^{1}

^{1}

^{1}

Nowadays, mobile services (applications) running on terminal devices are becoming more and more computation-intensive. Offloading the service requests from terminal devices to cloud computing can be a good solution, but it would put a high burden on the network. Edge computing is an emerging technology to solve this problem, which places servers at the edge of the network. Dynamic scheduling of offloaded service requests in mobile edge computing systems is a key issue. It faces challenges due to the dynamic nature and uncertainty of service request patterns. In this article, we propose a Dynamic Service Request Scheduling (DSRS) algorithm, which makes request scheduling decisions to optimize scheduling cost while providing performance guarantees. The DSRS algorithm can be implemented in an online and distributed way. We present mathematical analysis which shows that the DSRS algorithm can achieve arbitrary tradeoff between scheduling cost and performance. Experiments are also carried out to show the effectiveness of the DSRS algorithm.

With the rapid development of Information Technology and increasing promotion of terminal devices [

One of the key issues in MEC research is how to schedule service requests [

Some existing researches have studied the service request scheduling problem in MEC systems. Reference [

In this article, we introduce a dynamic online service request scheduling mechanism which requires no prior information of the statistical information of request arrivals. Specifically, the request scheduling among multiple MEC systems is formulated as an optimization problem, and the goal is to minimize request scheduling cost while providing performance guarantees. Based on Lyapunov optimization techniques, we propose a Dynamic Service Request Scheduling (DSRS) algorithm. DSRS uses a parameter

The remainder of this article is organized as follows. In Section

Consider

Notations and definitions.

Notation | Definition |
---|---|

| Services set. |

| MEC systems set. |

| Number of requests for service |

| Number of requests for service |

| Number of requests for service |

| Unit cost of scheduling requests for service |

| Queue length of service |

| Scheduling cost for all the services in time slot |

In each time slot

The request scheduling method in our article will make use of the diversity of different MEC systems to provide service in order to reduce scheduling cost while providing performance guarantees.

Let

Instead of studying the instantaneous scheduling cost, we focus on the long-term average cost. The time-average scheduling cost across time slots

Queueing delay is one of the most important performance metrics. According to

To reduce queueing delay and maintain system stability, we seek to bound the average queue length. Let the time-average queue length across the

To combine scheduling cost and performance, the request scheduling problem in this article is formulated as

Solving problem (

In this section, based on the Lyapunov optimization framework [

Based on Lyanuov optimization techniques, we define

A small value of

By reducing the value of

The parameter

In each time slot

By squaring the both sides of (

Then, we define

Taking the expectations on the condition of

Since it holds that

By adding

Substituting (

Following the design principles of Lyapunov optimization techniques, we design an efficient Dynamic Service Request Scheduling (DSRS) algorithm to minimize the upper bound of

In each time slot

As the request scheduling decisions

Problem (

After the scheduling decisions

1: In the beginning of each time slot

2:

3:

4:

5:

6:

7:

8:

9:

10:

11:

12:

13:

14:

15:

16:

17:

18:

In this section, we present mathematical analysis of the boundary of the time-average queue length and scheduling cost of our DSRS algorithm. It can be proven that our algorithm can achieve the scheduling cost arbitrarily close to the optimal value while maintaining the stability of the MEC systems. Let

We present in Lemma

For any service request arrival rate

Lemma

Since it is assumed that there exists upper bound

Assume that there exists

Furthermore, the time-average system scheduling cost can be bounded by (

Since it holds that

As our DSRS algorithm can achieve the minimum value of the R.H.S of (

Substituting (

Moving

To be general, we assume the queue length is empty when

Dividing both sides of (

By summing both sides of (

Dividing both sides of (

Taking a lim of (

Then, we analyze the time complexity of the DSRS algorithm. According to Algorithm

In this section, we conduct experiments to evaluate our DSRS algorithm. First, we analyze the impact of parameters. Then, we present comparison experiments which show the effectiveness of our DSRS algorithm.

In the experiments, we consider 4 MEC systems, each with an edge server providing services for the offloaded requests. There are two types of heterogeneous services. For each service

Figures

Scheduling cost with different values of

Queue length with different values of

We analyze the effect of service request arrival rate on the scheduling cost and queue length. In the experiments, for each application

Scheduling cost with different arrival rates.

Queue length with different arrival rates.

To analyze the effect of unit scheduling cost on the MEC systems, we scale the unit scheduling cost up or down to

Scheduling cost with different unit scheduling costs.

Queue length with different unit scheduling costs.

We conduct comparison experiment and compare our DSRS algorithm with Randomized algorithm to evaluate the effectiveness of the DSRS algorithm. The Randomized algorithm schedules all the service requests to each MEC system randomly. The scheduling costs and queue lengths of the two algorithms are shown in Figures

Scheduling cost under different algorithms.

Queue length under different algorithms.

We can see from Figure

In this article, we study dynamic request scheduling for MEC systems. We formulate it as an optimization problem, and the goal is to optimize scheduling cost while providing performance guarantee. We propose the DSRS algorithm to solve the optimization problem, which transforms it to a series of subproblems and solves each one efficiently in a distributed way. Mathematical analysis is presented which demonstrates that the DSRS algorithm can approach the optimal scheduling cost while bounding the queue length. Parameter analysis experiments and comparison experiments are both conducted to verify the effectiveness of the DSRS algorithm.

Most of the simulation experimental data used for supporting the study of this article are included within the article. Further additional information about the data is available from the corresponding author.

The authors declare that they have no conflicts of interest.

This work is supported by the National Natural Science Foundation of China (no. 61370065 and no. 61502040), the Key Research and Cultivation Projects at Beijing Information Science and Technology University (no. 5211823411), Beijing Municipal Program for Excellent Teacher Promotion (no. PXM2017 014224 000028), and the Supplementary and Supportive Project for Teachers at Beijing Information Science and Technology University (no. 5111823401).