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Mobile crowdsourcing takes advantage of mobile devices such as smart phones and tablets to process data for a lot of applications (e.g., geotagging for mobile touring guiding monitoring and spectrum sensing). In this paper, we propose a mobile crowdsourcing paradigm to make a task requester exploit encountered mobile workers for high-quality results. Since a task may be too complex for a single worker, it is necessary for a task requester to divide a complex task into several parts so that a mobile worker can finish a part of the task easily. We describe the task crowdsourcing process and propose the worker arrival model and task model. Furthermore, the probability that all parts of the complicated task are executed by mobile workers is introduced to evaluate the result of task crowdsourcing. Based on these models, considering computing capacity and rewards for mobile workers, we formulate a task partition problem to maximize the introduced probability which is used to evaluate the result of task crowdsourcing. Then, using a Markov chain, a task partition policy is designed for the task requester to realize high-quality mobile crowdsourcing. With this task partition policy, the task requester is able to divide the complicated task into precise number of parts based on mobile workers’ arrival, and the probability that the total parts are executed by mobile workers is maximized. Also, the invalid number of task assignment attempts is analyzed accurately, which is helpful to evaluate the resource consumption of requesters due to probing potential workers. Simulations show that our task partition policy improves the results of task crowdsourcing.

In recent years, the proliferation of crowdsourcing has shown significant potentials for many application areas. Crowdsourcing, a novel task-solving paradigm, means that human workers are recruited to solve complicated tasks. Extensive researchers are attracted to pay attention to crowdsourcing due to its success about human intrinsic applications.

Early successful examples are Wikipedia, Yahoo! Answers, and Yelp. As the great potential of crowdsourcing is realized in recent years, several general-purpose platforms, including oDesk and Amazon Mechanical Turks (AMT), make crowdsourcing more manageable and powerful. These online systems occur to make requesters define tasks and human workers execute them with rewards. For many online crowdsourcing systems, the common issue is inefficiency. For instance, no more than 15% tasks in Amazon mTurk system could be finished within an hour [

On the other hand, recent years witness the remarkable proliferation of intelligent mobile devices (e.g., smart phones and tablets) and the sharp growth of mobile-broadband services including data sharing and synchronization ultra-high-resolution video streaming and virtual and augmented reality. All these services continue to drive the demand for higher data rates and lead to crowdsourcing application in Internet-of-Things (IoT), where pervasive interconnected smart objects cooperates together to reach multiple goals. IoT technologies can effectively promote the interactions between environments and the human and enhance the reliability and efficiency of smart cities [

With the extensive use of mobile devices such as tablets and smart phones, mobile crowdsourcing systems (MCS) is a feasible solution to complete delay-sensitive tasks such as geotagging for mobile touring guiding monitoring and local parking space searching which are inevitable in smart cities. To improve the task-executing efficiency, a user tends to assign such delay-sensitive tasks to mobile devices to complete them and collect executing results through the wireless communication system, which is called mobile crowdsourcing. We should notice that these task-executing results must come back within delay requirement. However, mobile devices, which are portable but with less computing ability, are difficult to complete complex tasks within delay requirement. Hence, this is challenging to mobile devices and motivates us to develop a mobile crowdsourcing policy to divide large tasks into several small parts suitable for mobile devices to execute.

In this paper, we propose a mobile crowdsourcing paradigm, dividing a complicated task into small pieces and assigning small subtasks to mobile devices, to obtain high-quality executing results which means mobile devices execute as many subtasks as possible. We design the recruited process and present the worker arrival model and task model. Furthermore, the probability that all parts of the complicated task are executed by mobile workers is introduced to evaluate the result of task crowdsourcing. The higher probability means the result of the task crowdsourcing is better. According to these models, we take into consideration other factors such as the complexity and rewards of tasks which will influence mobile workers’ execution and formulate a task partition problem to maximize the probability that all parts of the complicated task are executed by mobile workers. Then, using the Markov chain, we derive a task division policy to realize high-quality results, and the invalid number of task assignment attempts is analyzed accurately based on probability generating function. Simulations show that our task partition policy improves the results of task crowdsourcing.

In this paper, we study the task partition problem of crowdsourcing process in the wireless system consisting of many mobile devices. The main contributions are summarized as follows:

Considering the mobility and capacity of mobile workers, we propose a mobile crowdsourcing paradigm to divide a complicated task into multiple subtasks and assign these subtasks to mobile workers. The mobile worker decides to execute such a subtask or not based on its computing capability and corresponding requirements.

To describe the attributes of each task, the task model is proposed to denote task load, delay requirement, and monetary reward to the mobile workers. Moreover, an arrival model of mobile workers is proposed to describe the encountered process between the requester and the mobile worker. Based on mobile worker features and task attributes, we establish the system model and formulate a task partition problem to maximize the probability that all subtasks are executed by mobile workers and guarantee the result of task crowdsourcing.

To realize the high-quality results of task crowdsourcing, using a Markov chain, the state transitions, denoting the number of subtasks executed by mobile workers, can be analyzed. Based on these state transitions within limited period, caused by delay requirement, the optimal task partition can be obtained. Then, according to the optimal task partition, the invalid number of subtask assignment is analyzed accurately with probability generating function in the total crowdsourcing process.

Simulation results show our proposed policy, compared to fix partition policy and the adaptive scheme, approaches the optimal solutions.

The rest of the paper is organized as follows. In Section

Human computation has been executed for many centuries. Specifically, if a “human” serves to “compute,” there will be a human computation which can be observed. This is the reason why there is a history of Human Computation, which is obviously longer than that of the electronic computer. With the rapid development of Internet web service, especially those facilitating online labor recruiting and managing (e.g., oDesk and Amazon MTurk), human computation begins to experience a new era where the sources of human are not designated exerts or employees but extended to a vast pool of crowds instead. This type of outsourcing to crowds, named crowdsourcing, is receiving countless success in several areas such as logistics, fund raising, monitoring, and so on.

With the extensive use of mobile devices such as tablets and smart phones, the new hybrid architecture occurs to support a massive ad hoc crowd which is composed of distributed mobile nodes and a massive social network around a smart city environment [

For indoor localization systems, a major bottleneck is the tradeoff between both localization accuracy and site survey costs. In [

To improve the executing efficiency, a complicated task is often divided into smaller pieces in crowdsourcing [

Due to the self-organized nature, requesters in mobile networks, however, do not obtain worker information in advance. Therefore, requesters have to probe worker ability and make sequential recruitment decision. This problem motivates us to design a task partition policy for mobile worker recruitment.

In [

In this section, at first, the task crowdsourcing process is described. Then, the system model, involving task attributes and mobile user features is developed, and the task partition problem is formulated to achieve optimal results.

A mobile user having a task is a requester. The requester can self-organize task crowdsourcing by recruiting several encountered mobile users who are workers in real-time. A mobile user encountering another user means they are close to establish a device-to-device (D2D) link. The term of “close” means the distance between two mobile users does not exceed WiFi-direct distance. The recruitment is described as follows.

When a mobile user (requester) launches a task, the requester is invoked to recruit some encountered mobile users (workers) in real-time. Since a complicated task is difficult for a worker to complete in time, the requester will divide the complex task into several subtasks and recruit corresponding number of workers to complete those subtasks. The requester sends attributes of a subtask including the reward, subtask load, and delay requirement to an arrived worker. The worker decides to execute this subtask or not based on available computing capacity, remaining energy, subtask reward, and delay requirement. If the worker decides to accept this subtask which means it can complete the subtask within delay requirement, its worker ability is set to 1. Otherwise, it is set to zero. Then, the worker ability value is sent to the requester. Finally, the requester decides to recruit the worker or not based on its worker ability.

If the requester decides to recruit the worker, the detailed content of a subtask is sent to the worker. During the subtask execution, it is not necessary for the requester and the worker to connect with each other all the time. After the subtask is finished by the worker, the corresponding subtask execution result will be sent back to the requester by a D2D link or cellular link satisfying the delay requirement. Once the requester receives the result in time, the subtask reward will be given to the worker. Otherwise, if the delay requirement is not satisfied, the requester thinks the worker is fraudulent and does not give the subtask reward to the worker.

The key rationale of the recruiting model is that opportunistic encounters of mobile devices are sufficient and prevalent in modern society [

Figure _{1}). Requester _{1} through a D2D link at position 1. Worker _{1} decides to execute the subtask and returns the worker ability to requester _{1}. During the period of subtask execution, worker _{1} and requester _{1} finishes the subtask, worker _{1} and requester _{1} and requester _{1} sends the result to requester _{1} sends the result to the base station at first. Then, the base station relays the result to requester _{1} by requester

Process of mobile crowdsourcing.

We use

A mobile requester can describe a task _{i}, _{i}, _{i}>, where _{i} denotes the task load of task _{i} denotes the total reward to workers after the results are returned within _{i}.

There are three parameters in the task model. Task load and delay requirement are determined by the category of the corresponding task such as content creation or information finding [

Since a task may be too complex for a mobile worker with less computing ability to complete in time, the task can be divided into many subtasks by the task requester. Then, each subtask of the task is suitable for a worker to finish.

Assume that task

The reward for a worker finishing a subtask is

The requester sends the subtask attributes including _{i}(_{i}(_{i} to a worker _{i}(_{i} with satisfying reward _{i}(

Let _{i}(_{i}(_{i}. Intuitively, _{i}(_{i}(_{i} will have negative impact on the accepting probability. However, the accepting probability is not simply defined as a function which is proportional to _{i}(_{i}(_{i} since the real case is more complicated. Let _{i}(_{i}(_{i} and its computing capacity _{i}(_{i}(_{i} change. When a mobile worker has the low remaining energy, its accepting probability will change slowly as other parameters change.

Based on the aforementioned description, the accepting probability should be the piecewise function. When the reward _{i}(_{i}(_{i}(_{iw} in this range. Then, _{iw} can be defined as

Using (_{iw} in Equation (

Since accepting probability _{iw} is the piecewise function based on the relationship between _{i}(_{i}(_{i} and _{iw} increases with the growth of subtask number _{i}/_{iw} decreases with the growth of the subtask number _{i}/_{i}/

Additionally, each worker needs some time to complete a subtask. The duration is determined by _{i}(

Therefore, the requester should assign subtasks to workers within _{i} (_{i}. Thus, _{i}. Since workers may accepting the subtasks following _{iw}, the number of accepting workers must be less than

To evaluate the result of task crowdsourcing, the probability

The task partition policy for task _{i}. Therefore, the optimal task partition problem can be formulated as

In this section, a Markov chain is used to describe the state transitions denoting subtasks assignment and calculate the optimal task partition. Then, using the transition matrix, the unsuccessful number of subtask assignment attempts before the crowdsourcing end can be analyzed. Furthermore, the time complexity of proposed algorithm is analyzed.

According to the description in Section _{i}. Additionally, each worker needs a duration _{i} to complete a subtask. The duration is determined by _{i}(

It is defined that each slot duration is _{s} equals

Figure

Slot division.

To realize the optimal task partition, we use a Markov chain to describe state transitions within task assignment duration _{0}, _{1}, _{2}, … ,_{N} to denote

The encountered worker will accept a subtask of task _{iw}, and refuse the subtask with the probability 1 − _{iw}. If the encountered worker accepts the subtask, the system moves to new state _{j} + 1 (_{j}. Otherwise, the system still stays at state _{j} if the worker refuses the subtask. When the system moves to state

When the system is currently in the state _{j} (0 ≤ _{j} + 1 with the probability _{iw} or stay at _{j} with the probability 1 − _{iw}. Thus for 0 ≤ _{j}, _{iw} and _{j}, _{iw}.

When the system is currently in the state _{j} (_{j} after one-step transition. Thus for _{j},

The one-step transition probability matrix

From the initial slot to the last slot, the system witnesses _{0} at the initial slot because no subtask is assigned. Hence, the initial distribution is _{i}(^{m−1} denotes the transition probability matrix of _{i}(

To maximize _{i}(

Then, using (_{max} denotes the allowable maximum partition number. After

For a complicated task, we use a Markov chain and the state transition matrix to obtain the optimal task partition. When the optimal partition

Total mobile workers’ arrival rate

Delay requirement _{i}

Task load _{i}

Monetary reward _{i} to a worker

Mobile workers’ computing capacity

The optimal task partition

Based on equation (_{i}(

Based on equation (_{iw} ⟵ The probability that worker

With _{iw}, transition probability matrix

Based on equation (_{i} ⟵ Duration for each worker to complete a subtask

Based on equation (

Within _{i}(

Using equation (

Using equation (

Based on equation (

The proposed task partition is optimal.

Since a complex task is difficult for a mobile device to execute, we divide a complex task into

At first, the states of the Markov chain are defined. We use _{0}, _{1}, _{2}, … , _{N} to denote _{j} means _{0} means no subtask is assigned while _{N} means all subtasks have been assigned successfully. Hence, these states describe how many subtasks are accepted.

If the encountered worker accepts the subtask with the probability _{iw}, the system moves to new state _{j} + 1 (_{j}. Otherwise, the system still stays at state _{j} if the worker refuses the subtask with the probability 1 − _{iw}. When the system moves to state _{N}, which means all subtasks of task

Within the delay requirement, the crowdsourcing process is completed if the system moves from _{0} to _{N}, which means all subtasks are accepted by workers. We use _{i}(_{0} to _{N}. This probability is determined by the partition value

Before a requester assigns all subtasks successfully, there may be some unsuccessful assignment attempts for the requester because some encountered workers do not accept the subtasks. These invalid attempts consume the requester’s resources such as energy and probing time. Based on the optimal task partition

After the optimal task partition

For 0 ≤ _{iw}, and _{iw}).

For

Note that

Let

Considering that

Let

In this section, “dummy variable

The proposed algorithm for unsuccessful assignment attempts is described as Algorithm

The probability _{iw} denoting that a worker accepts the subtask of task

The optimal task partition

The maximal value

The number

Average unsuccessful number of subtask assignment attempts

Based on transition probability matrix

Using

Using equations (

Using Equation (

The complexity of proposed algorithm is computed as follows.

We first discuss computation complexity of optimal task partition. In line 7 of Algorithm _{max}, the practical partition number cannot exceed this threshold. Meanwhile, the primary computation is matrix multiplication based on (_{max} limits the matrix size. Thus, the solution complexity is _{max})^{3m}), where _{max})^{3m}), which is determined by the allowable maximum partition number, the total arrival rate, and the delay requirement.

Then, we analyze the computation complexity of unsuccessful assignment attempts. In line 2 of Algorithm

In this section, our proposed task partition policy is evaluated by extensive simulations. Compared to the fixed partition scheme and adaptive scheme in [

For efficient comparison, in this section, we adopt two metrics: task service quality and invalid number of subtask assignment attempts.

The first metric, task service quality, is denoted by the ratio between the real completed subtasks and the total subtasks. Obviously, the more subtasks have been finished, the better task service quality can be realized. This metric can clearly illustrate how many subtasks are accepted and executed by mobile workers within the duration

The second metric calculates unsuccessful number of subtask assignment attempts within delay requirement. During the process of probing potential workers, some workers do not accept subtasks. Thus, these assignment attempts are unsuccessful. This leads to useless resource consumption of requesters and workers. The larger invalid subtask assignment attempts are, the higher invalid resource consumption is. This metric can clearly illustrate how many subtask assignment attempts are not accepted by mobile workers within the duration

The simulation environments are described as follows. As the user mobility model is widely used and validated by research works [_{i}, _{i}, and _{i} are all in the unit of slots. The requester and workers are able to communicate with others by cellular links or D2D links.

With the total arrival rate _{i} increases from 300 to 400. In Figure _{i} = 100, _{i} = 10, _{i} increases, the service quality decreases because it is difficult for workers with limited computing capacity to complete complex subtasks.

Task service quality varies with task load.

Figure _{i} increases from 80 to 100. In Figure _{i} = 10, _{i} = 350. As shown in Figure _{i} increases, because more time is permitted for workers to finish subtasks. Compared to the fix partition policies (

The task service quality varies with delay requirement.

Figure _{i} increases. In Figure _{i} = 350, _{i} = 80, _{i} increases. The reason is that the probability that workers accept subtask becomes higher with the larger _{i}. Our partition policy, even under the lower reward condition, can realize higher task service quality because our policy divides the task into small pieces based on the current reward to increase the worker’s accepting probability of each subtask. Furthermore, the fix partition policy of

The task service quality varies with rewards.

When total arrival rate of mobile workers changes, the task service quality of our partition policy also changes. In Figure _{i} = 350 and 400, respectively. Other parameters are set as follows: _{i} increases, the service quality decreases since it is difficult for workers with limited computing capacity to complete complex subtasks.

Task service quality varies with arrival rate.

Figure _{i} increases from 15 to 20, both our partition policy and the fixed partition policy experience less invalid number of subtask assignment attempts. The reason is that the workers are willing to accept subtasks with the high reward.

Invalid subtask assignment number.

In this paper, a mobile crowdsourcing paradigm has been proposed for a task requester to obtain high-quality results. We develop a recruitment process and propose system models. Jointly considering the mobile worker features (e.g., the worker computing capacity and mobility) and task partition, a task partition problem is formulated to maximize the service quality. To solve the optimal task partition problem, a Markov chain-based solution is developed to model and perform task partition. With this policy, the requester is able to divide a complex task into optimal number of subtasks and maximize the probability that all subtasks are accepted by workers within limited time. In addition, the invalid number of subtask assignment is precisely analyzed, which is helpful to evaluate the resource consumption of requesters due to probing potential workers. Simulations show that the proposed task partition policy improves the results of task crowdsourcing.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The work was supported in part by Key Research and Development Program of Shandong Province, China (no. 2017GGX10142) and in part by China Scholarship Fund.