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Mobile crowdsourcing, as an emerging service paradigm, enables the computing resource requestor (CRR) to outsource computation tasks to each computing resource provider (CRP). Considering the importance of pricing as an essential incentive to coordinate the real-time interaction among the CRR and CRPs, in this paper, we propose an optimal real-time pricing strategy for computing resource management in mobile crowdsourcing. Firstly, we analytically model the CRR and CRPs behaviors in form of carefully selected utility and cost functions, based on concepts from microeconomics. Secondly, we propose a distributed algorithm through the exchange of control messages, which contain the information of computing resource demand/supply and real-time prices. We show that there exist real-time prices that can align individual optimality with systematic optimality. Finally, we also take account of the interaction among CRPs and formulate the computing resource management as a game with Nash equilibrium achievable via best response. Simulation results demonstrate that the proposed distributed algorithm can potentially benefit both the CRR and CRPs. The coordinator in mobile crowdsourcing can thus use the optimal real-time pricing strategy to manage computing resources towards the benefit of the overall system.

With the explosion of mobile devices, mobile computing has become an overwhelming trend in the development of mobile networks and Internet of things (IoT) [

On the other hand, with the proliferation of increasingly powerful mobile devices, mobile users can collaboratively form a mobile cloud to provide pervasive services, such as data collection, processing, and computing [

Resource management is one of the fundamental issues in mobile networks and IoT for network utility maximization (NUM) [

To the best of our knowledge, this is an early effort towards providing a systematic framework of optimal computing resource management in mobile crowdsourcing. We hope that this pioneering work can throw light on coordinating the real-time interaction among the CRR and CRPs via the optimal real-time pricing strategy. Specifically, the original contributions of this paper are summarized as follows:

We model the CRR and CRPs behaviors and formulate the computing resource management in mobile crowdsourcing as an optimization problem. The proposed distributed algorithm does not require anyone to reveal its private information.

We take account of the interaction among CRPs and formulate the computing resource management as a game with Nash equilibrium achievable via best response.

Simulation results demonstrate that both the CRR and CRPs will benefit from the proposed algorithm.

The remainder of this paper is organized as follows. The system model is introduced in Section

Consider a mobile crowdsourcing system consisting of one CRR, one or multiple CRPs, and a coordinator. The time cycle is divided into

At the beginning, consider a simple case for a mobile crowdsourcing system consisting of one CRR, one CRP, and a coordinator. We formulate the interaction among the CRR, CRP, and coordinator as local and global optimization problems and obtain the solution in a distributed way. The resource price is taken as an incentive to reach the balance between the supply and demand, as well as the maximum benefit of both the CRR and CRP.

Firstly, in a certain time slot, under the resource price

Similarly, in a certain time slot, under the resource price

From the system perspective, it is desirable that the satisfaction of the CRR is maximized and the expense of the CRP is minimized. Mathematically, we define the system welfare as

Note that the problem is a concave maximization problem, which can be solved by convex optimization techniques in a centralized way [

However, the arising challenge is that the coordinator needs to know the exact utility function of the CRP and cost function of the CRP. Since such information is private and no one wants to reveal any, the coordinator may not have sufficient information to solve problem (

In order to solve problem (

Comparing (

Firstly, for the CRR, the locally optimal solution to (

Taking the resource price

Overall, by jointly solving (

In order to preserve everyone’s privacy, it is possible to approach the optimal resource price of the dual problem (

The coordinator begins with any initial resource price

On receiving the resource price

On receiving the local optimal computing resource demand

where

Repeat from

With the sufficiently small step size

The interaction among the CRR, CRP, and coordinator is shown in Figure

Interaction among CRR, CRP, and coordinator.

Note that the globally optimal price which balances between the supply and demand will also achieve the maximum benefit of both the CRR and CRP. Otherwise, if the supply is less than the demand, the exceeded computing resource demanded by the CRR will not be satisfied, which reduces its benefit; similarly, if the supply is larger than the demand, the exceeded computing resource supplied by the CRP will be wasted, which reduces its benefit too.

Now, consider another case for a mobile crowdsourcing system consisting of one CRR, multiple CRPs, and a coordinator.

Firstly, we focus on the interaction only between the coordinator and each CRP; that is, each CRP is expected to respond to the resource price announced by the coordinator. Under this paradigm, each CRP only communicates with the coordinator as depicted in Figure

Without interaction among CRPs.

The problem formulation of this case is similar to that in Section

From the system perspective, it is desirable that the satisfaction of the CRR is maximized and the sum of the expense of all CRPs is minimized. We take the utility function minus the sum of all cost functions as the objective with the constraint that the total supply should be at least equal to the demand. Thus the global optimization problem from the system perspective is

Note that the problem is a concave maximization problem, which can be solved by convex optimization techniques in a centralized way; for example, the Lagrangian is defined as

Similarly, in order to solve problem (

Similarly, in order to preserve everyone’s privacy, it is possible to approach the optimal resource price of the dual problem (

The coordinator begins with any initial resource price

On receiving the resource price

On receiving the local optimal computing resource demand

Repeat from

The interaction among the CRR, each CRP, and coordinator is shown in Figure

Interaction among CRR, each CRP, and coordinator.

Rather than focusing only on how each CRP behaves individually, we propose a framework with interaction among CRPs via message exchanges; for example, each CRP may share the information of its computing resource supply

With interaction among CRPs.

From (

Game theory is a study of selfish and rational players and a formal model of interactive decision-making situation [

Nash equilibrium (NE) is the most important concept of equilibrium condition in game theory. NE is such a static stable strategy vector that no player has any benefit from unilaterally deviating from this strategy. A strategy vector

A game can be shown to have NE if the following conditions are satisfied [

The player set is finite.

The strategy sets are closed, bounded, and convex.

The payoff functions are continuous in strategy space and quasi-concave.

An

A basic modeling assumption in this paper is that each CRP behaves rationally in a self-interested manner. Each one wants to adjust its strategy to maximize its own payoff. We model the computing resource management in mobile crowdsourcing as a game among CRPs:

Taking (

Initial condition: each player chooses a random strategy.

Adaption condition: each player chooses an optimal strategy according to the strategies of others to improve its own payoff:

Note that, at each iteration, each player updates its strategy while the others keep their strategies fixed.

Repeat

Note that (

Each CRP shares the information of its current computing resource supply

The CRP

On receiving the total supply, the CRR calculates the value of

On receiving the feedback, the CRP

Repeat from

The interaction among the CRR and each CRP is shown in Figure

Interaction among CRR and each CRP.

We provide numerical examples to evaluate the proposed distributed approach.

Consider a mobile crowdsourcing system with one CRR and one CRP. The simulation parameters are set as

Computing resource management in a mobile crowdsourcing system of the one-CRR and one-CRP case.

Next, in Figure

Impact of adjustable parameters.

Consider a mobile crowdsourcing system with one CRR and three CRPs. The simulation parameters for the CRR are the same as those in Section

In Figure

Computing resource management in a mobile crowdsourcing system of the one-CRR and multi-CRP case.

In Figure

CRP game in a mobile crowdsourcing system of the one-CRR and multi-CRP case (

In Figure

CRP game in a mobile crowdsourcing system of the one-CRR and multi-CRP case (

In Section

Comparison between solutions in Sections

In this paper, we propose an optimal real-time pricing strategy for computing resource management in mobile crowdsourcing, which is based on utility maximization. It can be implemented in a distributed manner such that the real-time interaction among the CRR and CRPs is coordinated through a limited number of message exchanges. We show that there exist real-time prices that can align individual optimality with systematic optimality. We also take account of the interaction among CRPs and formulate the computing resource management as a game with Nash equilibrium achievable via best response. Simulation results demonstrate that, by using our proposed optimization-based real-time pricing strategy, not only the CRR but also CRPs will benefit. The coordinator in mobile crowdsourcing can thus use the optimal real-time pricing strategy to manage computing resources towards the benefit of the overall system.

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

This work was supported by the State Key Laboratory of Industrial Control Technology, Zhejiang University, China.