Laxity dynamics and LLF schedulability analysis on multiprocessor platforms

LLF (Least Laxity First) scheduling, which assigns a higher priority to a task with a smaller laxity, has been known as an optimal preemptive scheduling algorithm on a single processor platform. However, little work has been made to illuminate its characteristics upon multiprocessor platforms. In this paper, we identify the dynamics of laxity from the system’s viewpoint and translate the dynamics into LLF multiprocessor schedulability analysis. More specifically, we first characterize laxity properties under LLF scheduling, focusing on laxity dynamics associated with a deadline miss. These laxity dynamics describe a lower bound, which leads to the deadline miss, on the number of tasks of certain laxity values at certain time instants. This lower bound is significant because it represents invariants for highly dynamic system parameters (laxity values). Since the laxity of a task is dependent of the amount of interference of higher-priority tasks, we can then derive a set of conditions to check whether a given task system can go into the laxity dynamics towards a deadline miss. This way, to the author’s best knowledge, we propose the first LLF multiprocessor schedulability test based on its own laxity properties. We also develop an improved schedulability test that exploits slack values. We mathematically prove that the proposed LLF tests dominate the state-of-the-art EDZL tests. We also present simulation results to evaluate schedulability performance of both the original and improved LLF tests in a quantitative manner.

Convex optimization framework for intermediate deadline assignment in soft and hard real-time distributed systems

It is generally challenging to determine end-to-end delays of applications for maximizing the aggregate system utility subject to timing constraints. Many practical approaches suggest the use of intermediate deadline of tasks in order to control and upper-bound their end-to-end delays. This paper proposes a unified framework for different time-sensitive, global optimization problems, and solves them in a distributed manner using Lagrangian duality. The framework uses global viewpoints to assign intermediate deadlines, taking resource contention among tasks into consideration. For soft real-time tasks, the proposed framework effectively addresses the deadline assignment problem while maximizing the aggregate quality of service. For hard real-time tasks, we show that existing heuristic solutions to the deadline assignment problem can be incorporated into the proposed framework, enriching their mathematical interpretation.

Real-time fieldbus communications using Profibus networks

This paper provides a comprehensive study on how to use Profibus fieldbus networks to support real-time industrial communications, that is, on how to ensure the transmission of real-time messages within a maximum bound time. Profibus is base on a simplified timed token (TT) protocol, which is a well-proved solution for real-time communication systems. However, Profibus differs with respect to the TT protocol, thus preventing the application of the usual TT protocol real-time analysis. In fact, real-time solutions for networks based on the TT protocol rely on the possibility of allocating specific bandwidth for the real-time traffic. This means that a minimum amount of time is always available, at each token visit, to transmit real-time messages, transversely, with the Profibus protocol, in the worst case, only one real-time message is processed per token visit. The authors propose two approaches to guarantee the real-time behavior of the Profibus protocol: (1) an unconstrained low-priority traffic profile; and (2) a constrained low-priority traffic profile. The proposed analysis shows that the first profile is a suitable approach for more responsive systems (tighter deadlines), while the second allows for increased nonreal-time traffic throughput

Pre-run-time schedulability analysis of P-NET fieldbus networks

P-NET is a fieldbus industrial communication standard, which uses a Virtual Token Passing MAC mechanism. In this paper we establish pre-run-time schedulability conditions for supporting real-time traffic with P-NET. Essentially we provide formulae to evaluate the minimum message deadline, ensuring the transmission of real-time messages within a maximum time bound

A communication support for real-time distributed computer controlled systems

In this paper, we analyse the ability of P-NET [1] fieldbus to cope with the timing requirements of a Distributed Computer Control System (DCCS), where messages associated to discrete events should be made available within a maximum bound time. The main objective of this work is to analyse how the network access and queueing delays, imposed by P-NET’s virtual token Medium Access Control (MAC) mechanism, affect the realtime behaviour of the supported DCCS.

Constraint solving over multi-valued logics - application to digital circuits

Due to usage conditions, hazardous environments or intentional causes, physical and virtual systems are subject to faults in their components, which may affect their overall behaviour. In a ‘black-box’ agent modelled by a set of propositional logic rules, in which just a subset of components is externally visible, such faults may only be recognised by examining some output function of the agent. A (fault-free) model of the agent’s system provides the expected output given some input. If the real output differs from that predicted output, then the system is faulty. However, some faults may only become apparent in the system output when appropriate inputs are given. A number of problems regarding both testing and diagnosis thus arise, such as testing a fault, testing the whole system, finding possible faults and differentiating them to locate the correct one. The corresponding optimisation problems of finding solutions that require minimum resources are also very relevant in industry, as is minimal diagnosis. In this dissertation we use a well established set of benchmark circuits to address such diagnostic related problems and propose and develop models with different logics that we formalise and generalise as much as possible. We also prove that all techniques generalise to agents and to multiple faults. The developed multi-valued logics extend the usual Boolean logic (suitable for faultfree models) by encoding values with some dependency (usually on faults). Such logics thus allow modelling an arbitrary number of diagnostic theories. Each problem is subsequently solved with CLP solvers that we implement and discuss, together with a new efficient search technique that we present. We compare our results with other approaches such as SAT (that require substantial duplication of circuits), showing the effectiveness of constraints over multi-valued logics, and also the adequacy of a general set constraint solver (with special inferences over set functions such as cardinality) on other problems. In addition, for an optimisation problem, we integrate local search with a constructive approach (branch-and-bound) using a variety of logics to improve an existing efficient tool based on SAT and ILP.

A PTAS for assigning sporadic tasks on two-type heterogeneous multiprocessors

Consider the problem of determining a task-toprocessor assignment for a given collection of implicit-deadline sporadic tasks upon a multiprocessor platform in which there are two distinct kinds of processors. We propose a polynomialtime approximation scheme (PTAS) for this problem. It offers the following guarantee: for a given task set and a given platform, if there exists a feasible task-to-processor assignment, then given an input parameter, ϵ, our PTAS succeeds, in polynomial time, in finding such a feasible task-to-processor assignment on a platform in which each processor is 1+3ϵ times faster. In the simulations, our PTAS outperforms the state-of-the-art PTAS [1] and also for the vast majority of task sets, it requires significantly smaller processor speedup than (its upper bound of) 1+3ϵ for successfully determining a feasible task-to-processor assignment.

An analysis of the impact of bus contention on the WCET in multicores

The use of multicores is becoming widespread inthe field of embedded systems, many of which have real-time requirements. Hence, ensuring that real-time applications meet their timing constraints is a pre-requisite before deploying them on these systems. This necessitates the consideration of the impact of the contention due to shared lowlevel hardware resources like the front-side bus (FSB) on the Worst-CaseExecution Time (WCET) of the tasks. Towards this aim, this paper proposes a method to determine an upper bound on the number of bus requests that tasks executing on a core can generate in a given time interval. We show that our method yields tighter upper bounds in comparison with the state of-the-art. We then apply our method to compute the extra contention delay incurred by tasks, when they are co-scheduled on different cores and access the shared main memory, using a shared bus, access to which is granted using a round-robin arbitration (RR) protocol.

Makespan computation for GPU threads running on a single streaming multiprocessor

Graphics processors were originally developed for rendering graphics but have recently evolved towards being an architecture for general-purpose computations. They are also expected to become important parts of embedded systems hardware -- not just for graphics. However, this necessitates the development of appropriate timing analysis techniques which would be required because techniques developed for CPU scheduling are not applicable. The reason is that we are not interested in how long it takes for any given GPU thread to complete, but rather how long it takes for all of them to complete. We therefore develop a simple method for finding an upper bound on the makespan of a group of GPU threads executing the same program and competing for the resources of a single streaming multiprocessor (whose architecture is based on NVIDIA Fermi, with some simplifying assunptions). We then build upon this method to formulate the derivation of the exact worst-case makespan (and corresponding schedule) as an optimization problem. Addressing the issue of tractability, we also present a technique for efficiently computing a safe estimate of the worstcase makespan with minimal pessimism, which may be used when finding an exact value would take too long.

Response time analysis of COTS-Based multicores considering the contention on the shared memory bus

The current industry trend is towards using Commercially available Off-The-Shelf (COTS) based multicores for developing real time embedded systems, as opposed to the usage of custom-made hardware. In typical implementation of such COTS-based multicores, multiple cores access the main memory via a shared bus. This often leads to contention on this shared channel, which results in an increase of the response time of the tasks. Analyzing this increased response time, considering the contention on the shared bus, is challenging on COTS-based systems mainly because bus arbitration protocols are often undocumented and the exact instants at which the shared bus is accessed by tasks are not explicitly controlled by the operating system scheduler; they are instead a result of cache misses. This paper makes three contributions towards analyzing tasks scheduled on COTS-based multicores. Firstly, we describe a method to model the memory access patterns of a task. Secondly, we apply this model to analyze the worst case response time for a set of tasks. Although the required parameters to obtain the request profile can be obtained by static analysis, we provide an alternative method to experimentally obtain them by using performance monitoring counters (PMCs). We also compare our work against an existing approach and show that our approach outperforms it by providing tighter upper-bound on the number of bus requests generated by a task.

Estudo Estratigráfico e Paleontológico do Jurássico do Algarve Ocidental

Algarve Province, Southern Portugal, corresponds in part to a meso-cenozoic basin running along the coast from Cabo S. Vicente to beyond Spanish border. Structurally it is a big monocline plunging southwards much deformed mainly by two East-West longitudinal flexures. Lithostratigraphical and chronostratigraphical studies dealt specially with Jurassic formations. This and the geological mapping of the post-Hercynian sedimentary formations allow us to define the following units: Triassic-Lower Liassic Arenitos de Silves (Silves sandstones sensu P. Choffat, pro parte) - At their base the Silves sandstones (0-150m) are represented mainly by cross-bedded red sandstones. This unit is Upper Triassic (Keuper) in age, on the evidence of some Brachiopoda. Complexo margo-carbonatado de Silves (Silves marl-limestone complex=Silves sandstones sensu P. Choffat, pro parte) (80-200m) overlies the preceding, it may be reported to the Upper Triassic-Hettangian. It consists of a thick pelite-marl-dolomite-limestone series with many intercalations of greenstones. Since no fossils were found it is not possible to conclude whether it is still Hettangian or if it does correspond, in the whole or in part, already to the Sinemurian. Liassic Dolomitos e calcários dolomíticos de Espiche (Espiche dolomite-rocks and dolomitic-limestones) - The usually massive and finely crystalline or saccharoidal dolomites and dolomitic-limestones are the toughest strata of the Algarve margin giving rise to several hills. Its thickness attains in certain points 60 metres at least. Based on geometry and on lithological similarities with the carbonated complex of the northern basin of Tagus river (Peniche, São Pedro de Muel, Quiaios), this formation can be accepted as Sinemurian in age. As it happens with the carbonated complex, here also the first dolomite beds are non-isochronal throughout the region; upper time-limit of the dolomitic facies is either Lower Carixian, Lower Toarcian or even Lower Dogger. The dolomitization is secondary but not much later than sedimentation. However, between Cabo S. Vicente-Vila do Bispo there is evidence of an even later secondary dolomitization related to the regional fault complex. Calcário dolomítico com nódulos de silex da praia de Belixe (Belixe beach dolomitic-limestone with silex nodules) (50-55m) - Ascribed to Lower or Middle Carixian on the basis of Platypleuroceras sp., Metaderoceras sp. nov. and M. gr. Venarense. Calcário cristalino compacto com Protogrammoceras, Fuciniceras e ? Argutarpites de Belixe (Belixe compact crystalline limestone with Protogrammoceras, Fuciniceras and ? Argutarpites) (30m) - Ascribed to Lower Domerian. Middle and Upper Domerian are indicated but by a single specimen of ? Argutarpites. Calcários margosos e margas com Dactylioceras semicelatum e Harpoceratídeos de Armação Nova (Armação Nova marly limestones and marls with D. semicelatum and Harpoceratidae) (25m) -Ascribed to Lower Toarcian. Middle and Upper Toarcian formations are not known in the Algarve. Dogger Calcários oolíticos, c. corálicos, c. pisolíticos, c. calciclásticos, c. dolomíticos e dolomitos de Almadena (Almadena oolitic-limestones, coral-reef-limestones, pisolite-limestones, limeclastic-limestones, dolomitic-limestones and dolomite-rocks) (more than 50 metres), with lagoonal facies. Ascribed to Aalenian-Bathonian-? Callovian. Margas acinzentadas e calcários detríticos com Zoophycos da praia de Mareta (Mareta beach greyish marls and detritical limestones with Zoophycos) (40m) - Pelagic transreef facies with Upper Bajocian and Bathonian ammonites. Calcários margosos e margas da praia de Mareta (Mareta beach pelagic marly-limestones and marls) (110m) - Ascribed to the Callovian on its ammonites. Malm Near Cabo S. Vicente and Sagres the first Upper Jurassic level consists of a yellowish-brown nodular, compact, locally phosphated and ferruginous, sometimes conglomeratic, marly limestone (0,35-1,50m) containing a rich macrofauna, which includes: 1) Callovian forms unknown at Lower Oxfordian; 2) Upper Callovian forms that still survived in Lower and Middle Oxfordian; 3) Lower Oxfordian forms (Mariae and Cordatum Zones); 4) Lower and Middle Oxfordian forms (Mariae to Plicatilis Zone); 5) Middle Oxfordian forms (plicatilis Zone), and some ones appearing in Middle Oxfordian. This condensed deposit is therefore dated from Middle Oxfordian (Plicatilis Zone). The other Upper Jurassic lithostratigraphical units were also mapped but their detailed study is not presented in this work. Correlations between lithostratigraphical and chronostratigraphical scales from P. Choffat, J. Pratsch, C. Palain and from the author are stated. Further correlations are attempted between zonc scales of Carixian-Lower Toarcian and Upper Bajocian-Middle Oxfordian of France, Spain (Asturias, Iberian and Betic Chains), Argel (Orania) and Portugal (northern Tagus basin and Algarve). The study of pyritous fossil assemblages common in Upper Bathonian-Lower Callovian marly levels of the praia da Mareta seems to suggest that these sediments were deposited in a bay or in an almost closed coastal re-entrance virtually without deep water circulation. Although such conditions may occur at any depth one may suppose that these ones actually correspond to an infralittoral neritic environment. The thaphocoenosis collected there are almost entirely composed of nektonic (ammonites, Belemnites) and planktonic (Bositra) faunas. The sedentary (crinoids, brachiopods) or free (sea-urchins, gastropods) epibenthonic forms are very scarce; endobenthonic forms are not known. The palaeontological study of all Nautiloids and Ammonoids of the Liassic and Dogger is presented (except Kosmoceratidae and Perisphinctaceae). Among the thirty one taxa dealt with, one is new (Metaderoceras sp. nov.) and the great majority of the others has been identified for the first time in Algarve. Some others have never been reported before in Portuguese formations. The evolution, during Jurassic times, of the sedimentary basins of the Portuguese plate margin is described. The absence of Cephalopods in the very extensive marly and dolomitic limestones, partly marine, suggests that, during Lower Liassic, palaeogeography underwent no great changes. Dolomitic-limestone with silex nodules from Cabo S. Vicente contain the first ammonites recorded at the base of the Middle Liassic. This facies, although very common in Tethys, is unknown north of the Tagus. The faunal assemblage has a mediterranean to submediterranean character. Comparisons between faunal assemblage" from Algarve with the ones known north of the Tagus show that communications between Boreal Europe and Tethys, virtually non-existent during Lower and Middle Carixian, became very easy during Lower Domerian. In earlier Pliensbachian times two distinct seas were adjacent to the Iberian plate. One, an epicontinental sea with a tethyan fauna, extended southwards from the Meseta margin. Another, was a boreal sea; during its transgressive episodes boreal faunas attained into the basin north of the Tagus. During Middle Carixian and Lower Domerian, owing to simultaneous transgressions, these two seas joined together allowing faunal exchanges along the epicontinental areas which limited the emerging hercynian chains belts. During Liassic, the Algarve belonged undoubtedly to the tethyan submediterranean province. The area north of the Tagus, on the contrary, was a complex realm where subboreal and tethyan affinities alternatively prevailed. In the Algarve the first Middle Jurassic deposits do frequently show lateral thickness reductions as well as unconformities contemporaneous with other generalized disturbances on the sedimentation processes in other parts of Europe. By this time, near Sagres, a barrier reef developed separating lagoonal or ante-reef facies from the transreef pelagic zone. The presence of tethyan fauna, the abundance of Phylloceratidae and the absence of boreal forms allow us to consider the Algarve basin as a submediterranean province. The presence of Callovian pelagic fossiliferous formations in the Loulé area shows that during Middle Jurassic the marl-limestone transreef sedimentation was not confined to the western Algarve. They would extend eastwards where they only can be seen in the core of some anticlines. This is due to the progressive sinking of the meso-cenozoic formations as we proceed towards the South of the Sagres-Algoz-Querença flexure. In the whole of the Peninsule, and as for the Middle Callovian, an important regression can be clearly recognized on the evidence of an erosion surface which strikes obliquely the Middle and Upper Callovian strata. The geographic boundaries of the different faunal provinces are not changed by the presence of many Kosmoceratidae in the phosphate nodules since they are but a minority in comparison with the tethyan forms. An abstract model can be constructed showing that in Western Europe the Kosmoceratidae may have migrated South and westwards through a channel of the sea that linked Paris basin to Poitou and Aquitaine. By migrating between the Iberian meseta and the Armorican massif this fauna reached northern Tagus basin at the beginning of Upper Callovian (Athleta Zone); this south and southwest bound migration would have proceeded, allowing such forms to reach Algarve basin only in latest Callovian times (Lamberti Zone). This migration means that during Middle Jurassic a widely spread North Atlantic sea would exist, flooding the western part of Portugal up to the Poitou.

The roman conquered by delay: reducing the number of preemptions using sleep states

Sleep-states are emerging as a first-class design choice in energy minimization. A side effect of this is that the release behavior of the system is affected and subsequently the preemption relations between tasks. In a first step we have investigated how the behavior in terms of number of preemptions of tasks in the system is changed at runtime, using an existing procrastination approach, which utilizes sleepstates for energy savings purposes. Our solution resulted in substantial savings of preemptions and we expect from even higher yields for alternative energy saving algorithms. This work is intended to form the base of future research, which aims to bound the number of preemptions at analysis time and subsequently how this may be employed in the analysis to reduced the amount of system utilization, which is reserved to account for the preemption delay.

Optimal virtual cluster-based multiprocessor scheduling

Scheduling of constrained deadline sporadic task systems on multiprocessor platforms is an area which has received much attention in the recent past. It is widely believed that finding an optimal scheduler is hard, and therefore most studies have focused on developing algorithms with good processor utilization bounds. These algorithms can be broadly classified into two categories: partitioned scheduling in which tasks are statically assigned to individual processors, and global scheduling in which each task is allowed to execute on any processor in the platform. In this paper we consider a third, more general, approach called cluster-based scheduling. In this approach each task is statically assigned to a processor cluster, tasks in each cluster are globally scheduled among themselves, and clusters in turn are scheduled on the multiprocessor platform. We develop techniques to support such cluster-based scheduling algorithms, and also consider properties that minimize total processor utilization of individual clusters. In the last part of this paper, we develop new virtual cluster-based scheduling algorithms. For implicit deadline sporadic task systems, we develop an optimal scheduling algorithm that is neither Pfair nor ERfair. We also show that the processor utilization bound of us-edf{m/(2m−1)} can be improved by using virtual clustering. Since neither partitioned nor global strategies dominate over the other, cluster-based scheduling is a natural direction for research towards achieving improved processor utilization bounds.

Notional processors: an approach for multiprocessor scheduling

Consider the problem of designing an algorithm with a high utilisation bound for scheduling sporadic tasks with implicit deadlines on identical processors. A task is characterised by its minimum interarrival time and its execution time. Task preemption and migration is permitted. Still, low preemption and migration counts are desirable. We formulate an algorithm with a utilisation bound no less than 66.¯6%, characterised by worst-case preemption counts comparing favorably against the state-of-the-art.

Online robust optimization framework for QoS guarantees in distributed soft real-time systems

In distributed soft real-time systems, maximizing the aggregate quality-of-service (QoS) is a typical system-wide goal, and addressing the problem through distributed optimization is challenging. Subtasks are subject to unpredictable failures in many practical environments, and this makes the problem much harder. In this paper, we present a robust optimization framework for maximizing the aggregate QoS in the presence of random failures. We introduce the notion of K-failure to bound the effect of random failures on schedulability. Using this notion we define the concept of K-robustness that quantifies the degree of robustness on QoS guarantee in a probabilistic sense. The parameter K helps to tradeoff achievable QoS versus robustness. The proposed robust framework produces optimal solutions through distributed computations on the basis of Lagrangian duality, and we present some implementation techniques. Our simulation results show that the proposed framework can probabilistically guarantee sub-optimal QoS which remains feasible even in the presence of random failures.