Managing Deadline-constrained Bag-of-Tasks Jobs on Hybrid Clouds with Closest Deadline First Scheduling

Abstract

Outsourcing jobs to a public cloud is a cost-effective way to address the problem of satisfying the peak resource demand when the local cloud has insufficient resources. In this paper, we studied the management of deadline-constrained bag-of-tasks jobs on hybrid clouds. We presented a binary nonlinear programming (BNP) problem to model the hybrid cloud management which minimizes rent cost from the public cloud while completes the jobs within their respective deadlines. To solve this BNP problem in polynomial time, we proposed a heuristic algorithm. The main idea is assigning the task closest to its deadline to current core until the core cannot finish any task within its deadline. When there is no available core, the algorithm adds an available physical machine (PM) with most capacity or rents a new virtual machine (VM) with highest cost-performance ratio. As there may be a workload imbalance between/among cores on a PM/VM after task assigning, we propose a task reassigning algorithm to balance them. Extensive experimental results show that our heuristic algorithm saves 16.2%-76% rent cost and improves 47.3%-182.8% resource utilizations satisfying deadline constraints, compared with first fit decreasing algorithm, and that our task reassigning algorithm improves the makespan of tasks up to 47.6%.

1. Introduction

Hybrid cloud, combining a local cloud (private cloud) and a public cloud, is a cost-efficient way to address the problem of insufficient resources in the local cloud when its users have a peak resource demand as the peak load is much larger than average, but transient [1]. Surveyed by the European Network and Information Security Agency (ENISA), most of the small to medium enterprises prefer a mixture of cloud computing models (public cloud, private cloud) [2].

Reducing total capital expenditure on resources is a main objective on hybrid clouds for a provider owning local resources. Generally, using the resources of the local cloud is costless or cheaper, considering that investment costs for the physical infrastructures are “sunk costs”, compared with leasing the resources from a public cloud. Thus minimizing the costs for a private cloud provider on a hybrid cloud is the integration of maximizing the resource utilizations of the local cloud and minimizing the rent cost from the public cloud.

There are various researches on scheduling the scientific computing applications on hybrid clouds. A few works focus on minimizing the rent cost with deadline constraints [3-9] or minimizing the makespan [10-12] for scientific computing applications by deciding which tasks should be outsourced to the public cloud. While, these works do not consider how the local cloud/cluster provisions resources, i.e. they do not provide the mapping between physical machines (PM) and provisioned resources in the local cloud.

Only a few hybrid cloud managements [13-15] have coordinated dynamic provisioning and scheduling that is able to cost-effectively complete applications within their respective deadlines. While these works separately scheduled tasks and provisioned resources, i.e., they first decided how many resources, each of which is either a virtual machine (VM) in public cloud or a PM in local cloud(s)/cluster(s), used for running tasks and then provisioned the resources from the resource pool, considering that all of the resources are homogeneous.

Different from these existing works, we study on cost-efficiently mapping the tasks to the resources for deadline-constrained Bag-of-Tasks (BoT) jobs, a kind of very common application in the parallel and distributed systems [16,17], such as parallel image rendering, data analysis, and software testing [18-20], on a hybrid cloud with heterogeneous local resources. BoT jobs are often composed of hundreds of thousands of independent tasks and are CPU-intensive.

In this paper, we modeled the task and resource managements of hybrid clouds into a binary nonlinear programming (BNP) model. The model minimizes the cost for the resources leased from the public cloud satisfying the deadline constraints of jobs. As BNP is NP-hard problem [21], we proposed a heuristic algorithm to solve this BNP problem. In brief, the contributions of this paper can be summarized as follows:

The rest of the paper is organized as follows. Section 2 discusses related work. Section 3 presents our unified model, the heuristic algorithm for solving the model, and our task reassigning algorithm. Section 4 evaluates our work and Section 5 concludes this paper.

 

2. Related Works

There are various researches on scheduling scientific applications on hybrid clouds.

To minimize the cost for leased resources from public clouds, W. Z. Jiang and Z. Q. sheng [22] modelled the mapping of tasks and VMs as a bipartite graph. The two independent vertex sets of the bipartite graph are task and VM collections, respectively. The weight of an edge is the VM cost of a discrete task, i.e. the product of the running time of the task and the cost of the VM per unit time. Then the problem minimizing the cost is to find a subset of the edge set, where the weighted sum of all the edges in the subset is the minimum. The authors used the Hopcroft-Karp algorithm [23] to solve the minimum bipartite match problem. This work does not consider whether a task could be finish within the deadline.

Some existing work studied on minimizing cost with deadline constraints in hybrid clouds. Van den Bossche et al. [3-5] proposed a set of algorithms to cost-efficiently schedule the deadline-constrained BoT applications on both public cloud providers and private infrastructure while taking into account data constraints, data locality and inaccuracies in task runtime estimates. The Hybrid Cloud Optimized Cost (HCOC) scheduling algorithm [6,7] tried to optimize the monetary execution costs resulting from the public nodes only while maintaining the execution time fitting deadline. HCOC first made an initial schedule using the Path Clustering Heuristic (PCH) algorithm [24] to schedule the tasks to the private cloud and then rescheduled some tasks to the public cloud if the deadline is missed. The algorithm can achieve cost optimization for workflow scheduling. Genez et al. [8] presented an integer linear program model. The numbers of each type of VM instances in both private and public clouds are obtained by solving this model to minimize cost without missing its deadline for a workflow. In this work, the authors considered the VM instances with same type being homogeneous, which is not apply to a private cloud with heterogeneous PMs. For completing the job on time and with minimum cost, Chu and Simmhan [9] first modelled a time-vary spot VM price as a Markov chain and then established a reusable table with three-tuple elements consisted of job compute requirement, deadline constraint of the job and a series of actions with minimal cost based on the price model. The subsequent action was decided by performing a simple table look-up. In this work, they considered that utilizing off local machines does not incur expense.

These above work studied on either resource provisioning or task scheduling. Moreover, most approaches for dynamic provisioning operate in a per-job level, and thus they are inefficient because they fail in consider that other tasks could utilize idle cycles of cloud resources. To address these problems, Aneka [13-15] coordinated dynamic provisioning and scheduling that is able to cost-effectively complete applications within their deadlines by considering the whole organization workload at individual tasks level when making decisions and an accounting mechanism to determine the share of the cost of utilization of public cloud resources to be assigned to each user. While Aneka separately scheduled tasks and provisioned resources, i.e., Aneka first decided how many resources, each of which is either a VM in public cloud or a PM in local cloud/grids, used for running tasks and then provisioned the resources from the resource pool, considering that these resources are homogeneous.

Besides minimizing cost, a few work focused on minimizing the makespan of scientific applications by cloud bursting. FermiCloud [10] despatched a VM on the PM that has the highest utilization but still have enough resource for the VM in private cloud. Only when all the resources in private cloud are consumed, VM are deployed on a public cloud. A new VM would be launched in a public cloud only when adding the VM can reduce the average job running time. Kailasam et al. [11,12] proposed four cloud bursting schedulers whose main ideas are outsourcing a job to a public cloud when the estimated time between now and beginning execution of the job is greater than the estimated time consumed by migrating the job to the public cloud.

These aforementioned work studied on the task and/or resource management with one objective minimizing financial cost for private cloud providers or minimizing the makespan of applications. There are a few work focusing on a balance between two objectives. Taheri et al. [25] proposed a bi-objective optimization model minimizing both the execution time of a batch of jobs and the transfer time required to deliver their required data for hybrid clouds, and used a PSO-based approach to find the relevant pareto frontier. They do not take the finance expenditure into account. V. A. Leena et al. [26] proposed an algorithm for the simultaneous optimization of execution time and cost, in hybrid cloud, by determining whether tasks have to be scheduled to either the private cloud or the public cloud, employing a genetic algorithm. This work does not consider the mapping between VMs and PMs in the private cloud. The VM instances of the same type are homogeneous, which is not true in a heterogeneous data center. Wang et al. [27] proposed a dual-objective multi-dimension multichoice knapsack problem to model the task scheduling with the two objectives of minimizing the cost and minimizing the makespan in hybrid clouds. As the high complexity of solving the problem, the adaptive scheduling algorithm (AsQ) was proposed. AsQ used MAX-MIN strategy [28] to schedule task in private cloud and outsourcing the smallest task to the public cloud when the private cloud has insufficient resources. AsQ allocated the public resource slot with minimal cost to a task, fitting the deadline constraint of the task, considering that using extra public resource slots does not incur extra expense. HoseinyFarahabady et al. [29-31] studied on the balance between the makespan and the cost for BoT applications in hybrid clouds. They first established a BNP model with the objective of minimizing the sum of the weighted costs, i.e., the product of cost per unit time of a task and the running time raised to the power of a predefined factor of the task, and then relaxed the model by removing the binary constraints. By Lagrange multiplier method, the relaxed model was solved to get the workload assigned to each resource (PM in the private cloud or VM in public clouds). At last, they used FFD algorithm [32] to assigned tasks to resources so that the total workload of a resource are close to the value obtained from the last step.

In this paper, we studied on cost-efficiently mapping the tasks to the resources for deadline-constrained BoT applications on a hybrid cloud with heterogeneous local resources. Our work has the following main differences from these above works. (I) We considered that the resources are heterogeneous in the local cloud, which is very common as PMs get installed and replaced over the lifetime of a data center. (II) We directly provided the mapping of tasks to cores of PMs/VMs, instead of only mapping tasks to PMs/VMs as done by above works which did not provide the mapping between tasks and cores in a PM/VM.

 

3. Hybrid Cloud Management

In a hybrid cloud, as shown in Fig. 1, a task of jobs runs on a core of a PM on the local cloud/cluster or of a VM leased from the public cloud. In this paper, the objective is to cost-efficiently provision resources to tasks and assign the tasks to the resources to meet the complete time within corresponding deadline in the hybrid cloud environment, i.e., to provide the mapping between the PMs or rented VMs and the tasks with minimal cost while fitting deadlines.

Fig. 1.Hybrid cloud environment. A task of jobs is assigned to either a PM in local cloud(s)/cluster(s) or a VM leased from public cloud(s).

3.1 Problem Formulation

We consider a hybrid cloud consisted of a local cloud/cluster and a public cloud. Multiple public clouds in a hybrid cloud can be seen as one big public cloud including the resources provisioned by these public clouds. Table 1 summarizes notations used in this paper.

Table 1.Notations

There are J jobs running on the hybrid cloud. Job i ( i = 1, ..., J ) is composed of Ti independent tasks, {ti,j | j = 1,...,Ti}. represents the number of all tasks. It needs ri,j resource amounts to complete ti,j. Job i must be completed before di. Without loss of generality, we assume that d1 ≤ d2 ≤ ⋯ ≤ dJ.

In the local cloud/cluster, there are P PMs. In the public cloud, at most V VMs are rented. The price per unit time of VM f (f =1,...,V ) is pf. PM k ( k = 1, ..., P ) and VM f ( f = 1,...,V ) has Nk and NP+f cores, respectively. Each core of PM k (VM f ) has rk(rP+f ) capacity. It takes τi,j,k = ri,j / rk(τi,j,P+f = ri,j / rP+f ) time for completing ti,j when running on a core of PM k(VM f ). If all the tasks scheduled to a core can be completed within respective deadlines, respectively, they can run in sequential order by their deadlines in ascending fashion to meet the deadlines. Then the deadline constraints can be formulated as follow (noticing that d1 ≤ d2 ≤ ⋯ ≤ dJ ):

and

where the binary variable xi,j,k,l (i = 1,...,J , j = 1,...,Ti, k = 1,...,P , l = 1,...,Nk ) or xi,j,P+f,l (i = 1,...,J , j = 1,...,Ti, f = 1,...,V , l = 1,...,NP+f ) represents whether ti,j is assigned to core l of PM k or VM f. If so, xi,j,k,l = 1 or xi,j,P+f,l = 1, otherwise, xi,j,k,l = 0 or xi,j,P+f,l = 0. The left sides of Inequations (1) and (2) represent the finish times of ti,j, i = 1,...,J , j = 1,...,Ti, respectively. The total time using a PM/VM is the maximum finish time of the task running on it,

Thus, the costs for leasing VMs from public cloud respectively are

where ⌈τP+f⌉ is the ceiling integer of τP+f.

We formulate the problem of hybrid cloud management as a BNP as follows:

subject to:

The decision variables are xi,j,k,l (j = 1,...,Ti, i = 1,...,J , l = 1,...,Nk, k = 1,...,P ) and xi,j,P+f,l (j = 1,...,Ti, i = 1,...,J , l = 1,...,NP+f, f = 1,...,V ). The objective (6) of this model is minimizing the rent cost for VMs to complete jobs within respective deadlines. Constraints (7) ensure that each task must be assigned to exactly one core. Constraints (8) and (9) represent the binary requirements for the decision variables. After solving this model, we achieve the task assignments, xi,j,k,l (i = 1,...,J , j = 1,...,Ti, k = 1,...,P , l = 1,...,Nk ) and xi,j,P+f,l (i = 1,...,J , j = 1,...,Ti, f = 1,...,V , l = 1,...,NP+f ), and the renting time for each VM, cf / pf ( f =1,...,V ).

3.2 The Heuristic Algorithm

As BNP is NP-hard [21], we propose a heuristic algorithm to solve the model presented in Section 3.1 in polynomial time. The main idea of the algorithm is to assign the task to a core so that the finish time of the task is closest to its deadline. If there is no enough resource, the algorithm adds an available PM with most capacity or leases a VM with best cost-performance ratio from the public cloud when there is no available PM in the local cloud. The details of the algorithm are described as follows, outlined in Algorithm 1.

Step 1: If there is no available resource (line 2), the algorithm would add an available PM (lines 3-8) or lease a VM (lines 9-14) from public cloud when there is no available PM in local cloud. The selection principle of a PM is to selecting the PM with most capacity (line 4). The selection principle of rented VM is that the selected VM has the capacity to complete any task when running alone (C1 in line 10) and has best cost-performance ratio (C2 in line 10). If there are multiple types of VMs having same cost-performance ratio, the algorithm selects the VM with minimal price per unit time (C3 in line 10). After selection, the algorithm adds the cores of selected PM (lines 6-8) or rented VM (lines 11-13) to the pool of available cores.

Step 2: When there are one or more available cores (line 15), the algorithm assigns the unassigned tasks to these cores (lines 15-24). For all of assignments between unassigned tasks and available cores, the algorithm examines the finish times of the tasks and selects the assignment that the difference between the finish time of the task and its deadline is minimal and that the task is finished within its deadline (lines 16-20). If no assignment that the task can be finished within its deadline, there is no available resource for the unassigned task (lines 21-22).

Step 3: The algorithm repeats Steps 1 and 2 until there is no unassigned task (line 1).

The computing resource consumed by the algorithm are mainly composed of the selection of an available PM or VM and the decision of an assignment between a task and a core. In real world, the numbers of VM instance types and cores in a PM/VM both are a few tens or fewer, thus the selection of a PM or VM and the decision of an assignment are O(P) and O(T), respectively, in time complexity. Therefore, assigning tasks to PMs is O(T · (P + T)) in time complexity. We assume that there are NRV VMs leased from public cloud for completing the tasks within their respective deadlines. Assigning tasks to a VM is O(T) in time complexity. Thus, assigning tasks to the rented VMs is O(T · NRV) in time complexity. Hence, the algorithm is O(T · (P + T + NRV)) in time complexity, overall.

3.3 Improvement on the Heuristic Algorithm

After task assignment, there may be some PMs/VMs on which the workloads are imbalance among cores. For these unbalanced PMs/VMs, the finish times of tasks or/and the lease time can be improved by balancing the workloads. For example, as shown in Fig. 2, four tasks are assigned to a VM with two cores, and the first three tasks are assigned to one core while the fourth task are assigned to another core. These four tasks will be finished within first, second, third, and second unit time, respectively. The lease time of the VM is 3 unit time. While if Task 3 is assigned to another core, the lease time would be reduced to 2 unit time and the finish time of Task 3 would be reduced to within second unit time.

Fig. 2.An example that the lease time of a VM instance and the finish time of a task are improved without additional cost by reassigning tasks.

For improving the imbalance on a PM/VM, we present the reassignment algorithm (RA), outlined in Algorithm 2. For each PM/VM (lines 1-3), the algorithm examines whether the finish time of the task with latest finish time (lines 8-10) could be reduced by reassigning the task to the core with the lightest load (lines 11-12) on a PM/VM, and, if so, reassigns the task to the core (lines 13-20). The algorithm repeats the step until the latest finish time can not be reduced (lines 21-22). The time complexity of the algorithm is no more than the number of tasks because only some of tasks are considered to reduce the latest finish time for a PM/VM, thus RA is O((P + NRV ) ·T) in time complexity at worst.

 

4. Experiments Results and Analysis

In this section, we introduce our testbed and experiment design, and then discuss the experimental results.

4.1 Testbed and Experiments Design

We use a 3-month trace collected from the University of Luxemburg Gaia cluster system and a 2-month trance collected from NASA Ames iPSC/860, i.e., UniLu Gaia log and NASA iPSC log in Parallel Workloads Archive [33], to evaluate the performance of our algorithms. We assume that the trace data are the information of tasks running on 1 GHz cores. The features of these two traces are shown in Table 2 where short and long tasks are considered as tasks whose running time shorter than and equal to 1 hour and longer than 1 hours, respectively. As shown in the table, we can see that the proportion of short tasks in Gaia trace is smaller than that in NASA trace. We set the deadline of each task as α (1, 2, 3, or 4) times of its run time on a 2 GHz core.

Table 2.The number of tasks and the proportions of short and long tasks in Gaia and NASA traces.

The PMs used as the local resources are shown in Table 3. In public cloud, we use a compute optimized instance type, c3.large in EC2 [34], because it has the best cost-performance ratio for CPU-intensive applications, compared with other instances provisioned by EC2. Each VM instance has 2 vCPUs with 2.7GHz. The price of a VM instance is $0.105 per hour (in US east (N. Virginia)).

Table 3.The CPU configurations and numbers of PMs used for local resources.

We compare our algorithm (HA) against a baseline algorithm, First Fit Decreasing (FFD) [32], one of the most popular task scheduling algorithm. FFD is assigning the longest task to the first core on which it will fit.

We compare task management algorithms in the following aspects:

4.2 Comparison of Task Management Algorithms

Figs 3, 4, 5, 6, 7, and 8 show rent costs, local loads, makespans of tasks, overall resource utilizations, energy consumption and overheads for finishing the tasks, managed by FFD and HA running on a Intel(R) Xeon(R) CPU E5410 @ 2.33GHz core, within their respective deadlines, respectively.

Fig. 3.The rent costs for finishing Gaia (a) and NASA (b) tasks within their deadlines

Fig. 4.The load assigned to local resources

Fig. 5.The times finishing Gaia (a) and NASA (b) tasks

Fig. 6.The utilizations of PMs/VMs running Gaia (a) and NASA (b) tasks

Fig. 7.The estimated energy consumed by PMs

Fig. 8.The CPU times consumed by task assignments

For completing Gaia and NASA tasks within their respective deadlines, respectively, as shown in Fig. 3, HA consumes less 16.2%-76% cost than FFD for leasing VMs from public cloud. The reason is that HA uses more local resources than FFD, reflected by Fig. 4 showing that HA assigns more 52.6%-231.1% loads to local resources than FFD, and thus consumes less resources leased from the public cloud. While HA postpones the finish time of these tasks to 11.8%-82.6% later, as shown in Fig. 5, compared with FFD, with completing the tasks within their respective deadlines. The less rent cost and longer finish time of HA imply that HA makes better use of resources, compared with FFD. From Fig. 6, we can see that the resource utilization of HA is 47.3%-182.8% more than that of FFD. These can be explained as follows. FFD schedules longest task first, and thus there will be small tasks left to be scheduled after assigning most of tasks. For finishing the left small tasks within their respective deadlines, only a few small tasks are assigned to one rented VM. Therefore, these VMs running only small tasks are under-utilised as rented VMs are charged by unit time, leading to high costs and low utilizations. While HA schedules the task closest to its deadline first, and thus rarely has the problem.

Fig.s 3 and 5 show that the rent cost is decreased with increasing the deadline while the finish time increases with deadline. The reason is that tasks are allocated less resources, which leads to longer waiting time of tasks and thus longer time to finish these tasks, if their deadlines are postponed. From Fig. 3, we can also see that, compared with FFD, HA has decreasing ratios increasing from 24.2% to 43.2% for Gaia trace and 16.2% to 62.5% for NASA trace in rent cost as the deadline factor α increases from 1 to 4, i.e., the cost improved by HA is more and more better than that by FFD as deadlines are postponed overall. The reason is that, when deadlines are postponed, more short tasks are consolidated in both PMs with long tasks and VMs with idle rent time which is less than 1 hour to reduce rent costs for HA, while for FFD, short tasks are hardly consolidated in PMs as FFD schedules long tasks to PMs first to increase resource utilizations. We also get the result that the increasing extent of decreasing ratios of rent costs for NASA trace is greater than for Gaia trace as increasing deadlines for HA compared with FFD, from Fig. 3. This can be explained as follows. The proportion of short tasks in NASA trace is larger than that in Gaia trace, as shown in Table 2. More short tasks mean more VMs with idle rent time when deadlines are short, and thus more room for improving rent costs by consolidating short tasks in PMs or VMs with idle rent time when postponing deadlines, and HA makes better usage of these improvements than FFD as analyzed above.

Assigning more loads to local resources increasing the energy consumed by local cloud. Here we examine the energy consumption of PMs for HA and FFD. To calculate energy consumption, we use the prevalent linear model [35,36] and the parameters of a modern mid-rang computer of which consumed powers with idle and full load respectively are 70W and 110W, given in [36], i.e. the energy consumption of a PM is

where Δτ is the time interval of using the PM to run tasks and u(τ) is the resource utilization at time τ. The results are shown in Fig. 7. As shown in this figure, HA consumes only less than 50% more energy than FFD. Compares with FFD, the increase rates of energy consumptions are much less than that of loads assigned to local resources, respectively, for HA. This implies that HA uses local resources much more effectively than FFD.

As shown in Fig. 8, HA consumes less time than FFD when the deadline is early (α = 1 or 2), while it consumes more time than FFD when it is late (α = 3 or 4). The reasons are as follows. The time complexities of HA and FFD are O(T · (P + T + NRV )) and O(T · (P + NRV )), respectively. When the deadline is earlier, the number of rented VMs is larger. When α = 1 or 2, the number of rented VMs used by FFD is larger than 4000, as shown in Fig. 9, which is above 288% more than that by HA and is larger than the number of tasks for both Gaia and NASA traces, and thus the time consumed by FFD is more than HA. When α ≥ 3 , the rented VM numbers are smaller than task numbers, therefore, FFD consumes less time than HA.

Fig. 9.The numbers of rented VMs for completing tasks within respective deadlines

Thus, HA is much better than FFD in minimizing costs and improving resource utilizations with only a few overheads for resource and task managements of hybrid clouds.

Next, we examine the scalabilities of HA and FFD on the number of local PMs. We scale the PM resources by a factor ranging from 1 to 10. For example, when the scale factor is 1, 15 PMs described in Table 2 are used for running tasks, while there would be 150 PMs when the scale factor is 10. Fig.s 10 and 11 show the changes of costs and time consumed by HA and FFD with the scale factor, respectively. We present the results of the case of α = 4 here. Other cases have similar results. As shown in Fig. 10, the cost is decreased with increasing of PM numbers because the resources should be leased from the public cloud are reduced in amount as the amount of local resources increases. From Fig. 11, we can see that HA costs less 24.1%-75.1% and about 20% than FFD for Gaia and NASA traces, respectively, for any scale of local cloud, i.e., HA always consumes less cost than FFD. As shown in Fig. 11, the times consumed by FFD and HA both are stable as the increase of PM number. The reason is that the increase of PM number results in the decreasing of rented VM number, leading to the total number of the PMs and rented VMs (P + NRV ) having almost no change as the PM number increases.

Fig. 10.The rent costs decreasing with increasing of PM numbers

Fig. 11.The times consumed by task assignments, stable when the local PM number is increasing

Now, we examine the scalabilities of HA and FFD on the number of tasks by changing the task scale from 1000 to 35000 in number using Gaia trace. Fig. 12 presents the result of the case of α = 1. Other cases have similar results. As shown in the figure, the consumed times of HA and FFD both are quadratically increasing with the task number, which is consistent with their respective time complexities. Fig. 12 shows that the costs have nearly linear increases with the increase of task number as more resources required for processing more tasks and that HA saves 25.7%-58.1% costs compared with FFD.

Fig. 12.The variations of rented costs and consumed times by task assignments with increasing the task number

These results above indicate that HA is better than FFD in minimizing rent cost and that both HA and FFD have good scalability.

4.3 Performance of the Improvement Method

In this section, we experimentally study on the improvement of our improvement method (RA presented in Section 3.3) on the performance of task managements by comparing these two task managements with (+RA) and without combining RA.

As shown in Fig. 3, we can see that RA is hardly improving rent costs. This is because that the imbalances mostly exist in PMs, leading to hardly reduction of the lease time of VMs by reassigning.

Fig. 5 shows that RA improves 36%-47.6% task makespans for FFD when α ≥ 2 while 22.3% for HA only when α = 3 , which indicates that the workloads managed by HA are much more balance than that by FFD on a PM/VM. RA also improves up to 20% and up to 7.8% energy consumptions for FFD and HA, respectively, as shown in Fig. 7, by reducing the finish time of the tasks running on PMs.

As shown in Fig. 6, the resource utilizations are almost not improved by HA. This is because the lease times of VMs are almost not reduced by HA, leading to almost no improvement of resource utilizations for VMs. The numbers of VMs are much more than that of PMs, respectively, resulting in negligible improvement of overall resource utilizations when the resource utilizations of PMs are improved.

RA consumes only less than 0.005s CPU time which is negligible, as shown in Fig. 8, and does not change the number of rented VMs for hybrid cloud managements, as shown in Fig. 9.

These above observations indicates that RA improves the hybrid cloud managements in improving rent costs, makespans of tasks, and resource utilizations with negligible overheads.

 

5. Conclusion

In this paper, we studied the hybrid cloud management for Deadline-constrained BoT jobs. We first model the hybrid cloud management to a BNP problem which minimizes the rent costs for leasing VMs from public cloud. As BNPs are NP-hard problems, we propose the heuristic algorithm to solve the BNP problem in polynomial time. The algorithm's main idea is assigning a task to a core such that the difference between the finish time of the task and its deadline is minimal in all of feasible assignments. If none of unassigned tasks can be completed within its deadline, the algorithm adds an available PM with most capacity or rents a new VM with highest cost-performance ratio and assigns tasks to the new PM/VM as previous step. As there are workload imbalances between cores on a PM/VM after task assigning, we propose a task reassigning algorithm to balance them. Extensive experiments using real world traces have been conducted to study on the effectivenesses and efficiencies of our heuristic algorithm and reassigning algorithm.

In this paper, we focused on BoT jobs consisted of independent tasks. In the future, we will study the management of workflow jobs containing tasks which can be started only when the tasks they depend on are finished on hybrid clouds.