Utilization Difference Based Partitioned Scheduling of Mixed-Criticality Systems
UUtilization Difference Based Partitioned Schedulingof Mixed-Criticality Systems
Saravanan Ramanathan, Arvind Easwaran
Nanyang Technological University, SingaporeEmail: [email protected], [email protected]
Abstract —Mixed-Criticality (MC) systems consolidate multiplefunctionalities with different criticalities onto a single hardwareplatform. Such systems improve the overall resource utilizationwhile guaranteeing resources to critical tasks. In this paper, wefocus on the problem of partitioned multiprocessor MC schedul-ing, in particular the problem of designing efficient partitioningstrategies. We develop two new partitioning strategies basedon the principle of evenly distributing the difference betweentotal high-critical utilization and total low-critical utilizationfor the critical tasks among all processors. By balancing thisdifference, we are able to reduce the pessimism in uniprocessorMC schedulability tests that are applied on each processor, thusimproving overall schedulability. To evaluate the schedulabilityperformance of the proposed strategies, we compare them againstexisting partitioned algorithms using extensive experiments. Weshow that the proposed strategies are effective with both dynamic-priority Earliest Deadline First with Virtual Deadlines (EDF-VD)and fixed-priority Adaptive Mixed-Criticality (AMC) algorithms.Specifically, our results show that the proposed strategies improveschedulability by as much as . and . for implicit andconstrained-deadline task systems respectively. I. I
NTRODUCTION
Growing complexity in safety-critical real-time systems hasled to the concept of consolidating multiple applications withvarying criticalities on a common hardware platform. In orderto provide guaranteed execution and safe isolation for thecritical functions from non-critical ones, the resources aregenerally reserved using static partitioning. The drawback ofthis approach is that reserving the resources for the criticalfunctions can potentially lead to under-utilization of the systemresources. To overcome this challenge, Vestal [1] proposed themixed-criticality (MC) model, and since then MC schedulinghas received a lot of attention. See [2] for a very good reviewon MC scheduling algorithms.Efficient algorithms that are capable of scheduling a largeclass of MC systems are highly desired. There are several MCalgorithms designed for both uniprocessor and multiprocessorsystems. Most of the multiprocessor algorithms are designedbased on either global scheduling or partitioned scheduling.In this work, we focus on partitioned MC scheduling mo-tivated by the fact that 1) they have a better schedulabilityperformance compared to global MC scheduling [3], and 2)safety-critical industries have a preference for them becausethey are a natural extension of uniprocessor scheduling [4].The partitioned MC scheduling problem comprises twomain challenges: 1) Statically assigning tasks to proces-sors ( partitioning strategy ), and 2) Scheduling the tasks oneach processor using uniprocessor MC scheduling algorithms. The partitioning strategies can be classified into two types: criticality-aware partitioning in which tasks of a higher crit-icality are assigned to processors before tasks of a lowercriticality, and criticality-unaware partitioning in which nosuch allocation order exists. The choice of partitioning strategyhas a significant impact on the performance of any partitionedscheduling algorithm. Although for conventional (non-MC)systems, first-fit decreasing utilization/density is known to bethe best performing strategy, for MC systems there is noknown partitioning strategy that performs well in all cases.In this paper, we propose a new partitioning strategy fordual-criticality MC systems called Utilization Difference basedPartitioning (UDP) inspired by the following observation.In dual-criticality systems, there are tasks with two critical-ity levels, namely high and low . The high-criticality taskshave two processor utilization values, a low mode utilizationfor execution behaviours in which all tasks are required tomeet deadlines, and a high mode utilization for executionbehaviours in which only the high-criticality tasks are requiredto meet deadlines. The performance of many uniprocessor MCscheduling algorithms depend on the sum of difference betweenthese two utilization values (denoted in short as utilizationdifference ) across all the high-criticality tasks assigned to aprocessor. A smaller utilization difference on a processor gen-erally implies that the MC tasks allocated on that processor ismore likely to be schedulable, because the additional demandof high-criticality tasks when the system switches from low tohigh mode is also small. Therefore, under the UDP strategywe aim to distribute this utilization difference evenly acrossall processors.We propose two partitioning strategies based on UDP;a criticality-aware strategy called
CA-UDP as well as acriticality-unaware strategy called
CU-UDP . We use threedifferent scheduling algorithms with both these strategies;Earliest Deadline First with Virtual Deadlines (EDF-VD) [5],Earliest Carry-over Deadline First (ECDF) [6] and AdaptiveMixed-Criticality (AMC) [7]. We chose these algorithms be-cause they cover both dynamic and fixed-priority schemes, andtheir schedulability tests are such that the pessimism in thosetests can be reduced by a smaller utilization difference. Notethat the EDF-VD test also has an optimal speed-up bound of / for implicit-deadline MC task systems, implying that Speed-up bound denotes the smallest increase in processor-speed necessaryto schedule all feasible MC task systems. Systems in which relative deadlines of tasks are equal to their minimumrelease separation time or period. a r X i v : . [ c s . O S ] M a r he resulting partitioned MC scheduling algorithms also havea speed-up bound of / (see Section II for a discussion onthis speed-up bound).We performed extensive experimental evaluation of the pro-posed partitioned scheduling algorithms and compared themwith existing algorithms. For implicit-deadline task systems,the schedulability improvement using our algorithms is asmuch as . with EDF-VD when compared to an existingalgorithm with a known speed-up bound, and . withECDF and . with AMC when compared to existingalgorithms without a known speed-up bound. For constrained-deadline task systems, the schedulability improvement usingour algorithms is as much as . with AMC and . with ECDF when compared to existing algorithms. We alsoobserved that the performance of our algorithms improvesignificantly with increasing number of processors, indicatingtheir scalability. Among the two partitioning strategies, CA-UDP and
CU-UDP , CU-UDP has a better performance overallbecause it allocates high utilization low-criticality tasks earlier,and hence is more likely to find a feasible allocation for suchheavy utilization tasks.
Related Work.
There have been few studies on partitionedMC scheduling algorithms. Kelly et al. [8] introduced thefixed-priority, partitioned multiprocessor MC scheduling andshowed that decreasing criticality and first-fit partitioning per-forms well in comparison to decreasing utilization and worst-fit partitioning. Lakshmanan et al. [9] presented a criticality-aware hybrid partitioning strategy with decreasing utilization.Baruah et al. [3] presented a partitioned scheduling algorithmbased on EDF-VD and proved that the algorithm has a speedupof / . They also showed that partitioned scheduling performsbetter than the global variant in terms of schedulability.Rodriguez et al. [10] evaluated different partitioning strategiesunder EDF-VD and showed that criticality-aware partitioningperforms better than criticality-unaware partitioning. Guanet al. [11] presented a criticality-aware partitioning strategywith worst-fit allocation for high-criticality tasks and first-fit allocation for low-criticality tasks, additionally also givingpreference to heavy utilization low-criticality tasks. They ap-plied this partitioning strategy to a demand bound functionbased test and virtual deadline based algorithm presentedin [12]. None of the above studies considered partitioningstrategies based on evenly distributing the utilization differenceof high-criticality tasks among all processors.II. S YSTEM M ODEL AND S CHEDULING A LGORITHMS
We consider a dual-criticality (namely LC for low-criticalityand HC for high-criticality) sporadic task system τ comprising n tasks scheduled on a multiprocessor platform with m cores.Each task τ i is defined by a tuple ( T i , χ i , C Li , C Hi , D i ), where T i ∈ R + denotes the minimum release separation time, χ i ∈{ LC, HC } is the criticality level of the task, C Li and C Hi are the LC and HC execution requirements respectively (weassume C Li ≤ C Hi for HC tasks), and D i ∈ R + is the relativedeadline of the task; D i = T i for all i in the case of an Systems in which relative deadlines of tasks are no more than theirminimum release separation time or period. implicit-deadline task system and D i ≤ T i for all i in thecase of a constrained-deadline task system.LC task set τ L and HC task set τ H are defined as τ L def = { τ i ∈ τ | χ i = LC } and τ H def = { τ i ∈ τ | χ i = HC } respectively. Also, the LC and HC utilization of a task τ i is u Li def = C Li /T i and u Hi def = C Hi /T i respectively. Normalizedsystem-level utilizations are defined as U LL def = (cid:80) τ i ∈ τ L u Li /m , U LH def = (cid:80) τ i ∈ τ H u Li /m and U HH def = (cid:80) τ i ∈ τ H u Hi /m .The system is said to be either in the LC mode or inthe HC mode. If all tasks τ i ∈ τ signal completion beforeexceeding their LC execution requirement, the system is saidto be in the LC mode and all task deadlines are required tobe met in this mode. If any HC task τ i ∈ τ H executes beyondits LC execution requirement, but signals completion beforeexceeding its HC execution requirement, the system is saidto be in the HC mode. Mode switch instant is defined as thefirst time instant in a busy interval when the system modechanges from LC to HC. No LC task deadlines are requiredto be met after mode switch, and hence several MC algorithmsimmediately discard all LC tasks.We now briefly describe the uniprocessor MC scheduling al-gorithms and tests used in our experiments. We consider threeof them: fixed-priority Adaptive Mixed-Criticality (AMC) [7],dynamic-priority Earliest Deadline First with Virtual Dead-lines (EDF-VD) [5], and dynamic-priority Earliest Carry-over Deadline First (ECDF) [6]. This choice of algorithmsis motivated by two facts: 1) it enables us to show that theproposed partitioning strategies work well with both dynamicas well as fixed-priority algorithms, and 2) all these algorithmshave schedulability tests whose pessimism can be reduced byreducing the difference between total HC and LC utilizationsof HC tasks allocated on a processor; therefore these tests arewell suited to be used with the proposed strategies.Under AMC, each task has a fixed-priority and all LC tasksare immediately dropped upon a mode switch. We use a pre-viously developed response time analysis based uniprocessorschedulability test for this algorithm (AMC-max test in [7]).Since a worst-case mode switch instant is unknown, this testconsiders all possible mode switch instants until the low moderesponse time of the task.Under EDF-VD, each HC task is assigned a virtual deadlineto be used in the LC mode that is no larger than the actualdeadline. These virtual deadlines are assigned using a singlescaling factor so that the slack in the low mode is uniformlydistributed among all HC tasks. Tasks are then scheduled usingEDF in both modes, and LC tasks are immediately droppedupon a mode switch. For implicit-deadline task systems, anutilization based uniprocessor schedulability test for EDF-VDwith an optimal speed-up bound of / has been developed(Theorems and in [5]). This test has also been com-bined with a simple first-fit partitioning strategy to derivea partitioned scheduling algorithm with a speed-up boundof / [3]. In fact, this work shows that any partitioningstrategy which considers all processors for allocation of atask before declaring failure has the same speed-up boundof / when used with this test (Theorem in [3]). Sinceour proposed strategies have this property, by combining thetrategies with this EDF-VD test, the resulting partitionedalgorithms also have a speed-up bound of / for implicit-deadline task systems .Similar to EDF-VD, ECDF is also based on assigningvirtual deadlines to HC tasks in the LC mode, and uses EDFfor scheduling. But, unlike EDF-VD, it uses a demand boundfunction based test and a greedy deadline assignment strategy(Theorem in [6]). This test can be used for both implicit aswell as constrained-deadline task systems, but it does not havea known speed-up bound. Partitioned versus global scheduling.
There is a fundamentaldifference in the behaviours of partitioned versus global MCscheduling algorithms when a mode switch is triggered. Underglobal scheduling, when a HC task on a processor triggersa mode switch, it is reflected instantaneously on the otherprocessors, meaning all LC tasks are discarded thereafter.Whereas, under partitioned scheduling, the mode switch isrestricted only to that particular processor. Essentially, thetasks executing on other processors, including LC tasks, areunaffected by the mode switch. This isolation between pro-cessors is feasible under partitioned scheduling because theMC schedulability tests are applied independently on eachprocessor. It is an important property because it also reducesthe impact on LC tasks, and this could be one of the reasonswhy partitioned MC scheduling may find preference in safety-critical industries.III. U
TILIZATION D IFFERENCE B ASED P ARTITIONING (UDP) S
TRATEGIES
In this section, we present two partitioning strategies basedon evenly distributing the utilization difference among allprocessors; a criticality-aware strategy called CA-UDP anda criticality-unaware strategy called CU-UDP. The guidingprinciple behind both these strategies is the same, which isto reduce the maximum gap between the total HC utilizationand total LC utilization of the HC tasks allocated on eachprocessor, i.e., max { U HH ( φ k ) − U LH ( φ k ) | ≤ k ≤ m } .We use φ k to denote the k th processing core. At anypoint during the partitioning strategy, we use τ ( φ k ) todenote the set of tasks assigned to processor φ k untilthat point. Then, the system-level utilizations for processor φ k at that point can be defined as follows: U LL ( φ k ) def = (cid:80) τ i ∈ τ ( φ k ) ∧ χ i = LC u Li , U LH ( φ k ) def = (cid:80) τ i ∈ τ ( φ k ) ∧ χ i = HC u Li and U HH ( φ k ) def = (cid:80) τ i ∈ τ ( φ k ) ∧ χ i = HC u Hi .Algorithm 1 presents a detailed pseudocode for CA-UDP.Under this strategy, all HC tasks ( τ H ) are assigned to proces-sors before assigning any of the LC tasks. To successfullyassign tasks having very high utilization values, we sortthe tasks in decreasing order of utilization values at theirrespective criticality levels, i.e., tasks in τ H are sorted based on u Hi , whereas tasks in τ L are sorted based on u Li . For tasks in τ H , CA-UDP uses a worst-fit allocation strategy based on theparameter U HH ( φ k ) − U LH ( φ k ) , i.e., processors are considered inincreasing order of U HH ( φ k ) − U LH ( φ k ) . This strategy ensuresan even distribution of the utilization difference among allprocessors. For tasks in τ L , CA-UDP uses a simple first-fitallocation strategy. Before assigning any task to a processor, we evaluate the feasibility of this allocation using one of theschedulability tests mentioned in Section II depending on thechosen scheduling algorithm. If the test fails on a processor,then the next processor in the fitting order is considered. If thetest fails on all processors, then the partitioning is declared afailure. Algorithm 1
CA-UDP (cid:46)
Partitioning τ H Sort τ H in decreasing order of u Hi . for j := 1 to length( τ H ) do Sort φ k in increasing order of U HH ( φ k ) − U LH ( φ k ) . for k := 1 to m do if τ ( φ k ) ∪ τ i is schedulable then τ ( φ k ) = τ ( φ k ) ∪ τ i and break. end if end for if τ i could not be allocated then Return partitioning failed. end if end for (cid:46)
Partitioning τ L Sort τ L in decreasing order of u Li . for j := 1 to length( τ L ) do for k := 1 to m do if τ ( φ k ) ∪ τ i is schedulable then τ ( φ k ) = τ ( φ k ) ∪ τ i and break. end if end for if τ i could not be allocated then Return partitioning failed. end if end for
Return τ ( φ k ) , ∀ k ∈ [1 , . . . , m ] . Example.
Consider an example task set as shown in Figure 1to be scheduled on processors ( φ and φ ) using partitionedEDF-VD algorithm. To illustrate the benefit of CA-UDP, wecompare it with another criticality-aware partitioning strategythat uses worst-fit allocation based on total HC utilizationalone for HC tasks and an identical strategy as CA-UDP forLC allocations (denoted as CA-Wu-F). Figure 1 shows the taskallocation under both these strategies when applied to EDF-VD. Under CA-Wu-F, task τ is assigned to φ and tasks τ and τ are assigned to φ . Although task τ can fit on either φ or φ based on its utilization, it fails to get allocated onany of the processors because the EDF-VD schedulability test (cid:0) U LL ( φ k ) ≤ (1 − U HH ( φ k )) / (1 − ( U HH ( φ k ) − U LH ( φ k ))) (cid:1) fails.Whereas, under CA-UDP, tasks τ and τ are allocated onone processor and task τ is allocated on the other processorin order to balance the utilization difference. Then, task τ can be successfully allocated on the processor with τ . Thus,by balancing the utilization difference, we are able to providemore processor choices for LC tasks, which consequently im-proves schedulability. One of the challenges with a criticality-aware partitioning strategy such as CA-UDP is that it oftenfails to allocate LC tasks with very high utilization values,ig. 1: Comparison of CA-UDP and CA-Wu-Fbecause these tasks are considered after all the HC tasks havebeen allocated. To address this problem, a simple approach isto consider a criticality-unaware partitioning strategy in whichall tasks (HC and LC) are allocated in the decreasing orderof their utilization values at their respective criticality levels.Based on this principle of criticality-unaware allocation, wepropose another UDP strategy called CU-UDP. Under thisstrategy, all tasks in τ are collectively sorted in decreasingorder of utilization; u Hi is used as utilization for tasks in τ H and u Li is used as utilization for tasks in τ L . The rest of thestrategy is identical to CA-UDP; a worst-fit allocation strategybased on the parameter U HH ( φ k ) − U LH ( φ k ) for HC tasks, anda simple first-fit allocation strategy for LC tasks. Example.
Figure 2 shows an example task set to be scheduledon processors using EDF-VD. For this example, CU-UDPgives a successful partition while CA-UDP fails as shownin Figure 2. Under CA-UDP, tasks τ and τ are allocatedto φ and tasks τ and τ are allocated to φ . As a result,the EDF-VD schedulability test fails on both processors whenallocating τ . In the case of CU-UDP, tasks τ and τ areallocated to φ and φ respectively. Also, due to criticality-unaware partitioning, task τ is allocated to φ before tasks τ and τ . Then, tasks τ and τ are successfully allocated to φ . In this example, CU-UDP was able to prioritize allocationfor a heavy utilization LC task τ while still balancing theutilization difference, and hence gave a successful partition.Fig. 2: Comparison of CA-UDP and CU-UDPIV. E VALUATION
In this section, we evaluate the proposed partitioning strate-gies by combining them with three uniprocessor MC schedul-ing algorithms as discussed in Section II, EDF-VD, ECDF andAMC. Specifically, we compare their schedulability against thefollowing existing partitioned MC algorithms: • CA(nosort)-F-F-EDF-VD [3], which is the only par-titioned scheduling algorithm with a known speed-up bound. It uses criticality-aware partitioning without sort-ing the tasks, first-fit allocation strategy for both HC aswell as LC tasks and employs EDF-VD algorithm. • ECA-Wu-F-EY [11], which is an enhanced critical-awarepartitioning strategy with worst-fit allocation based on HCutilization alone for HC tasks and a first-fit allocation forLC tasks. The enhancement is that preference is givento heavy utilization LC tasks over HC tasks, while therest of the allocation uses critical-aware partitioning. Thetasks are sorted based on the utilization values at theirrespective criticality levels before being allocated. ECA-Wu-F-EY employs a virtual deadline based uniprocessorMC scheduling algorithm called EY that is identical toEDF-VD and ECDF [12], except that the schedulabilitytest is based on demand bound functions as in ECDF butit is relatively less efficient in terms of schedulability. • CA-F-F-EY [10], is also a criticality-aware partitioningstrategy with a simple first-fit allocation for both HC andLC tasks. The tasks are sorted based on utilization valuesat their respective criticality levels before being allocated,and scheduled using EY algorithm. It has been previouslyshown that this algorithm dominates all other existingcriticality-aware partitioning strategies in experiments.
Experiment Setup.
We use the task set generator proposedin [13] for our experiments. The task set parameters used inour generator are as follows: • m ∈ { , , } is the total number of processors. • u min ( = 0 . ) and u max ( = 0 . ) denote the minimumand maximum individual task utilization respectively. • The normalized system utilizations are given by U HH ∈ [0 . , . , . . . , . , . , U LH ∈ [0 . , . , . . . , U HH ] and U LL ∈ [0 . , . , . . . , . − U LH ] . • The total number of tasks in a task system is lowerbounded by m + 1 and upper bounded by ∗ m . • P H = 0 . denotes the percentage of HC tasks. • The period T i of a task τ i is drawn log-uniformly ([14])at random from [10 , . • Utilizations u Li and u Hi are derived using standard tech-niques ([13], [14]) that ensure a uniform distribution ofvalues. LC and HC executions C Li and C Hi are thenderived as (cid:100) u Li ∗ T i (cid:101) and (cid:100) u Hi ∗ T i (cid:101) respectively. • The deadline D i of the task τ i is drawn uniformly from [ C Hi , T i ] for constrained-deadline task systems.We generate 1000 task sets for each value of total normal-ized utilization U B ( U B = max ( U LH + U LL , U HH ) ). Results.
In Figures 3, 4 and 5, we present the overallschedulability performance of the algorithms for varying m and P H = 0 . , where we plot the acceptance ratios of thealgorithms, i.e., fraction of task sets deemed to be schedulableversus total normalized utilization U B . As shown, both CA-UDP and CU-UDP based algorithms perform much better thanall the existing algorithms. In addition, the performance gapbetween our algorithms and the existing algorithms increaseas m increases, depicting its scalability.In Figure 3, we compare the performance of UDP strategieswith EDF-VD against CA(nosort)-F-F-EDF-VD for implicit-deadline task systems. All the three algorithms use the same a) EDF-VD ( m = 2 ) (b) EDF-VD ( m = 4 ) (c) EDF-VD ( m = 8 ) Fig. 3: Comparison of Acceptance Ratio (implicit-deadline with speed-up bound) (a) m = 2 (b) m = 4 (c) m = 8 Fig. 4: Comparison of Acceptance Ratio (implicit-deadline w/o speed-up bound) (a) m = 2 (b) m = 4 (c) m = 8 Fig. 5: Comparison of Acceptance Ratio (constrained-deadline)EDF-VD schedulability test, and consequently have a speed-upbound of / . As shown, the performance improvement overCA(nosort)-F-F-EDF-VD due to UDP is as much as . , . and . for m = 2 , and respectively.In Figures 4 and 5, we compare the performance of UDPstrategies with ECDF and AMC against ECA-Wu-F-EY andCA-F-F-EY, for implicit- and constrained-deadline task sys-tems respectively. The performance of CA-UDP based algo-rithms is similar to that of CU-UDP based algorithms but withthe slightly lower performance. For clarity of presentation, weonly present the results of CU-UDP based algorithms. Forimplicit-deadline task systems the performance improvementover existing algorithms is as much as . , . and . under AMC, and . , . and . under ECDF, for m = 2 , and respectively. Correspondingly for constrained-deadline task systems, it is as much as . , . and . under AMC, and . , . and . under ECDF, for m = 2 , and respectively.In Figure 6 we compare the weighted acceptanceratio (WAR) of the algorithms for varying P H ∈{ . , . , . , . , . } and m ∈ { , } . Weighted acceptanceratio is defined as W AR ( S ) = (cid:80) UB ∈ S ( AR ( U B ) XU B ) (cid:80) UB ∈ S U B , where S isthe set of U B values and AR( U B ) is the acceptance ratio fora specific value of the total normalized utilization U B . Eachdata point in the plot corresponds to at least task sets.In Figure 6a, we present the performance of the UDPstrategies with EDF-VD for implicit-deadline task systems.As it can be seen, the performance of CA-UDP decreaseswith increasing percentage of task criticality. At very high P H values, the task set comprises mainly of HC tasks andas a result, the LC tasks in the system have high utilization a) Implicit-deadline (EDF-VD)(b) Constrained-deadline Fig. 6: Varying Percentage of Task Criticalityvalues. Hence, CA-UDP performs poorly. In Figure 6b, wecompare the performance of UDP strategies with AMC andECDF for constrained-deadline task systems. The performanceof all the strategies with criticality-aware worst-fit allocation ofHC tasks decreases as P H increases. This is expected becausewhen a large number of HC tasks are present in the system,criticality-aware partitioning behaves like a traditional (non-MC) system where worst-fit allocation is known to performpoorly. Algorithms with CU-UDP strategy perform well irre-spective of the P H values.An interesting observation from these plots is the very goodperformance of CA-UDP and CU-UDP with AMC. It is worthnoting that there is no existing partitioned MC algorithm thatemploys a fixed-priority scheme such as AMC. This is mainlybecause AMC is known to perform poorly when compared todynamic-priority schemes such as ECDF and EY. Our resultsshow that in the case of partitioned multiprocessor scheduling,the choice of partitioning strategy has a significant impacton algorithm performance. This improved performance underAMC is also important because fixed-priority scheduling isgenerally preferred in safety-critical industries.Another interesting observation is that the performance ofCU-UDP strategy is slightly better than CA-UDP, irrespectiveof the schedulability test being used. This is due to theprioritized allocation of heavy utilization LC tasks, while stillensuring a balanced distribution of the utilization differenceof HC tasks under CU-UDP. Although CA-UDP balances thisutilization difference, it does so at the cost of non-allocatingheavy utilization LC tasks.Thus, we can conclude that the proposed UDP strategies sig-nificantly improve schedulability across a variety of schedulingalgorithms. The fact that schedulability under AMC is also better than for strategies using EY, shows that the observedimprovements are primarily because of the partitioning strate-gies, rather than due to difference in schedulability tests.V. C ONCLUSION
In this paper, we considered the problem of partitioningdual-criticality task systems on a multiprocessor platform. Weproposed a utilization difference based partitioning scheme forallocating the HC tasks to the processors, which essentiallybalances the workload between the two criticality levels oneach processor. We compared our partitioning strategies withexisting approaches using three different scheduling algo-rithms. Our results show that the proposed strategies for bothcriticality-aware and criticality-unaware partitioning performmuch better than the existing approaches under both dynamicas well as fixed-priority scheduling.A
CKNOWLEDGEMENT
This work was funded in part by the Ministry of Education,Singapore, grant number ARC9/14.R
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