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# Dynamic Service Request Scheduling for Mobile Edge Computing Systems

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## Abstract and Figures

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.
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Research Article
Dynamic Service Request Scheduling for
Mobile Edge Computing Systems
Ying Chen , Yongchao Zhang, and Xin Chen
Computer School, Beijing Information Science and Technology University (BISTU), Beijing 100101, China
Correspondence should be addressed to Ying Chen; chenying@bistu.edu.cn
Received 20 April 2018; Accepted 3 July 2018; Published 13 September 2018
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Nowadays, mobile services (applications) running on terminal devices are becoming more and more computation-intensive.
Ooading 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 ooaded 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.
e DSRS algorithm can be implemented in an online and distributed way. We present mathematical analysis which shows that
the DSRS algorithm can achieve arbitrary tradeo between scheduling cost and performance. Experiments are also carried out to
show the eectiveness of the DSRS algorithm.
1. Introduction
With the rapid development of Information Technology and
increasing promotion of terminal devices [], the mobile ser-
vices (applications) running on terminal devices are becom-
ing more and more complex and computation-intensive [,
]. However, the computing capacity and battery life of
terminal devices are generally limited, and these devices
cannot aord to process all these service requests locally on
devices. To solve this problem, some researches propose to
ooad the service requests from terminal devices to cloud
computing, which has more computing resources and larger
capacity [–]. Nevertheless, cloud computing is usually
located remotely that is far away from terminal devices.
Besides, with the increasing popularity of mobile services
running on terminal devices, scheduling all the ooaded
service requests to cloud computing can put a signicant
burden on the networks [, ]. To meet this challenge,
recent researches have been proposed to put edge servers
with computing capacities at the edge of the networks in
close proximity to terminal devices. Mobile Edge Computing
(MEC) is an emerging technology based on this idea [–],
and it has drawn extensive attention from both academy and
industry [–].
One of the key issues in MEC research is how to schedule
servicerequests[,,]:whenalargenumberofservice
requests are ooaded, how to schedule service requests
among multiple MEC systems in order to reduce scheduling
costwhileprovidingperformanceguarantees.Itisintuitive
that there exist tradeos between scheduling cost and per-
formance. Besides, the service request scheduling problem
among multiple MEC systems is challenging due to several
reasons. Firstly, as terminal devices are moving and the
service environment varies over time [, ], how to make
dynamic request scheduling decisions in accordance with the
uncertainty of request patterns and changing environment
is a great challenge []. Secondly, with the increasing
promotion of terminal devices and mobile services, both the
number of terminal devices and mobile services are rising
dramatically, making the service request scheduling problem
more complicated.
Some existing researches have studied the service request
scheduling problem in MEC systems. Reference [] mod-
elled the server in the MEC as one //1queue. Reference
Hindawi
Wireless Communications and Mobile Computing
Volume 2018, Article ID 1324897, 10 pages
https://doi.org/10.1155/2018/1324897
Wireless Communications and Mobile Computing
system according to a Poisson process. ese works assumed
the request arrival followed certain distribution. However,
in reality, the request arrival process is highly dynamic, and
the statistical information of request arrival can hardly be
obtained or precisely predicted [, ]. Besides, with the
number of terminal devices and mobile services increasing,
traditional centralized optimization techniques such as com-
bination optimization and dynamic programming may suer
from high-complexity and result in long execution time.
request scheduling mechanism which requires no prior
information of the statistical information of request arrivals.
Specically, 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 Schedul-
ing (DSRS) algorithm. DSRS uses a parameter to control
the tradeo between scheduling cost and queue length.
Mathematical analysis is presented which proves that DSRS
is (1/)-optimal with respect to the average scheduling
cost while still bounding the average queue length by ().
Experiments are also conducted which demonstrate that
DSRS can make dynamic control decisions to adjust to
variable environments and achieve the tradeo between
scheduling cost and queue length.
InSection,wepresentthesystemmodelfordynamic
request scheduling among multiple MEC systems and for-
mulate the optimization problem. In Section , based on
Lyapunov optimization techniques, we propose an online and
Dynamic Service Request Scheduling algorithm. eoretical
analysis of the scheduling algorithm is presented in Section .
Experiments are conducted to evaluate the eciency and
eectiveness of the scheduling algorithm in Section . We
2. System Model
2.1. Overview. Consider mobile edge computing (MEC)
systems. Each MEC system has an edge server virtualized to
virtual machines to process ooaded requests of types of
services from the terminal devices [, ]. More specically,
the -th virtual machine on each edge server in the MEC sys-
tem serves the ooaded requests for the -th type of service.
Let be the collection of indexes for applications and be
the collection of indexes for edge server in the MEC systems.
Without loss of generality, the edge servers in dierent MEC
systems are supposed to be heterogeneous. We consider a
time-slotted model and the length of time slot is denoted by
. e main notations in this section are listed in Table .
2.2. Problem Formulation
2.2.1. Service Request Scheduling. In each time slot ∈
{0,1,...,−1}, a number of service requests for the types
of services are ooaded. Let 𝑖() be the number of requests
for service ooaded to the MEC systems in time slot .In
our article, we require no prior knowledge of the statistics of
𝑖(), which is generally hard to obtain or precisely predict in
real-life. 𝑖𝑗() represents the number of requests for service
that are scheduled to the edge server in the -th MEC system
in time slot .𝑖𝑗() is the request scheduling control variable.
It should be satised that
𝑗∈𝐽𝑖𝑗 ()=𝑖(),∀. ()
e request scheduling method in our article will make
use of the diversity of dierent MEC systems to provide
service in order to reduce scheduling cost while providing
performance guarantees.
2.2.2. Scheduling Cost. Let 𝑖𝑗()betheunitcostofscheduling
requests for service to the -th MEC system. 𝑖𝑗() can
be dierent among dierent services and dierent MEC
systems . It can also vary across time for other factors such
as trac, wireless fading, the available resources, etc. e
request scheduling cost of service in time slot can be
calculated as 𝑗∈𝐽 𝑖𝑗()𝑖𝑗(). e total scheduling cost for all
the services can be expressed as
()=
𝑖∈𝐼
𝑗∈𝐽𝑖𝑗 ()𝑖𝑗 ().()
Instead of studying the instantaneous scheduling cost,
we focus on the long-term average cost. e time-average
scheduling cost across time slots {0,1,...,1}can be
expressed as
= lim
𝑇󳨀→∞ 1
𝑇−1
𝑡=0
E(). ()
is the minimization objective of the request scheduling
2.2.3. Performance. Queueing delay is one of the most impor-
tant performance metrics. According to Little’s Law, queueing
delayisinproportiontothenumberofrequestswaitingin
the queue. us, we seek to reduce queue length and maintain
low congestion states. Let 𝑖𝑗()represent the queue length of
service in the -th MEC system in time slot .𝑖𝑗() denotes
the number of requests for service that can be served by the
-th MEC system. us, the queue length 𝑖𝑗() evolves as
𝑖𝑗 (+1
)=max 𝑖𝑗 ()−
𝑖𝑗 (),0+𝑖𝑗 ().()
To reduce queueing delay and maintain system stability,
we seek to bound the average queue length. Let the time-
average queue length across the  ∈ {0,1,..., 1}slots
represented by 𝑖𝑗. e service request scheduling method in
𝑖𝑗 =lim
𝑇󳨀→∞ 1
𝑇−1
𝑡=0
E𝑖𝑗 ()<, ∃∈R+.()
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T : Notations and denitions.
Notation Denition
Services set.
MEC systems set.
𝑖() Number of requests for service in time slot .
𝑖𝑗() Number of requests for service that are scheduled to the -th MEC system in time slot .
𝑖𝑗() Number of requests for service that can be served by the -th MEC system in time slot .
𝑖𝑗() Unit cost of scheduling requests for service to the -th MEC system.
𝑖𝑗() Queue length of service on the -th MEC system in time slot .
() Scheduling cost for all the services in time slot .
2.2.4. Unied Framework. To combine scheduling cost and
is formulated as
minimize = lim
𝑇󳨀→∞ 1
𝑇−1
𝑡=0
E(); ()
subject to constraints (), ().
Solving problem () oine requires the future informa-
tion (such as requests arrival information, scheduling cost
information) which is generally hard to obtain or precisely
predict in practice. us, we propose an online Dynamic
Service Request Scheduling algorithm to solve the problem,
which will be shown in Section .
3. Dynamic Request Scheduling
Algorithm Design
In this section, based on the Lyapunov optimization frame-
work [], we decompose the original optimization problem
into a series of independent subproblems. en, we design
a Dynamic Service Request Scheduling algorithm to solve
these subproblems in a distribute way.
3.1. Problem Transformation Using Lyapunov techniques.
Based on Lyanuov optimization techniques, we dene Θ() =
(𝑖𝑗())as the queue length matrix of the MEC systems. en,
we denote (Θ()) as the Lyanuov function as follows, which
is a scalar measure of the queue congestion state in the system,
(Θ()) =1
2
𝑖∈𝐼
𝑗∈𝐽2
𝑖𝑗 ().()
Asmallvalueof(Θ()) indicates that the queue lengths
of all MECs are small, which represents a low congestion state
of the MEC systems according to the Little’s Law.Inorderto
reduce queue length and maintain system stability, we seek to
keep the Lyanuov function at a small value. en, we dene
the conditional Lyapunov dri(Θ()),
(Θ()) =E{(Θ(+1
)) −(Θ()) ()}.()
By reducing the value of (Θ()),wecanpushthe
Lyanuov function towards to a small value. To integrate
scheduling cost and queue length in the MEC systems, we
dene the dri plus cost according to Lyapunov optimization
framework, which is expressed as
(Θ())+E()(). ()
e parameter can be considered as the tradeo
parameter between the scheduling cost and queue length,
which can be determined by service providers or users
according to their requirements in real applications. Next in
eorem , we show that the dri plus cost is upper bounded
if the service arrival rate can be upper bounded.
eorem 1 (bounding dri plus cost). In each time slot ,
under any algorithm, for all possible values of Θ() and any
parameter value of ,ifthereexitsapeakvalue𝑚𝑎𝑥
𝑖that
upper bounds the number of requests arrived in each time slot,
the dri plus cost can be upper bounded by
(Θ())+E()()
≤+
𝑖∈𝐼
𝑗∈𝐽𝑖𝑗 ()E𝑖𝑗 ()−
𝑖𝑗 ()()
+
𝑖∈𝐼
𝑗∈𝐽
E𝑖𝑗 ()𝑖𝑗 ()(),
()
where  = (1/2)[∑𝑖∈𝐼(𝑚𝑎𝑥
𝑖)2+∑𝑖∈𝐼 𝑗∈𝐽
2
𝑖𝑗]is a constant.
Proof. By squaring the both sides of () and applying the
inequality that (max[𝑖𝑗() − 𝑖𝑗(),0])2≤(
𝑖𝑗() − 𝑖𝑗())2,
we have
2
𝑖𝑗 (+1
)≤
𝑖𝑗 ()−
𝑖𝑗 ()2+
2
𝑖𝑗 ()
+2
𝑖𝑗 ()max 𝑖𝑗 ()−
𝑖𝑗 (),0. ()
en, we dene 𝑖𝑗() as the actual number of requests for
service served by the -th MEC system in time slot ,
𝑖𝑗 ()=
𝑖𝑗 (),
𝑖𝑗 ()≤
𝑖𝑗 ()
𝑖𝑗 (),. ()
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We can obtai n that max[𝑖𝑗()𝑖𝑗(), 0] = 𝑖𝑗() 𝑖𝑗() and
rewrite () as follows:
2
𝑖𝑗 (+1
)≤
2
𝑖𝑗 ()+
2
𝑖𝑗 ()+2
𝑖𝑗 ()
+2
𝑖𝑗 ()𝑖𝑗 ()−
𝑖𝑗 ()
−2
𝑖𝑗 ()𝑖𝑗 ().
()
Because 𝑖𝑗()𝑖𝑗 () ≥ 0,wehave
1
22
𝑖𝑗 (+1
)−
2
𝑖𝑗 ()
1
22
𝑖𝑗 ()+2
𝑖𝑗 ()+𝑖𝑗 ()𝑖𝑗 ()−
𝑖𝑗 ().
()
Taking the expectations on the condition of Θ() to both
sides in () and summing over ∈and ∈,itcanbe
obtained that
(Θ()) 1
2
𝑖∈𝐼
𝑗∈𝐽
E2
𝑖𝑗 ()+2
𝑖𝑗 ()()
+
𝑖∈𝐼
𝑗∈𝐽𝑖𝑗 ()E𝑖𝑗 ()−
𝑖𝑗 ()(). ()
Since it holds that 𝑗∈𝐽 𝑖𝑗() = 𝑖() and 𝑖() ≤ 𝑚𝑎𝑥
𝑖,
we have
𝑗∈𝐽
E2
𝑖𝑗 ()()≤E2
𝑖()()≤
𝑚𝑎𝑥
𝑖2.()
𝑖𝑗 as the upper bound of 𝑖𝑗() over all
the time slots. We can obtain that
𝑖∈𝐼
𝑗∈𝐽
E2
𝑖𝑗 ()+2
𝑖𝑗 ()()
≤
𝑖∈𝐼 𝑚𝑎𝑥
𝑖2+
𝑖∈𝐼
𝑗∈𝐽
2
𝑖𝑗.()
By adding E{() | Θ()} to both sides and letting
take the value of (1/2)[∑𝑖∈𝐼(𝑚𝑎𝑥
𝑖)2]+∑
𝑖∈𝐼 𝑗∈𝐽
2
𝑖𝑗,itcanbe
obtained that
(Θ())+E()()
≤+E()()
+
𝑖∈𝐼
𝑗∈𝐽𝑖𝑗 ()E𝑖𝑗 ()−
𝑖𝑗 ()().
()
Substituting () into the right-hand-side (R.H.S.) of (),
we can obtain ().
3.2. Dynamic Request Scheduling Algorithm. Following the
design principles of Lyapunov optimization techniques, we
design an ecient Dynamic Service Request Scheduling
(DSRS) algorithm to minimize the upper bound of dri plus
cost in each time slot . By decomposing the minimization of
upper bound problem into a series of independent subprob-
lems, our DSRS algorithm optimizes the average scheduling
cost concurrently in a distributed way. In addition, it will be
proven that DSRS algorithm can achieve a long-term time-
average scheduling cost that is arbitrarily close to the optimal
value while maintaining the stability of the MEC systems.
In each time slot , based on the current queue length
matrix Θ() of the MEC systems, the DSRS algorithm makes
request scheduling decisions 𝑖𝑗() to minimize the upper
bound of R.H.S. of (). Since and 𝑖𝑗 can be considered
as constant in the optimization problem, we can rewrite the
minimization of upper bound as
min
𝑎𝑖𝑗(𝑡)
𝑖∈𝐼
𝑗∈𝐽𝑖𝑗 ()𝑖𝑗 ()+
𝑖𝑗 ()𝑖𝑗 ().()
subject to
𝑗∈𝐽𝑖𝑗 ()=𝑖(),∀. ()
As the request scheduling decisions 𝑖𝑗 ()are independent
among dierent services, the above centralized minimization
problem () can be decomposed into the following subprob-
lem () for each service ∈, i.e.,
min
𝑎𝑖𝑗(𝑡)
𝑗∈𝐽𝑖𝑗 ()𝑖𝑗 ()+
𝑖𝑗 (). ()
subject to
𝑗∈𝐽𝑖𝑗 ()=𝑖().()
Problem () can be regarded as a generalized min-weight
problem, where the number of requests scheduled to the
MEC systems is weighted by the value of 𝑖𝑗 () + 𝑖𝑗().
erefore, for each service ∈, the optimal solution is
to schedule all the requests to the MEC system with the
minimum value of 𝑖𝑗()+𝑖𝑗(); i.e.,
𝑖𝑗 ()=
𝑖(),=
0,  ()
where argmin(𝑖𝑗() + 𝑖𝑗()) for all ∈.
Remark. ere exist tradeos between the scheduling cost
and queue length of the MEC systems. Scheduling all the
service requests to the MEC system with low cost can reduce
the overall scheduling cost; however, the queue length of the
MEC system can be very large. e DSRS algorithm combines
scheduling cost and queue length, and 𝑖𝑗()+𝑖𝑗() can be
regarded as the penalty factor for each MEC system. Recall
that represents the tradeo between scheduling cost and
queue length. e intuition of the optimal scheduling policy
obtained by the DSRS algorithm is to minimize the penalty
function of the MEC systems in each time slot. In this way,
the DSRS algorithm can reduce both the scheduling cost and
the queue length. In addition, by changing the value of ,the
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: In the beginning of each time slot , observe the current queue length 𝑖𝑗().
: for all ∈do
: Set auxiliary variable  = −∞;
: Set =1;
: for all ∈do
: Calculate the penalty factor 𝑗=
𝑖𝑗() + 𝑖𝑗();
: if 𝑗<then
: =;
: end if
: end for
: for all ∈do
: if==
then
: Set 𝑖𝑗() = 𝑖();
: else
: Set 𝑖𝑗() = 0;
: end if
: end for
: end for
A : Dynamic Service Request Scheduling (DSRS).
DSRS algorithm can achieve the arbitrary tradeo between
scheduling cost and queue length.
Aer the scheduling decisions 𝑖𝑗() are determined, the
queue length 𝑖𝑗() updates according to (). e detailed
algorithm is shown in Algorithm .
4. Algorithm Analysis
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 denote the long-term time-average queue
length,
= lim
𝑇󳨀→∞ 1
𝑇−1
𝑡=0
𝑖∈𝐼
𝑗∈𝐽
E𝑖𝑗 (). ()
We present in Lemma  that if the arrival 𝑖() is
independent and identically distributed (i.i.d.) over time
slots, there exists a randomized policy which can achieve
the minimum cost dened in (), where the control
decision 𝑖𝑗() follows certain xed probability distribution
independent of the queue length matrix Θ().
Lemma 2. For any service request arrival rate ∈Λ,where
Λis the capacity region of the system, if the arrival 𝑖() is
i.i.d. over time slots, there exists a randomized policy that
determines the control decision 𝑖𝑗() in each time slot and
achieves the following:
E𝜋()=
();
E
𝑗∈𝐽𝜋
𝑖𝑗 ()
E
𝑗∈𝐽𝑖𝑗 ()
.()
where ()denotes the minimum time-average cost under the
arrival rate .
Proof. Lemma  can be proven by Caratheodory’s theorem
in [], we omit the detailed proof here for simplicity and
brevity.
Since it is assumed that there exists upper bound 𝑚𝑎𝑥
𝑖of
the service request arrival rate, there also exists upper bound
and lower bound
of the objective . en, we derive the
boundary of queue length and scheduling cost of the DSRS
algorithm based on Lemma .
eorem 3. Assume that there exists satisfying +Λ,
then, under our DSRS algorithm, for any value of the parameter
, the time-average queue length dened in (24) is bounded as
≤+
−

.()
Furthermore, the time-average system scheduling cost can
be bounded by (27), which shows the cost derived by our DSRS
algorithm can approach the optimal value by increasing the
parameter . Here, is the constant dened in eorem 1.
𝐷𝑆𝑅𝑆 ≤
+
.()
Proof. Since it holds that +∈Λ, we can obtain that there
exists a randomized policy 󸀠which satises () and ()
according to Lemma .
E𝜋󸀠() =
(+
);()
E
𝑗∈𝐽𝜋󸀠
𝑖𝑗 ()
E
𝑗∈𝐽𝑖𝑗 ()
−. ()
Wireless Communications and Mobile Computing
As our DSRS algorithm can achieve the minimum value
of the R.H.S of () among all feasible policies (including
policy 󸀠), it can be obtained that
(Θ())+E()()
≤+E𝜋󸀠(𝑡) ()
+
𝑖∈𝐼
𝑗∈𝐽𝑖𝑗 ()E𝜋󸀠
𝑖𝑗 ()−
𝑖𝑗 ()().
()
Substituting () and () into the R.H.S. of (), taking
expectations on both sides, and then using iterated expecta-
tions, we can yield
E{(Θ(+1
)) −(Θ())}+E ()
≤+
(+)−
𝑖∈𝐼
𝑗∈𝐽
E𝑖𝑗 (). ()
Moving E{()} to the R.H.S. of (), it can be obtained
that
E{(Θ(+1
))−(Θ())}
≤+
(+
)E()
−
𝑖∈𝐼
𝑗∈𝐽
E𝑖𝑗 ()
≤+
−
 − 
𝑖∈𝐼
𝑗∈𝐽
E𝑖𝑗 ().
()
To be general, we assume the queue length is empty when
=0. By summing both sides of () over {0,1,...−1}
and applying the fact that (Θ()) ≥ 0,wecanobtain
𝑇−1
𝑡=0
𝑖∈𝐼
𝑗∈𝐽
E𝑖𝑗 ()≤+
−

E{(Θ())}
≤+
−
.
()
Dividing both sides of () by and taking a lim as 
yield ().
By summing both sides of () over {0,1,...1}and
applying the fact that E{𝑖𝑗()} ≥ 0,itcanbeobtained
𝑇−1
𝑡=0
E()≤
(+)+. ()
Dividing both sides of () by ,wehave
1
𝑇−1
𝑡=0
E()≤
(+
)+
.()
Taking a l i m o f (  ) a s →∞, applying Lebesgue’s
dominated convergence theorem, and letting →0yield
().
Remark. eorem  shows that our DSRS algorithm can
achieve a [(1/),()] tradeo between the time-average
scheduling cost and queue length. According to (), the gap
between the time-average scheduling cost obtained by our
DSRS algorithm and the optimal value is within (1/).By
setting the value of suciently large, the DSRS algorithm
can approach the optimal scheduling cost. However, a large
will cause a large queue backlog of the MEC systems. Nev-
ertheless, the queue length obtained by our DSRS algorithm
is also bounded according to (). And constraint () can be
satised by letting take the value of (+(
−
))/.
en, we analyze the time complexity of the DSRS algo-
rithm. According to Algorithm , for the two inner loops (line
- and line -), DSRS algorithm traverses each edge serv-
er once. erefore, each loop terminates in () operations,
where isthenumberofedgeservers.Fortheouterloop
(line -), since the request scheduling of dierent service
applications is independent, it terminates in ()operations.
us,thetimecomplexityoftheDSRSalgorithmis().
5. Evaluation
In this section, we conduct experiments to evaluate our
DSRS algorithm. First, we analyze the impact of parameters.
en, we present comparison experiments which show the
eectiveness of our DSRS algorithm.
In the experiments, we consider  MEC systems, each
with an edge server providing services for the ooaded
requests. ere are two types of heterogeneous services. For
each service ∈, the request arrival process is generated
according to Poisson distribution with arrival rate 𝑖[].
Note that the DSRS algorithm actually requires no knowledge
of the statistical information of request arrivals. e comput-
ing capacity of the MEC systems is set as 𝑖⋅𝑖where 𝑖>1.
Without loss of generality, we assume the MEC systems are
heterogeneous with dierent computing capacities. And the
unit scheduling costs of dierent MEC systems are set to be
positively related to its computing capacity.
5.1. Parameter Analysis
5.1.1. Eect of Tradeo Parameter. Figures  and  show the
time-average scheduling cost and queue length of the MEC
systems with dierent values of .InFigure,itcanbeseen
that the scheduling cost decreases as the value of increases,
whichisinaccordancewith() ineorem.isisbecause
as increases, more weight is put on scheduling cost, and
the DSRS algorithm would schedule more service requests
to the MEC system with lower unit cost in order to reduce
the overall scheduling cost. However, Figure  shows that
the queue length also rises with the increase of ,whichis
consistent with () in eorem . Nevertheless, the queue
length would stabilize gradually with far more increase of
. Together with Figures  and , we can see that the DSRS
algorithm can make a tradeo between scheduling cost and
queue length by adjusting the value of .
5.1.2. Eect of Service Request Arrival Rate. We analyze t h e
eect of service request arrival rate on the scheduling cost and
Wireless Communications and Mobile Computing
220
240
260
280
300
320
340
360
380
400
scheduling cost
523410
Vx105
F : Scheduling cost with dierent values of .
x105
x105
123450
V
0.5
1
1.5
2
2.5
queue length
F : Queue length with dierent values of .
queue length. In the experiments, for each application ∈,
we scale the service request arrival rate up or down to ⋅𝑖.
We consider three dierent cases, where =,1.2 and 1.4,
respectively. Figures  and  show that both of the scheduling
cost and queue length increase as the request arrival rate
increases. Nevertheless, the queue length can stabilize quickly
with the increase of service request arrival rate. is shows
that our DSRS algorithm can dynamically adjust the request
scheduling decisions according to dierent service request
arrivals and maintain the stability of the MEC systems.
5.1.3. Eect of Unit Scheduling Cost. To analyze the eect of
unit scheduling cost on the MEC systems, we scale the unit
scheduling cost up or down to ⋅
𝑖𝑗.Weconsiderthree
dierent cases, where =,1.2 and 1.4, respectively. We
can see from Figure  that the overall scheduling cost rises
as the unit scheduling cost increases, since the scheduling
cost of each request increases. In Figure , we can see that
the queue length of the MEC systems also increases with the
p=1
p=1.2
p=1.4
200
250
300
350
400
450
500
550
scheduling cost
200 400 600 800 10000
t
F : Scheduling cost with dierent arrival rates.
p=1
p=1.2
p=1.4
200 400 600 800 10000
t
150
200
250
300
350
400
450
500
550
600
queue length
F : Queue length with dierent arrival rates.
increase of unit scheduling cost. e reason is that our DSRS
algorithm tries to achieve low scheduling cost by scheduling
more requests to the MEC with smaller unit scheduling cost.
MEC systems.
5.2. Comparison Experiment. We con d u c t comp a r i s o n
experiment and compare our DSRS algorithm with
Randomized algorithm to evaluate the eectiveness of
the DSRS algorithm. e Randomized algorithm schedules
all the service requests to each MEC system randomly. e
scheduling costs and queue lengths of the two algorithms are
shown in Figures  and , respectively.
We can see from Figure  that the scheduling cost of
our DSRS algorithm is smaller than that of Randomized
Wireless Communications and Mobile Computing
250
300
350
400
450
500
550
600
scheduling cost
200 400 600 800 10000
t
q=1
q=1.2
q=1.4
F : Scheduling cost with dierent unit scheduling costs.
200
300
400
500
600
700
800
900
1000
queue length
200 400 600 800 10000
t
q=1
q=1.2
q=1.4
F : Queue length with dierent unit scheduling costs.
algorithm, which shows the eectiveness of our DSRS algo-
rithm in reducing cost. In Figure , we can observe that the
queue length of the Randomized algorithm is slightly smaller
than our DSRS algorithm at the very beginning. However, as
time goes by, the queue length of the Randomized algorithm
increases continuously along with the time. e queue length
of our DSRS algorithm stabilizes quickly and maintains at
a small level. e reason is that our DSRS algorithm can
adjust scheduling decisions dynamically according to the
current queue backlog and maintain low congestion state in
the MEC systems. Together with Figures  and , we can see
the eectiveness of our DSRS algorithm in optimizing both
scheduling cost and queue length.
3000
3500
4000
4500
5000
5500
6000
scheduling cost
500 1000 1500 2000 2500 30000
t
Randomized
DSRS
F : Scheduling cost under dierent algorithms.
500 1000 1500 2000 2500 30000
t
0
1000
2000
3000
4000
5000
6000
7000
8000
queue length
Randomized
DSRS
F : Queue length under dierent algorithms.
6. Conclusion
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 eciently 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 experi-
ments are both conducted to verify the eectiveness of the
DSRS algorithm.
Wireless Communications and Mobile Computing
Data Availability
Most of the simulation experimental data used for supporting
corresponding author.
Conflicts of Interest
e authors declare that they have no conicts of interest.
Acknowledgments
is work is supported by the National Natural Science
Foundation of China (no.  and no. ), the
Key Research and Cultivation Projects at Beijing Information
Science and Technology University (no. ), Beijing
Municipal Program for Excellent Teacher Promotion (no.
PXM  ), and the Supplementary and Sup-
portive Project for Teachers at Beijing Information Science
and Technology University (no. ).
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... About the request scheduling problem, Chen et.al. [17] pay close attention to the dynamic scheduling of offloaded service requests in MEC systems while Mao et.al. [16] develop an effective computation offloading strategy to provide satisfactory computation performance as well as achieving green computing. ...
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... Fairness [101], [102], QoS [103], [104], throughput [105], energy [106]- [109], among others, can be utilized as criteria to design resource management schemes. Other than resource management criteria, we can use optimization-based schemes [110], game theory-based schemes [111], heuristic [112], graph theory-based schemes [58], and hybrid schemes (which jointly utilize optimization and game theory) [113], for resource allocation. An optimization-based technique can be either dynamic programming, linear programming, convex optimization, or integer programming. ...
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Full-text available
Recent years have disclosed a remarkable proliferation of compute-intensive applications in smart cities. Such applications continuously generate enormous amounts of data which demand strict latency-aware computational processing capabilities. Although edge computing is an appealing technology to compensate for stringent latency related issues, its deployment engenders new challenges. In this survey, we highlight the role of edge computing in realizing the vision of smart cities. First, we analyze the evolution of edge computing paradigms. Subsequently, we critically review the state-of-the-art literature focusing on edge computing applications in smart cities. Later, we categorize and classify the literature by devising a comprehensive and meticulous taxonomy. Furthermore, we identify and discuss key requirements, and enumerate recently reported synergies of edge computing enabled smart cities. Finally, several indispensable open challenges along with their causes and guidelines are discussed, serving as future research directions.
... Chen et.al. [27] further discussed the dynamic service request scheduling problem in edge computing to minimize the scheduling cost. Unfortunately, no related work has been done on the scheduling strategies of hybrid service requests. ...
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