Schedulability analysis of globally scheduled multiprocessor schedulers for real time system: A Review

— In recent years, massive migration from single processor devices to multi-core computing devices has taken place in industry. General purpose and real time embedded systems have found a great market in multiprocessor systems. Researchers have suggested number of solutions to address computational demand on multiprocessor applications. So many scheduling policies have been designed and established to meet the real time requirements on multiprocessor systems.This paper provides the analysis of schedulabilityfor periodic and sporadic tasks of Real-Time systems which is having Symmetric Multi-Processor (SMP).We will focus on job level dynamic priority EDF (global scheduling algorithm), where tasks can transfer from processor to processor during execution.


II. Task Model
Liu and Layland developed simplest prototype for real time sporadic process [1]. In this model, a sporadic task is categorizedby three factors: a worst-case execution requirement equal to Ci time unit, a comparative deadline Diperiod unit later its arrival time, and a successive job-arrivals separation periodTi time unit which is also referred as period of task. Liu and Layland task-model can be signified by , , .Such a sporadic task represents anendlessarrangement of jobs. We refer to the interval, of size Di, between such a job's arrival instant and deadline as its window of scheduling.A task of sporadic system is comprised of several such sporadic tasks. A pool of sporadic tasks is mentioned as a system ofsporadic task and is denoted as τ.Tsk system can be signified by τ = {τ1, τ2, . . . τn}, with τi = (Ci, Di, Ti) for all i, 1 ≤i≤ n. Task system τ is said to be a controlled task system if it is assured that each and every task τi∈ τ has its comparative deadline factor no greater than its period: D i ≤T i , and an implicit-deadline task system if D i = T i for all τ i ∈ τ. (Implicit-deadline systems are also known as Liu and Layland [1] task systems.) In this paper, our attention is limited to controlled and implicit deadline task systems.We also assume aentirelypreemptive execution model where any executing job may be interjected at any instant in time, and its execution can be resumed later with no cost or penalty. In this paper, focus is only on collection of independent tasks, all with hard real-time requirement, and preempt able scheduled with symmetric multiprocessors using global algorithm.

Task and System Characteristic
Utilization is the most important concept used in analysis of systems of sporadic task on multiprocessor. The utilization u i of a task τ i is the ratio C i /T i of its completing time C i to its durationT i . The total utilization u sum (τ) is summation of utilization of all tasks and the largest utilization u max (τ) of a task system τ is defined as maximum u i of all the task from task system τ. In similar manner density utilization δ i of a task τ i is the ratio C i /D i of its completing time C i to its time limit D i . The total density δ sum (τ) is summation of density of all tasks and the largest density δ max (τ) of a task system τ is defined as maximum δ i of all the task from task system τ. Another important parameter used for schedulability analysis is Demand Bound Function (DBF). For any slot length t, demand bound function DBF(τ i ,t) of task τ i confines the extremeaggregate execution necessity by jobs.Demand bound function of a job τ i that both arrive in, and deadlines within any interval of length tcan be defined as [2] , max 0, 1

Schedulability
System of real-time task is said to be A-schedulable in compare to a given scheduling algorithm A, if the algorithm A schedules the system such that any job of any task will not miss deadline and all jobs of all tasks will successfully execute, under all acceptablemixtures of job-arrival arrangements by the dissimilar tasks covering the system. A schedulability test for scheduling algorithm Atakes as input the configuration of a realtime system, and determines whether the system is A-schedulable or not. An A-schedulability test is said to be exact if it correctly identifies all A-schedulable systems, and sufficient if it may fail to identify some Aschedulable systems (it must guarantee, though, that all identified systems are indeed A schedulable.)A tasksystem τ is schedulable by an algorithm A if Aconfirms that the timing restrictions of all available tasks in τ are metpositively. τ is said to be possible under a class C of scheduling algorithms if τ is schedulable by some algorithm A∈C. An algorithm A is said to be idealregarding class C if A∈C and Aappropriately schedules each and every task system that is feasible under C. When the class C is not specified, it should be assumed to include all possible scheduling algorithms.

III. Global Scheduling Algorithms
A global scheduling algorithm maintains a system wide queue in which ready tasks are arranged in a priority order. Priority of task is assigned by policies based on priority like RM, EDF etc. Whenever processor becomes idle the job having priority highest is scheduled on available processor. Every time a task with higher priority than tasks executing on the processors is released lowest priority task amongst accomplishing tasks is preempted back to ready queue and higher priority task is scheduled. Later if a processor becomes idle,preempted job may be scheduled on that available processor though newly available processor is different than the processor from which it was preempted.Thus a task can migrate over available processors. This mechanism guarantees of executing m-highest priority task for multiprocessor platform having m processors. While in view of global scheduling, schedulers may be approximatelydistributed in three groups according to the priority of a task which it has for the duration of its execution. If the priority of a task cannot modifyduring the entire task lifespan, the scheduling algorithm having "fixed task priority". If the priority can modify only at job margins, as with EDF, then the algorithm will be having "fixed job priority". The above classes are frequentlystated as "priority driven". Lastly, if the priority of task can modify also in the duration of the job accomplishment, as for the P-fair class of algorithms mentioned in [3], then the algorithm has "(fully) dynamic priority". Algorithms from the final class can have a greaterconsumption bound, reaching the number of processors when deadlines are identical to periods. On the second side, they have a greater number of preemptions and relocations and a more difficult implementation. Due to these causes, it may be more promising to use a priority driven scheduler that has all the mentioned advantages related to the global scheduling. Study of global schedulers on multiprocessor environment is very much complex compared to that of uniprocessor platform. Hong and Leung proved that without knowing future arrival, period and deadline it is not possible to build an online scheduler for more than one processor [4].Dertouzos and Mok proved that without previous knowledge of start-time, computation time and deadline no scheduling algorithm can be ideal for environmentcollected by two or more than two processors [5]. When considering dynamic-job priority scheduling algorithms, Pfair algorithms [6], [7] are optimal for implicit time limit periodic and sporadic task systems, allowing a schedulable utilization equal to the available system capacity.

IV. Global Algorithm Schedulability
For guaranteed schedulability in m multiprocessor system load of all task should be less than m is the necessary condition but not sufficient. The global multiprocessor scheduling of implicit-deadline (Liu and Layland) sporadic task systems was studied in [8]. For m multiprocessor system adequatesituation for implicitdeadline sporadic task system τ to be global EDF schedulable is 1 . To this schedulability condition minor extension can be applied and density test [8]for global EDF schedulability of controlled sporadic task systems achieved is 1 .Baker [9], [10], Bertogna et at. [11] and Baruah et al. [12] each designed test for global EDF schedulability analysis.

The Goossens, Funk and Baruah Test (GFB Test)
Let SMP platform π consist of mequivalent processors and each has computing capacity s i . If a job executes on the i-th processor for t time units than it completes s i *t units of its total execution time. Let S π and s π be the sum of the computing capacities of all processors and the computing capacity of the fastest processor of platform π, respectively. The relation between an optimal algorithm for a SMP platform and global EDF scheduling [13] can be shown as ∑ ∈ and . If than set of jobs can be scheduled with global EDF on SMP having unit capacity multiprocessors. Relating all these results A periodic task setπ is EDF-schedulable upon SMP system composed by m processors with unitary capacity, if 1 This result is obtained for implicit deadline task having period same as deadline. The same result was extended for task having deadlines less than or equal to periods which states the condition of schedulabilitiy of sporadic tasksetπ with global EDF upon SMP system composed by m processors with unitary capacity, that is 1

BAKER test
Baker used another approach to derive sufficient schedulability condition [10].Assuming that task misses the deadline d k . If job arrived at r k time than between [r k , d k ] time duration load should be at least 1 and all processors should be executing job other than forD k -C k time. If during [r k , d k ] load is less than schedulability is guaranteed. Analyzing loads in[r k , d k ] is not always possible, so Backer increased this observation interval such that calculation of carry in of interfering task is possible. Here carry in time is the time consumed by job instance before between [r k , d k ]. So Backer instead used largest possible interval [a, d k ], called busy window, so that load is greater than 1 . So overall proposed condition for task set τ having n taskwith global EDFon SMP system for guaranteed schedulability is

EDF-US Test
Srinivasan and Baruah [14]studied the global EDF scheduling for periodic tasks on multiprocessors. Using hybrid scheduling policy they suggested a new method to deal with tasks having high utilization. In their hybrid approach they defined a constant ξ and give fixed highest priority to the task having higher utilization than ξ. Tasks with lower utilization than ξ were scheduled with priority assigned by conventional EDF algorithm. This algorithm is called EDF-US [ξ]. In this research they showed that any system of independent periodic tasks for which the consumption of each and every specific task is at most 2 1 ⁄ can be scheduled positively on m processors if the total utilization is at most 2 1 ⁄ .

BCL Test
Bertogna,Cirinei and Lipari used very similar ideas to that used in [9]and made extraperfections in global EDF schedulability tests. In BCL test analysis start time set to , which is different than BAK test.They observed that the proof of the utilization bound test of [15] extends naturally to cover pre-period deadlines if the utilization is replaced by / . The same proof extends to the case of post-period deadlines if / is replaced by /min , .Bertognaet. al came with schedulability test which suggests constraint deadline task set is global EDF schedulable on SMP if for each task one of the following is true Bertogna observed that any task failures to meet a deadline due to interference of other tasks, and the extremesegment of the workload of any job that can give to their inferences is 1 .

V. Conclusion
Global scheduling can have higher overhead least two cases: the contention delay and the synchronization overhead. Overhead of synchronization for a singletransmitting queue is greater than for perprocessor queues. The cost of continuing a task may be greater if it is on a distinct processor than on the processor where it last accomplished because in global scheduling we allow migration of tasks on other processors. The latter cost can be quite variable, since it depends on the actual portion of a task's memory that remains in cache when the task resumes execution, and how much of that remnant will be referenced again before it is overwritten. Backer test implements more sophisticated analysis than BCL test. BCL, GBF and BAK tests are not comparable. BCL tests performs beers in case of high utilizations tasks.BCL can discover more schedulable tasks than GBF and BAK.