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Profitoriented task scheduling algorithm in Hadoop cluster
EURASIP Journal on Embedded Systems volume 2016, Article number: 6 (2016)
Abstract
Nowadays, many enterprises provide cloud services based on their own Hadoop clusters. Because the resources of a Hadoop cluster are limited, the Hadoop cluster must select some specific tasks to allocate limited resources in order to get the maximal profit. In this paper, we study the maximal profit problem for a given candidate task set. We describe the candidate task set with a valid sequence and propose a sequencebased scheduling strategy. In order to improve the efficiency of finding a valid sequence, we design some pruning strategies and give the corresponding scheduling algorithm. Finally, we propose a timeout handling algorithm when some task runs timeout. Experiments show that the total profit of the proposed algorithm is very close to the ideal maxima and is obviously bigger than related scheduling algorithms under different experimental settings.
Introduction
With the rapid development of computer networks and sensor networks, data are exponentially increased, especially on the Internet. In order to deal with largescale data efficiently, a parallel and distributed cluster with good scalability, flexibility, and fault tolerance is needed. The MapReduce architecture [1], proposed by Google, applies a divide and conquer method to deal with dataintensive tasks and is a de facto standard in big data field. The researches on MapReduce have attracted more and more researchers and engineers. In Google, it uses a largescale cluster running MapReduce and its related techniques, such as GFS [2] and Bigtable [3], to handle hundreds of petabyte data every week. Based on the analyzing results upon these data, it provides a series of services to people around the world, such as searching, Google earth, advertisements, and so on.
Hadoop [4, 5], contributed by Yahoo!, is the opensource implementation of MapReduce and its related techniques. Hadoop is studied extensively in both academia and industry and has been deployed in many enterprises. Currently, a lot of IT enterprises build their Hadoop/MapReduce clusters and provide all kinds of cloud services to customers. While paying only a little money, the customers can use the powerful Hadoop/MapReduce cluster on demand. During this kind of service process, the service details between enterprises and customers are usually described by a service level agreement (SLA) [6, 7]. The SLAs usually include two kinds, pricing for quantity and pricing for effectiveness. The pricing for quantity SLAs charges the customers proportional to the scale of hardware and the service time. The pricing for effectiveness SLAs charges the customers according to the service effectiveness. Taking the spam email detection service [8] for example, the service must be finished in a certain time, so if only the service finishes within the required time, money would be paid.
In this paper, we study how to schedule customers’ tasks to maximize the total profit of a Hadoop cluster. In our research, we mainly focus on the timed MapReduce tasks, which are priced for effectiveness of time, i.e., tasks must be finished within the given time. Here, we abstract each task with four parts, i.e., userdefined Map/Reduce functions, time to complete, profit, and penalty, and we try to find a scheduling algorithm that maximizes the total profit of the Hadoop cluster.
The rest of the paper is organized as follows. In Section 1.1, we briefly describe the MapReduce programming environment and review related works about scheduling algorithms in MapReduce/Hadoop. In Section 1.2, we formalize the problem of maximal profit. In Section 1.3, we propose a sequencebased scheduling strategy and present a corresponding scheduling algorithm. Experiments and conclusions are given in Sections 1.4 and 2, respectively.
Background and related works
In this section, we give a short introduction to MapReduce and then review related works about task scheduling in MapReduce.
Background
MapReduce is a popular programming model for dataintensive tasks and has been widely used in many fields [9–14]. Hadoop is an opensource implementation of MapReduce, and a Hadoop cluster can be made up of thousands of commodity computers. The Hadoop cluster runs on top of the Hadoop distributed file system (HDFS). In the HDFS, data are partitioned into many small chunks and each chunk has multiple backup copies. The multiple backup copy mechanism of HDFS makes the running MapReduce tasks faulttolerant.
Another advantage of Hadoop is that it is easy to program for programmers. Programmers only need to implement the Map and Reduce functions while processing their massive data, and the details of computing, such as data partitioning, fault tolerance, and communication, are executed automatically by the underlying MapReduce framework. The MapReduce framework is illustrated in Fig. 1. In the userdefined Map function, the input is a keyvalue pair and the output is zero or more keyvalue pairs. In the group step, the system group keyvalue pairs with the same key and they are sent to the same Reduce node. In the userdefined Reduce function, the grouped keyvalue pairs are handled to generate the results. MapReduce tasks usually need several Map/Reduce iterations.
Related works
In MapReduce, there are some general task schedulers, such as FIFO scheduler [15], capacitybased scheduler [16], and fairnessbased scheduler [17]. Concerning the specific applications, Sandholm and Lai [18] proposed a scheduling algorithm, which allows users to adjust the required computing resources dynamically according to the importance of MapReduce tasks, Zaharia et al. [19] proposed a scheduling algorithm for heterogeneous cluster environments, and Kwon et al. [20] proposed the Skewtune algorithm for dealing with skewness in the processes of MapReduce tasks.
In addition, there are some scheduling algorithms, which concern the MapReduce tasks to be finished within a given time. Polo et al. [21] proposed a performancedriven task coscheduling algorithm, which estimates the required finish time for each task and allocates resources prior for the tasks that cannot be completed timely. Kc and Anyanwu [22] proposed a deadline constraint (DC) scheduler, which tries to allocate a fixed number of Map jobs to each task according to the size of tasks and assumes that each task can utilize all job slots in the Reduce step. However, the workload complementary (WC) scheduling mechanism, proposed by Verma et al. [23, 24], tries to allocate a fixed number of both Map and Reduce jobs to each task according to the size of tasks and to minimize the number of job slots for each task.
Problem statement
In this paper, we aim to maximize the total profit of a homogeneous Hadoop cluster, where the computing abilities of all nodes are the same. In a Hadoop cluster with M Map jobs and M Reduce jobs, for each submitted task j, we assume the following parameters:

j. N _{ m }, the number of Map jobs in j.

j. N _{ r }, the number of Reduce jobs in j. In order to get high efficiency, both j. N _{ m } and j. N _{ r } are the integer multiples of M.

j. deadline, the required time or deadline of j.

j. profit, the profit of j if finished before deadline. Here, we must note that if j does not finish before deadline, then the penalty of j is j. profit. α.
When a lot of customers submit their tasks to a Hadoop cluster at the same time, these tasks form a candidate task set J = {j _{1}, j _{2}, …, j _{J}}. The Hadoop cluster needs to select an acceptable task set \( J=\left\{{j}_1^{\prime },{j}_2^{\prime },\dots, {j}_{\leftJ\right}^{\prime}\right\} \) from J and schedules the selected tasks via a suitable algorithm to finish them. For each task \( {j}_i^{\prime}\in A \), if \( {j}_i^{\prime } \) finishes before \( {j}_i^{\prime } \), then \( {j}_i^{\prime } \) is effective, and the profit is \( {j}_i^{\prime }.\mathrm{profit} \); if \( {j}_i^{\prime } \) does not finish before \( {j}_i^{\prime }.\mathrm{deadline} \), then \( {j}_i^{\prime } \) is not effective, and the penalty is \( {j}_i^{\prime }.\mathrm{profit}.\alpha \), i.e., the profit is \( {j}_i^{\prime }.\mathrm{profit}.\alpha \). So, the total profit of the Hadoop cluster is
where E(⋅) indicates whether or not the given task is effective.
The proposed scheduling algorithm
In this section, we first propose a sequencebased task scheduling strategy and then propose a scheduling algorithm based on that strategy and finally present an approach for handling timeout.
Sequencebased scheduling strategy
For each task j ∈ J, we can estimate its average processing time for Map jobs, j. T _{ m }, and its average processing time for Reduce jobs, j. T _{ r }. If all task slots are used to process task j, then it needs TC _{ m }(j) = ⌈j. N _{ m }/M⌉ × j. T _{ m } time to finish all Map jobs and needs TC _{ r }(j) = ⌈j. N _{ r }/M⌉ × j. T _{ r } time to finish all Reduce jobs.
Definition 1. Sequence
For a task set JS (the number of tasks is JS), a sequence S is a permutation of all tasks in JS, and it specifies the order or jobs according to their finished times. If the finished time of j in the Map step is COT _{ m }(j), then for a given sequence S = {j _{1}, j _{2}, …, j _{JS}}, let COT _{ m }(j _{ i }) < COT _{ m }(j _{ i + 1}) for ∀ j _{ i } ∈ S(0 < i < JS).
Based on a given sequence S, we propose a scheduling strategy as follows:

Map: When an idle task slot requires a Map job, select a Map job of the first task in sequence S. When all Map jobs of the first task in S are allocated, remove the first task from S.

Reduce: Sort the tasks in JS increasingly according to their times to finish and then get a sorted queue \( {L}_a=\left\{{j}_1^{\prime },{j}_2^{\prime },\dots, {j}_{\leftJS\right}^{\prime}\right\} \). When an idle task slot requires a Reduce job, search in L _{ d } orderly for a task whose Map jobs have all finished and then select a Reduce job of the selected task.
According to the above scheduling strategy, for a given sequence S, we can compute the finished time of the Map step, COT _{ m }(j), and the finished time of the Reduce step, COT _{ r }(j), for any COT _{ m }(j). The computation of COT _{ m }(j) and COT _{ r }(j) is as follows:

Given a sequence S = {j _{1}, j _{2}, …, j _{JS}}, for ∀ j _{ i } ∈ S, COT _{ m }(j _{ i }) = COT _{ m }(j _{ i − 1}) + TC _{ m }(j) = ∑_{ k ∈ [1,i]} TC _{ m }(j _{ k }).

Given JS and L _{ d }, for the first task \( {j}_1^{\prime } \) in L _{ d }, its finished time of the Map step can be calculated out, i.e., \( CO{T}_m\left({j}_1^{\prime}\right) \), using the above method, then \( CO{T}_r\left({j}_1^{\prime}\right)=CO{T}_m\left({j}_1^{\prime}\right)+T{C}_r\left({j}_1^{\prime}\right) \). We tag the time slice \( \left[CO{T}_m\left({j}_1^{\prime}\right),CO{T}_r\left({j}_1^{\prime}\right)\right] \) as occupied. For the ith task in L _{ d }, we first computed \( CO{T}_m\left({j}_i^{\prime}\right) \) and then find a series of unoccupied time slices, whose sum to be \( T{C}_r\left({j}_i^{\prime}\right) \), beginning with the moment \( CO{T}_m\left({j}_i^{\prime}\right) \), and tag these time slices as occupied. Then, the finished time of the Reduce step of \( {j}_i^{\prime } \), i.e., \( CO{T}_r\left({j}_i^{\prime}\right) \), is the finished time of the latest time slices.
Based on the above scheduling strategy and the computation of finished time, we give the definition of a valid sequence.
Definition 2. Valid sequence
Given a task set JS and for any sequence S, if for ∀ j _{ i } ∈ JS, we have COT _{ r }(j) ≤ j. deadline based on the above scheduling strategy; then, S is a valid sequence.
Theorem 1
For a task set JS and a sequence S, the proposed scheduling strategy can make sure that, for ∀ j _{ i } ∈ JS, j _{ i } can finish its Map step with minimal time under the constraint of S.
Proof. Given the sequence S = {j _{1}, j _{2}, …, j _{JS}} and its ith task j _{ i }, S ensures that the Map step of j _{ i } starts after all Map steps of j _{ k }(1 ≤ k < i) finish, i.e., the earliest finished time of the Map step of j _{ i } is ∑_{ k ∈ [1,i]} TC _{ m }(j _{ k }). At the same time, allocating jobs based on the proposed scheduling strategy, the finished time of the Map step of j _{ i }, COT _{ m }(j _{ i }), also equals to ∑_{ k ∈ [1,i]} TC _{ m }(j _{ k }). For ∀ j _{ i } ∈ S, we can have the same conclusion.
Theorem 2
For a task set JS and a sequence S, if task timeout occurs when using the proposed scheduling strategy, then whatever scheduling strategy is used, it is impossible to finish all tasks in JS on time, and thus, S must be not a valid sequence.
Proof. From theorem 1, we know that the proposed scheduling strategy is optimal in the Map step. Here, we only consider the Reduce step. Assuming that j is a timeout task based on the proposed scheduling strategy, it can be classified into two situations:

COT _{ m }(j) + TC _{ r }(j) > j. If the Reduce step of j run immediately when its Map jobs finish and still cannot finish on time, then whatever scheduling strategy is used, j cannot finish on time.

COT _{ m }(j) + TC _{ r }(j) ≤ j. deadline and COT _{ r }(j) > j. deadline. The finished time of the Reduce step of j is later than deadline. According to the proposed scheduling strategy, there must be some period in time slice [COT _{ m }(j _{ i }), COT _{ r }(j _{ i })] occupied by other tasks’ Reduce jobs, whose time to finish is less than j. deadline. Select the task with minimal time required to finish its Map step and denote it as j′. For all tasks, whose Reduce steps run in time slice \( \left[CO{T}_m\left({j}_1^{\prime}\right),CO{T}_r\left({j}_1^{\prime}\right)\right] \), judge whether or not the tasks, whose time to finish is less than j. deadline, exist. If the tasks exist, repeat the above progress until we find a final task j _{ f }, such that all tasks, whose Reduce step runs in time slice [COT _{ m }(j _{ f }), COT _{ r }(j)], and finish later than j. deadline. Obviously, there is no any idle time slice in time slice [COT _{ m }(j _{ f }), COT _{ r }(j)]. So, if we use other scheduling strategies to make j finish on time, then there must be some other tasks that will be timeout.
In both of the above situations, it is impossible to finish all tasks in JS on time, so S must be not a valid sequence.
Based on theorems 1 and 2, we can conclude that the proposed scheduling strategy is optimal for a fixed sequence S. That means if timeout tasks under the proposed strategy exist, then they must exist in any other scheduling strategy.
Scheduling algorithm
Based on the proposed sequencebased scheduling strategy, we propose a scheduling algorithm. Firstly, when the candidate task set is static, we use a scoring strategy to specify priorities for all tasks, apply an efficient pruning strategy to find the set of acceptable tasks, and then find a valid sequence. Secondly, when the candidate task set is updated dynamically, we implement an incremental method for judging the set of acceptable tasks and update the valid sequence when necessary.
For a candidate task set c, we need to find the set of acceptable tasks \( A=\left\{{j}_1^{\prime },{j}_2^{\prime },\dots, {j}_{\leftA\right}^{\prime}\right\} \), ascertain the valid sequence of A, and then maximize the total profit. However, there are 2^{J} different acceptable sets for J, and for an acceptable set \( A=\left\{{j}_1^{\prime },{j}_2^{\prime },\dots, {j}_{\leftA\right}^{\prime}\right\} \), there are still A ! different sequences.
In order to improve the efficiency of judging an acceptable set, we first sort all tasks in J and then determine the priority for each task. Upon the features of MapReduce tasks, we mainly consider the following two aspects:

As the ability of Hadoop cluster is limited, in order to maximize the total profit, the tasks with a bigger profit ratio should be accepted prior. For ∀ j ∈ J, the consumed time of the system can be quantified as STC(j) = TC _{ m }(j) ⋅ M/(M + R) + TC _{ r }(j) ⋅ R/(M + R) and then the profit ratio of j is P _{ r }(j) = j. profit/STC(j), i.e., the profit per second when running j.

In MapReduce, if some task j is too long, then most task slots will be idle when running Map/Reduce jobs of j. This would waste lots of resources and affect the accept of other tasks.
Based on the above aspects, we propose a scoring function aiming to maximize the total profit. For a task j, the score is
where Ad(j) is the adjusting coefficient of j and STC(j) ⋅ Ad(j) is the adjusting time of j. By Eq. 2, the task with a higher score would be given a higher priority.
Let the total consumed time of Map jobs for all j ∈ J be Total TC _{ m } = ∑_{ j ∈ J } TC _{ m }(j). For task j, compute the average consumed time of all Map jobs for other tasks, \( \overline{T}{\overline{C}}_m(j)=\left(\mathrm{Total}\kern0.5em T{C}_mT{C}_m(j)\right)/\left(\leftJ\right1\right) \). Given a penalty threshold β(β > 1), if \( T{C}_m(j)>\overline{T}{\overline{C}}_m\cdot \beta \), then we think that the Map step of j is too long, and with the same reason, if \( T{C}_r(j)>\overline{T}{\overline{C}}_r\cdot \beta \), then we think that the Reduce step of j is too long. The computation of the adjusting coefficient Ad(j) for task j is as follows:
If \( T{C}_m(j)>\overline{T}{\overline{C}}_m(j)\cdot \beta \), \( T{C}_r(j)>\overline{T}{\overline{C}}_r(j)\cdot \beta \),
then \( \frac{T{C}_m(j)\overline{T}{\overline{C}}_m(j)\cdot \beta }{T{C}_m(j)}\cdot \frac{M}{M+R}+\frac{T{C}_r(j)\overline{T}{\overline{C}}_r(j)\cdot \beta }{T{C}_r(j)}\cdot \frac{M}{M+R}+1 \);
if \( T{C}_m(j)>\overline{T}{\overline{C}}_m(j)\cdot \beta \), \( T{C}_r(j)\le \overline{T}{\overline{C}}_r(j)\cdot \beta \),
then \( \frac{T{C}_m(j)\overline{T}{\overline{C}}_m(j)\cdot \beta }{T{C}_m(j)}\cdot \frac{M}{M+R}+1 \);
if \( T{C}_m(j)\le \overline{T}{\overline{C}}_m(j)\cdot \beta \), \( T{C}_r(j)>\overline{T}{\overline{C}}_r(j)\cdot \beta \),
then \( \frac{T{C}_r(j)\overline{T}{\overline{C}}_r(j)\cdot \beta }{T{C}_r(j)}\cdot \frac{M}{M+R}+1 \);
and if \( T{C}_m(j)\le \overline{T}{\overline{C}}_m(j)\cdot \beta \), \( T{C}_r(j)\le \overline{T}{\overline{C}}_r(j)\cdot \beta \),
then Ad(j) = 1.
Now, we analyze how to improve the efficiency of finding a valid sequence. Assuming that the candidate set is sorted by Eq. 2, i.e., ∀ j ∈ J, Score (j _{ i }) ≤ Score (j _{ i + 1}). The brute force searching method needs (A + 1) ! complexity to traverse all candidate sequences. In order to improve the searching speed, we give the following two approaches.
Theorem 3
Given a task set A and one of its valid sequences S = {j _{1}, j _{2}, …, j _{ n }}, for a new task j _{new}, there are n + 1 locations that can be inserted by j _{new}. If TC _{ m }(j _{new}) + COT _{ m }(j _{ i }) + TC _{ r }(j _{ i }) > j _{ i }. deadline, then j _{new} cannot be inserted into locations [1, i].
Proof. Obviously, if j _{new} is inserted into any location of [1, i], then j _{new} will be timeout.
Theorem 4
Given a task set A and one of its valid sequences S = {j _{1}, j _{2}, …, j _{ n }}, for a new task j _{new}, if TC _{ m }(j _{new}) + COT _{ m }(j _{ i }) + TC _{ r }(j _{new}) > j _{ i }. deadline, then j _{new} cannot be inserted into locations [i + 1, n + 1].
Proof. Assuming that j _{new} can be inserted into one location in [i + 1, n + 1], according to the proposed scheduling strategy, we have that the earliest finished time of j _{new} is equal to or larger than TC _{ m }(j _{new}) + COT _{ m }(j _{ i }) + TC _{ r }(j _{new}). So, j _{new} must be timeout.
Based on theorems 3 and 4, we proposed an algorithm for rapidly finding the acceptable set and its corresponding valid sequence, and the details are in algorithm 1. With the proposed algorithm, the maximum profit for the candidate task set can be got.
Timeout handling approach
We propose the above scheduling algorithm in the homogeneous Hadoop cluster, and in most cases, the estimation values of j. T _{ m } and j. T _{ r } are close to real values. However, in some abnormal situations, such as network congestion and node crashes, some accepted tasks cannot finish on time. In these situations, we must adjust the running tasks in order to get the maximum profit.
According to Eq. 1, in order to get the maximum profit, we should drop the task with the lowest profit while making other tasks finish on time. Based on this idea, we propose a timeout handling algorithm, and the details of the algorithm are in algorithm 2.
Experiments
Experimental setting
In the experiments, the Hadoop cluster contains one master node and 40 slave nodes, and each node contains an Intel Core i3 3.1 GHz CPU, 8 GB memory, and 500 GB storage and runs Redhat Linux 6.1. In the slave nodes, each node is configured with two Map task slots and two Reduce task slots.
The dataset we use in the experiments is the enwiki (https://dumps.wikimedia.org/enwiki/20150204/), and we run three classical tasks on the dataset, i.e., statistics of word frequencies, inverted index, and distributed grep. The dataset is stored on the Hadoop file system (HDFS), each chunk is 64 MB, and each data chunk has three copies. For a candidate task set J, we mainly consider the following three parameters that affect the performance:

Average task size L, i.e., the average size (number of chunks) of all tasks in L;

Task number N, i.e., the number of tasks in L;

Average deadline D, i.e., the average deadline (time to finish) of all tasks in L.
The computation of total profit is in Eq. 1. In addition, we define receive rate and finish rate as follows:
Results
The baseline algorithms we use in the experiments are DC [22] and WC [24].
Firstly, we evaluate the effect of task number on the total profit, and the results are in Fig. 2. In Fig. 2a, the ideal curve is the ideal profit, and with the increasing of average task size, all profit values decrease, but our proposed approach is close to the ideal value. In Fig. 2b, all of the three receive rates decrease gradually, but our approach has the highest value, which means that our approach can receive the most candidate tasks. In Fig. 2c, the proposed approach has a much higher finish rate than the other two. As our approach not only receives the most candidate tasks but also finishes most of them, so it can bring the most total profit.
Meanwhile, we observe the effects of task number and average deadline on the total profit, and the results are shown in Figs. 3 and 4, respectively. With the same reason, our approach not only receives the most candidate tasks but also finishes most of them, so it can bring the most total profit. In addition, the total profits of our approach for three situations are very close the ideal values.
Finally, we dynamically submit the tasks to the Hadoop cluster and observe the changes of the total profit. In Fig. 5, the horizontal axis is the elapsed time and the vertical axes are the total profit, receive rate, and finish rate, respectively. As we can see from the figure, our approach not only receives the most candidate tasks but also finishes most of them, so it can bring the most total profit. This illustrates that the proposed approach is also suitable to tasks that are submitted dynamically.
Conclusions
In this paper, we study the problem of maximal profit in a Hadoop cluster, where the resources are not enough for the whole candidate task set. In order to maximize the total profit, we select some highprofit ratio tasks based on the valid sequence of a candidate task set. Furthermore, in order to improve the efficiency of finding a valid sequence, we design some pruning strategies and give the corresponding scheduling algorithm. We also propose a timeout handling algorithm. Experiments show that the total profit of the proposed algorithm is very close to the ideal maxima and is obviously bigger than related scheduling algorithms under different experimental settings.
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Acknowledgements
This work was supported by the following funds: Department of Science and Technology of Henan (9412012Y0004, 9412012Y0005) and Education Department of Henan (13A510520, 2013gh12, 14A520053, SKL2014795).
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Chai, X., Dong, Y. & Li, J. Profitoriented task scheduling algorithm in Hadoop cluster. J Embedded Systems 2016, 6 (2016). https://doi.org/10.1186/s136390160026x
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Keywords
 MapReduce
 Scheduling algorithm
 Profit
 Big data