEE Authorized licensed use limited to: UNIVERSITA PISA S ANNA. Downloaded on October 7, 2008 at 6:33 from IEEE Xplore. Restrictions apply.