Actas JP2011 - Universidad de La Laguna

Actas XXII Jornadas de Paralelismo (JP2011) , La Laguna, Tenerife, 7-9 septiembre 2011term in the equation is the total bandwidth requiredby all the nodes associated with job j in cluster C k .The second term represents the communication percentageof job j in other cluster nodes (not in C k )that will use the inter-cluster link k.The saturation degree of inter-cluster links relatesthe available bandwidth of each link (ABW k ) withthe bandwidth requirements of the allocated parallelapplications, which is calculated by equation 5.BWk sat = ABW k∑j,k BW j k∀ k ∈ 1..α (5)When the required bandwidth is lower than theavailable, the link is not saturated and the communicationswill not suffer delays. Otherwise, thenetwork link is saturated, drastically reducing theperformance of all the jobs sharing the link. Thus,the job communicating slowdown (SC) is obtainedfrom the slowest, most saturated, communicationlink used by the job, calculated as the inverse of thesaturation bandwidth with equation 6.SC j = max{(BW satk ) −1 |k ∈ 1..α} (6)The goodness of this analytic performance modelwas its ability to capture the performance for eachindividual application based on the characteristicsand load conditions of the multi-cluster environment.Thus, we can use this slowdown model as a performancemetric from parallel application point ofview, allowing the scheduler to take best allocationresourcedecisions according to stablished criteria.III. Multiple-Job Co-allocation StrategyA common feature of most on-line schedulingstrategies in cluster, multi-cluster and grid environmentsis the individual allocation of resources to applications.First, the scheduler selects the next job tobe executed according to a priority criterion. Whenthere are insufficient resources to run the selectedjob, the scheduler can wait for the release of enoughresources in order to follow a First Come First Served(FCFS) schema, or select a new job from the waitingqueue that can be executed with the availableresources by applying such a schema as Fit ProcessorsFirst Served (FPFS) or backfilling, etc. Oncea job is selected, it is individually allocated to themost appropriate resources according to the establishedcriteria.However, allocating the best available resources toa job without considering the requirements of therest of the jobs in the waiting queue can impair theperformance of future allocations and therefore theoverall system performance. With the aim of overcomingthis drawback, in [3], we proposed a twophasescheduling strategy, named Package AllocationScheduling (PAS). Firstly, a Job Package Selectionfunction determines those suitable jobs in the waitingqueue that will be allocated simultaneously. Secondly,a Mixed-Integer Programming (MIP) modelreturns the allocation that minimizes their globalslowdown while preventing the saturation of theinter-cluster links and applying co-allocation whenit is necessary.A. Job Package SelectionThe main aim of the selection function is to packagethe most suitable jobs from the waiting queueto be executed simultaneously, according to certaincriteria established in terms of desired system performanceobjectives. The job package selection function(F) can be expressed as P CK = F(Q, R, C) whereQ is the set of jobs in the waiting queue, R the set ofmulti-cluster resources and C the criteria to be metby resources to allocate the job package.There is a wide variety of criteria that can be appliedfrom the point of view of resource utilizationor the nature of the parallel applications. In thepresent work, in order to assess the effects of themulti-cluster configuration and resource availabilityon the scheduling strategies, we selected the mostcommonly used criterion which selects the set of jobsin the waiting queue that fits the free multi-clusterresources, and is expressed as∑∃ P CK ⊆ Q | τ | |R ′ ||∈PCKwhere P CK is the subset of jobs from the waitingqueue (Q) whose total number of tasks is less than,or equal to, the multi-cluster resources in R ′ , whichrepresents the subset of multi-cluster resources (R ′⊆R) that meet the criteria (C), which, in our case, arethose resources non-assigned to other parallel jobs.B. MIP Allocation ModelOnce a package of waiting jobs was selected, thePAS Strategy must allocate the most suitable resourcesaccording to established performance criteria.Using the slowdown model expressed by equation2 as a parallel application performance metricand defining the resource allocating problem as aMixed-Integer programming model, as in [3], we obtainedan allocation model that minimizes the globalresponse time for the target job package.The goodness of the PAS strategy was its abilityto obtain the best resources for each parallel job consideringthe other applications that can be executedconcurrently in the multi-cluster environment, andthus reducing the global response times while makingbetter use of the resources and also preventingthe saturation of the inter-cluster links.However, the effectiveness of the scheduling strategiesin these dynamic and heterogeneous environmentsis highly sensitive to the multi-cluster configurationand its availability. Therefore, it is necessaryto conduct a thorough analysis of the effect ofthese parameters on the effectiveness of the schedulingstrategies, allowing the scheduler to adjust accordingto the system characteristics and its status.In the next section, we assess the effects of the resourceheterogeneity and availability on the effectivenessof the scheduler decisions.JP2011-527