A Double Auction Mechanism for Coded Distributed Computing in

Smart Vehicles

Jer Shyuan Ng

1,2

, Wei Yang Bryan Lim

1,2

, Zehui Xiong

, Sahil Garg

Yang Zhang

, Dusit Niyato

and Cyril Leung

7,8

Alibaba Group, Singapore

Alibaba-NTU Joint Research Institute (JRI), Singapore

Pillar of Information Systems Technology and Design, Singapore University of Technology Design, Singapore

Ecole de Technologie Sup

erieure, Montreal, Canada

Nanjing University of Aeronautics and Astronautics, China

School of Computer Science and Engineering, Nanyang Technological University, Singapore

LILY Research Center, Nanyang Technological University, Singapore

Department of Electrical and Computer Engineering, The University of British Columbia, Canada

Keywords:

Coded Distributed Computing, Double Auction, Straggler Effects, Resource Allocation.

Abstract:

The development of smart vehicles and rich cloud services have led to the emergence of vehicular edge com-

puting. To perform the distributed computation tasks efﬁciently, Coded Distributed Computing (CDC) was

proposed to reduce communication costs and mitigate the straggler effects through the use of coding tech-

niques. In this paper, we propose a double auction mechanism to allocate the resources of the edge servers to

the vehicles in order to complete the CDC tasks. Speciﬁcally, the vehicles use the PolyDot codes to manage

the tradeoff between communication costs and recovery threshold. Given the requirements of various vehicles,

the double auction mechanism matches the edge servers with the required resources to the vehicles. Besides,

the double auction mechanism also determines the prices that the vehicles need to pay for the resources of

the edge servers. The double auction mechanism satisﬁes the properties of individual rationality, incentive

compatibility and budget-balance.

1 INTRODUCTION

With the advent of vehicular applications, there has

been a signiﬁcant transformation in the way that data

are managed, where we observe a paradigm shift from

the traditional centralized cloud computing toward

ﬂexible distributed vehicular edge computing. Instead

of processing the data at the central cloud server, the

computing and storage services are ofﬂoaded to the

vehicles, extending the cloud computing services to

the edge of the networks. Instead of performing the

large-scale computations individually, the vehicles

can leverage on the resources of the edge servers, e.g.,

roadside units (RSUs) and base stations, to complete

their computation tasks efﬁciently over the distributed

vehicular edge computing networks (Xu et al., 2019).

Coded Distributed Computing (CDC) has been

proposed to perform distributed computation tasks ef-

ﬁciently. Coding techniques can be used to achieve an

optimal tradeoff between computation and communi-

cation loads, thus reducing the communication costs

required for the distributed computation tasks. Be-

sides, the computation strategies are designed to di-

vide and allocate the datasets to the edge servers so

that the vehicles are able to reconstruct the ﬁnal result

with the computed results from only a subset of edge

servers. By reducing the number of edge servers re-

quired to return their results, the computation latency

can be minimized.

However, the edge servers are not motivated to fa-

cilitate the CDC tasks of the vehicles. As such, incen-

tive mechanisms are essential to encourage the edge

servers to complete the CDC tasks by offering them

monetary rewards in exchange for their resources. In

order to ensure efﬁcient completion of the CDC tasks,

the incentive mechanisms need to allocate the CDC

tasks to the edge servers and determine the payment

prices to the edge servers. Since there are multiple ve-

hicles competing for the resources of the edge servers,

we propose a double auction mechanism to model

the competition between different vehicles and edge

servers as well as to maximize the utility of the auc-

tioneer.

Ng, J., Lim, W., Xiong, Z., Garg, S., Zhang, Y., Niyato, D. and Leung, C.

A Double Auction Mechanism for Coded Distributed Computing in Smart Vehicles.

DOI: 10.5220/0010615801070114

In Proceedings of the 18th International Conference on Wireless Networks and Mobile Systems (WINSYS 2021), pages 107-114

ISBN: 978-989-758-529-6

107

In this paper, we consider that there are multi-

ple vehicles that aim to perform machine learning

tasks using the data they collected. Due to the lack

of computation resources, the vehicles leverage on

the computation and communication resources of the

edge servers. In order to perform the distributed com-

putation tasks efﬁciently, the vehicles use PolyDot

codes (Dutta et al., 2020) to divide and allocate the

dataset to the edge servers. By using PolyDot codes,

the vehicles are able to determine the number of edge

servers that they require to complete their CDC tasks.

Speciﬁcally, for time-sensitive applications, the vehi-

cles aim to minimize the straggler effects and hence

need fewer edge servers to compute the CDC tasks.

However, since each of the edge servers is allocated

a larger size of dataset for computation, larger com-

munication costs are needed to transmit the computed

results and thus, the vehicles need to pay higher prices

to the edge servers. Hence, there is a tradeoff be-

tween the recovery threshold, i.e., the number of edge

servers that need to return their computed results to

the vehicles in order to recover the ﬁnal result, and

the communication costs. Each vehicle requires dif-

ferent number of edge servers, depending on their ur-

gency to complete their CDC tasks. Given the dif-

ferent objectives of the vehicles and the heterogene-

ity of the edge servers, the double auction mechanism

matches the edge servers to the vehicles as well as

determines the payment and selling prices. The dou-

ble auction mechanism is managed by an auctioneer,

which is represented by a third-party platform, that

aims to maximize its total proﬁt. Thus, the payment

prices of the buyers for the resources are larger than

the selling prices of the sellers. In other words, the

proﬁt of the auctioneer for each match of winning

buyer and seller is the difference between the payment

and selling price of the winning buyer and seller re-

spectively.

2 SYSTEM MODEL AND

PROBLEM FORMULATION

The system model comprises a set M =

{1,...,m,...,M} of M vehicles and a set

N = {1,...,n,...,N} of N edge servers in a

distributed vehicular edge computing network.

Equipped with more sophisticated sensors, the

vehicles collect data from their surroundings, which

offer meaningful insights, e.g., by using machine

learning techniques (Radu et al., 2020), (Fusco et al.,

2015). Given the massive amount of constantly

changing data, AI models have shown their effective-

ness in obtaining valuable information from every

piece of vehicular data generated, ranging from the

understanding behaviour pattern of consumers of a

particular in-vehicle application to improving the

productivity of businesses to monitoring large-scale

phenomena such as tracking of road conditions.

However, the vehicles may not have sufﬁcient

resources, e.g., CPU power, to handle the growing

datasets individually. Instead, the vehicles can lever-

age on the resources of the edge servers to facilitate

their computation tasks, e.g., training of AI models.

2.1 Coded Distributed Computing

We consider that each vehicle m aims to compute

the matrix multiplication of two Q

× Q

square in-

put matrices A

and B

, i.e., C

= A

. In or-

der to mitigate the straggler effects in performing the

distributed computation tasks, the vehicles can adopt

coding techniques to divide the datasets and allocate

the subsets of data to the edge servers. The objective

of various coding techniques is to minimize the re-

covery threshold, i.e., the number of edge servers that

need to return their computed results to the vehicles in

order to recover the ﬁnal result. However, a smaller

recovery threshold means that there are fewer edge

servers that are working on the computation task.

Hence, each edge server is allocated a larger dataset

to compute and has greater communication costs in

terms of number of symbols communicated to the ve-

hicles.

To manage the tradeoff between the recovery

threshold and the communication costs of the edge

servers, PolyDot codes (Dutta et al., 2020) are pro-

posed where Polynomial codes (Yu et al., 2017) and

MatDot codes (Dutta et al., 2020) are special in-

stances of this coding framework by considering the

extreme cases: to either minimize communication

costs or recovery threshold. In particular, Polynomial

codes achieve minimum recovery threshold at the ex-

pense of higher communication costs whereas Mat-

Dot codes minimize communication costs but require

larger recovery threshold.

Unlike Polynomial codes and MatDot codes

that split the input matrices either horizontally or

vertically, each vehicle m uses PolyDot codes to split

the input matrices A

and B

both horizontally and

vertically such that:

WINSYS 2021 - 18th International Conference on Wireless Networks and Mobile Systems

108







0,0

··· A

0,s

−1

−1,0

··· A

−1,s

−1













0,0

··· B

0,t

−1

−1,0

··· B

−1,t

−1







(1)

where A

j,i

and B

i, j

are Q

× Q

and Q

submatrices respectively for i = {0,1,..., s

−

1} and j = {0,1,...,t

− 1}. The values of parame-

ters s

and t

are chosen such that s

= ω

, where

is the number of submatrices of vehicle m.

For PolyDot codes, the encoding polynomials

(x,y) and p

(y, z) for each vehicle m are as fol-

lows:

(x,y) =

−1

∑

i=0

−1

∑

j=0

i, j

(y, z) =

−1

∑

k=0

−1

∑

l=0

k,l

−1−k

(2)

where variables x, y and z are assigned to the encod-

ing polynomials where each of the encoding polyno-

mials p

(x,y) and p

(y, z) is assigned two variables.

The encoding polynomials with three variables are

transformed to polynomials with a single variable by

choosing y = x

and z = x

(2s

− 1).

There are three major steps in completing the

CDC tasks:

1. Encoding: The vehicles divide and encode the

submatrices. Then, the vehicles distribute the en-

coding polynomials to the edge servers. Each

edge server n receives p

) and p

)

where y

= x

and z

= x

(2s

−1)

2. Computation: Each edge server n computes

the matrix multiplication of the encoding poly-

nomials and produces the result C

) =

). Upon completion, the edge

servers transmit the result back to the vehicles.

3. Decoding: Each vehicle m is able to recon-

struct the ﬁnal result C

= A

upon receiv-

ing the computed results from any t

(2s

−

1) edge servers. In particular, the vehicle

uses the computed results from the edge servers

to recover the coefﬁcient of x

i−1

−1

l−1

(x,y, z). By using the transformed single-

variable encoding polynomials, the vehicles com-

pute the coefﬁcient of x

i−1+t

−1)+t(2s

−1)(l−1)

in C

(x,x

(2s

− 1)).

By using PolyDot codes, the recovery threshold,

, that can be achieved by vehicle m is deﬁned as

follows:

= t

(2s

− 1). (3)

To complete the CDC subtasks of vehicle m, the

number of symbols that each edge server is required

to transmit, which is denoted as µ

, is represented as

follows:

. (4)

Hence, in order to complete the CDC task of vehi-

cle m, the total number of symbols communicated by

the edge servers to vehicle m is

× t

(2s

− 1) =

(2s

− 1)Q

The number of computations that each edge server

requires to complete the CDC subtasks of vehicle m,

which is denoted as α

, is deﬁned as follows:

. (5)

The total number of computations that are performed

by the edge servers that facilitate in the CDC task of

vehicle m is

×t

(2s

− 1) =

(2s

− 1).

In our system model, we consider the matrix mul-

tiplication of two square matrices. Matrix multiplica-

tion is an important basic mathematical operation for

many useful AI algorithms. It may involve the mul-

tiplication of non-square matrices or more than two

matrices. Our system model can be easily extended to

compute the matrix multiplication of non-square ma-

trices and more than two matrices by using PolyDot

codes.

2.2 Double Auction Model

Since there are multiple vehicles and edge servers in

the network, a double auction mechanism is adopted.

The objectives of the double auction mechanism are

(i) to match the edge servers to the vehicles, and (ii)

to determine the payment prices of vehicles and the

selling prices of edge servers.

In this double auction mechanism, there are sev-

eral entities, where their roles are described as fol-

lows:

1. Vehicles (Buyers): The vehicles are buyers that

pay the edge servers for their resources in facili-

tating the CDC subtasks. In order to participate in

the auction, the vehicles submit their buy-bids to

the auctioneer. The buy-bid of vehicle m, which is

denoted by b

, represents the maximum price that

vehicle m is willing to pay for each edge server to

A Double Auction Mechanism for Coded Distributed Computing in Smart Vehicles

109

complete its CDC subtask. The vehicles are able

to decide on the recovery threshold and the com-

munication costs required to complete the CDC

tasks by using the PolyDot codes. Speciﬁcally, for

vehicles that require their CDC tasks to be com-

pleted within a shorter period of time, they need a

smaller recovery threshold, which in turn results

in higher communication costs required by each

edge server. As such, the vehicles need to pay

more for the edge servers to complete the CDC

subtasks. Conversely, for vehicles that need to

complete CDC tasks without time constraint, they

aim to reduce communication costs of the edge

servers in order to reduce the payment prices to

the edge servers. The buy-bid of vehicle m is ex-

pressed as follows:

= λ

+ λ

, (6)

where λ

and λ

are the unit prices that vehicle m

is willing to pay for the communication and com-

putation resources respectively.

2. Edge Servers (Sellers): The edge servers are sell-

ers that provide their computation and commu-

nication resources to facilitate the CDC subtasks

of the vehicles. In return, they receive monetary

rewards for the provision of their resources. By

participating in the double auction mechanism,

the sellers submit their sell-bids to the auctioneer.

The amounts of computation and communication

resources of each edge server n are represented by

and r

respectively. The unit costs of com-

putation and communication resources are repre-

sented by c

and c

respectively. Based on the

values of these parameters, the sell-bid of seller

n, which is the price that the seller n wants to re-

ceive for providing its resources to complete the

CDC subtask, can be computed as follows:

= r

+ r

. (7)

3. Auctioneer: Typically, the service provider plat-

form plays the role of the auctioneer as a trusted

third-party in order to ensure fairness and trans-

parency of the transaction between the buyers and

sellers. The auctioneer collects the buy-bids and

sell-bids from the buyers and sellers respectively.

Then, it allocates the edge servers to the vehicles.

Besides, the auctioneer determines the payment

price of the vehicles for the resources of the edge

servers. In order to prevent malicious buyers and

sellers from threatening the security of the net-

work, the auctioneer can also implement an au-

thentication system (Lin et al., 2012) (Liu et al.,

2014) to ensure the trustworthiness of the buyers

and sellers. The auctioneer can be regarded as the

uniﬁed API that aggregates the resources of the

edge servers and provides the vehicles with their

required resources for a price, a fraction of which

is paid to the corresponding edge servers that fa-

cilitate the CDC tasks.

The utility of buyer m, which is denoted as u

, is

expressed as follows:

(

− p

), if b

∈ W

0, otherwise,

(8)

where p

payment price of buyer m. The set W

con-

sists of the buy-bids of the winning buyers. If buyer

m is not matched with any seller, the utility of buyer

m is zero.

The utility of seller n is denoted as follows:

(

− q

, if q

∈ W

0, otherwise,

(9)

where γ

is the price paid by the auctioneer to seller n

for its resources. The set W

consists of the winning

sell-bids of successfully matched sellers. If seller n

is not successfully matched to any buyer, its utility is

zero.

The double auction mechanism is managed by the

third-party auctioneer. The utility of the auctioneer,

, is the difference between the payment received by

all successfully matched buyers and the payment paid

to all successfully matched sellers, which is expressed

as follows:

∑

∈W

−

∑

∈W

. (10)

The design of the double auction mechanism has

several properties:

• Individual Rationality: Each buyer and seller

achieves individual rationality in this double auc-

tion mechanism. In other words, each of the buy-

ers and sellers receives non-negative utility by

participating in the auction. In particular, each

buyer m pays a price that is lower than or equal to

its buy-bid, i.e., b

− p

≥ 0, ∀m ∈ M , and each

seller n receives a payment that is higher than or

equal to its sell-bid, i.e., q

− γ

≤ 0, ∀n ∈ N .

• Incentive Compatibility: There is no incentive for

the buyers and sellers to submit buy-bids and sell-

bids respectively other than their true valuations.

In other words, the buyers and sellers submit their

bids truthfully.

• Budget-balance: As a third-party platform that de-

termines the allocation of edge servers to the ve-

hicles and the corresponding payment and selling

WINSYS 2021 - 18th International Conference on Wireless Networks and Mobile Systems

110

prices, the auctioneer needs to gain a non-negative

utility. Speciﬁcally, the total payment price that is

received from all winning bidders is higher than or

equal to the total price paid to all winning sellers,

i.e., u

≥ 0.

The objectives of this double auction mechanism

are to match the buyers and sellers as well as to de-

termine the payment and selling prices of the buyers

and sellers respectively in order to complete the CDC

tasks. As a platform that manages the transactions

between buyers and sellers, the aim of the auction-

eer, which is to maximize its total proﬁt and thus util-

ity while ensuring that the double auction mechanism

is individually-rational and incentive-compatible, can

be expressed as follows:

max u

s.t. b

≥ p

, ∀m ∈ M ,

≤ γ

, ∀n ∈ N ,

− p

≥ b

− p

, ∀m ∈ M ,

− q

≥ γ

− q

, ∀n ∈ N ,

(11)

where b

and q

are the untruthful buy-bid of buyer

m and sell-bid of seller n respectively. The terms p

and γ

are the payment price and selling price, given

the untruthful buy-bid b

and q

respectively.

3 DOUBLE AUCTION

MECHANISM

In this section, we discuss the design of the double

auction mechanism. There are two important stages in

the double auction mechanism: matching of the buy-

ers and sellers and the determination of the payment

prices of buyers and the selling prices of sellers.

3.1 Matching between Buyers and

Sellers

Given the buy-bids from the buyers, the auctioneer

sorts the buy-bids in the descending order, which is

represented by the set B = {b

(1)

,...,b

(m)

,...,b

(M)

where:

(1)

≥ b

(2)

≥ ··· ≥ b

(M)

, (12)

and b

(1)

and b

(M)

are the largest and smallest buy-bids

which are offered by buyer m respectively.

The sell-bids from the sellers are sorted in the

ascending order in set S = {q

(1)

,...,q

(n)

,...,q

(N)

}

where:

(1)

≤ q

(2)

≤ ··· ≤ q

(N)

, (13)

and q

(1)

and q

(N)

are the smallest and largest sell-bids

that are submitted by seller n respectively .

Given the sorted buy-bids and sell-bids, the auc-

tioneer matches the vehicles and edge servers that sat-

isfy the following inequalities:

≥ q

, ∀m ∈ M , ∀n ∈ N , (14)

≥ µ

, ∀m ∈ M , ∀n ∈ N , (15)

≥ α

, ∀m ∈ M , ∀n ∈ N , (16)

where g

is the amount of communication resources

needed to transmit each symbol and h

is the amount

of computation resources needed for each computa-

tion. The inequality (14) requires the buy-bid of buyer

m to be larger than or equal to the sell-bid of the seller

n for a successful match in order to satisfy the prop-

erty of individual rationality of the auction mecha-

nism. Inequalities (15) and (16) ensure that the seller

n has sufﬁcient communication and computation re-

sources to perform the CDC subtasks of buyer m re-

spectively. If there are multiple sellers that satisfy that

conditions for a particular buyer m, the seller with the

smallest sell-bid wins.

The match results between the buyers and sellers

can be represented by a matching matrix, which is ex-

pressed as follows:

β =







··· β







, (17)

where β

= 1 if seller n is matched to buyer m

whereas β

= 0 if the match between buyer m and

seller n is not successful.

3.2 Determination of Payment and

Selling Prices

In order to determine the payment prices of the win-

ning buyers to the auctioneer as well as the selling

prices of the winning sellers, we present a pricing

scheme which is similar to the second-price auction.

In particular, if buyer m is matched with seller n,

∀n ∈ N , the payment price of winning buyer m equals

the next largest buy-bid, given its buy-bid. The selling

price of winning seller n equals the next smallest sell-

bid in the feasible set of sellers, i.e., the sellers with

sell-bids that fulﬁl inequalities (14), (15) and (16)

A Double Auction Mechanism for Coded Distributed Computing in Smart Vehicles

111

and thus can possibly matched to buyer m, given the

seller’s sell-bid.

The difference between the payment price of win-

ning buyer m and selling price of winning seller n is

equal to the proﬁt of the auctioneer.

4 SIMULATION RESULTS

We consider a distributed vehicular edge comput-

ing network that consists of 6 vehicles and 50 edge

servers. The values of system simulation parameters

are summarized in Table 1. We set Q

= 10 and

= 4, ∀m ∈ M , where all vehicles have the input

matrices of the same size and split the input matrices

into 4 submatrices. Given the requirements of the ve-

hicles, they split their input matrices horizontally and

vertically and encode their submatrices using PolyDot

codes. The splits of input matrices are determined by

variables s

and t

as shown in Equation (1).

Table 1: System Simulation Parameter Values.

Parameter Values

Unit cost of communication resources, c

[0.1,1]

Unit cost of computation resources, c

[0.1,1]

Total amount of communication resources, r

1-50 Gbps

Total amount of computation resources, r

10-200MHz

Amount of communication resources required

for each transmission, g

100-500Mbps

Amount of computation resources required for

each computation, h

100-500kHz

Unit price of communication resources, λ

[0.1, 1]

Unit price of computation resources, λ

[0.1, 1]

Table 2: Simulation Parameter Values of Buyers.

Buyer ID s

Buyer 1 1 4 16 0.6 0.5

Buyer 2 1 4 16 0.5 0.4

Buyer 3 2 2 12 0.3 0.8

Buyer 4 2 2 12 0.4 0.4

Buyer 5 4 1 7 0.4 0.5

Buyer 6 4 1 7 0.4 0.3

The values of the simulation parameters of the 6

buyers are shown in Table 2. The buyers with larger t

and smaller s

have larger recovery threshold. Given

the number of symbol transmissions and computa-

tions required for the CDC tasks as well as the unit

Figure 1: Utility of Buyers.

Figure 2: Utility of Sellers.

prices that the buyers are willing to pay for the re-

sources, the buy-bids of the buyers can be computed.

Figure 1 shows the utilities of the buyers given

the buy-bids of the buyers. We observe that for buy-

ers that submit buy-bids of lower than 60, their util-

ities are zero. This implies that by bidding a value

of smaller than 60, the buyers are unable to complete

their CDC tasks as they do not have sufﬁcient edge

servers to facilitate their CDC tasks. There are several

reasons for the failure in their bids for edge servers.

Firstly, the buyers are not matched to sellers that have

larger sell-bids than the buyers’ buy-bids to ensure

individual rationality of the double auction mecha-

nism. Thus, only a small number of sellers that can be

matched to buyers with smaller bids. Secondly, since

each edge server can only facilitate the CDC task of

one of the vehicles, the buyers with small bids lose

out to those with large bids in the auction, reducing

further the number of sellers that can possibly match

to the buyers with small bids. Besides, we observe

that the buyer with a buy-bid of 115 receives a utility

of zero but the buyer with a smaller buy-bid of 107.5

receives a utility of 570, resulting in a discontinuity

in the curve in Fig. 1. The vehicles require a num-

ber of edge servers, which is deﬁned by the recov-

ery threshold, to complete their CDC tasks. However,

there may not be enough edge servers that have suf-

ﬁcient communication and computation resources to

complete the CDC tasks of the vehicles. Hence, even

by submitting a larger buy-bid, the buyers may still

not be allocated any seller for their CDC tasks.

In Fig. 2, we observe that sellers with sell-bids of

larger than 122 are not allocated to any buyer and thus

WINSYS 2021 - 18th International Conference on Wireless Networks and Mobile Systems

112

Figure 3: Utilities of winning sellers and buyers under dif-

ferent number of sellers and 6 buyers.

Figure 4: Utilities of winning sellers and buyers under dif-

ferent number of buyers and 50 sellers.

their utilities are zero. The reasons are similar to those

of the buyers. Firstly, the buyers that can be matched

to the sellers need to have larger buy-bids than the

sellers’ sell-bids. This reduces the number of pos-

sible buyers that can be matched to the sellers with

large sell-bids. Secondly, the sellers with large sell-

bids lose out to those with small sell-bids. We also

observe that sellers with smaller sell-bids, e.g., 14.8

and 45.2, are also not allocated to any buyer. This

is because they may not have sufﬁcient resources to

complete the CDC subtasks of the buyers. For sellers

that have sufﬁcient resources for the CDC subtasks of

the buyers, the match between the seller and buyer is

still not successful if the number of possible sellers

that can be matched to the buyers does not meets the

buyer’s recovery threshold requirement.

Given that the double auction mechanism is

individually-rational and incentive-compatible, we

study the effect of different number of buyers and sell-

ers on their utilities as well as the utility of the auc-

tioneer. Figure 3 shows the utilities of winning buyers

and sellers in a distributed vehicular edge computing

network that consists of 6 buyers and different num-

ber of sellers. As the number of sellers increases, the

total utility of winning sellers decreases. Since the

competition among the sellers increases, the sellers

submit lower sell-bids to the auctioneer, resulting in

lower selling prices. Hence, the utilities of the win-

ning sellers decrease. However, the buyers beneﬁt

from an increase in number of sellers. We observe

that as the number of sellers increase from 70 to 80,

the total utility of the winning buyers increases from

920 to 973. With a larger number of sellers in the net-

work, more buyers are able to be matched with the

sellers and win the buy-bids, hence completing their

CDC tasks and receiving positive utilities.

Similar trend can be observe when the number of

buyers varies. In Fig. 4, as the number of buyers in-

creases, the total utility of winning buyers generally

decreases. The increase in competition between the

buyers results in larger buy-bids submitted by the buy-

ers and hence, higher payment prices for the resources

of the sellers. As such, the utilities of the winning

buyers decrease. However, the total utility of the win-

ning sellers increases. As the number of buyers in-

creases, there is a larger demand for the resources of

the sellers and more sellers are allocated to facilitate

the CDC tasks of the buyers. Thus, the total utility of

the winning sellers increases.

5 CONCLUSION

In this paper, we proposed a double auction mecha-

nism to incentivize the edge servers to facilitate the

vehicles in completing their CDC tasks. Firstly, the

vehicles use PolyDot codes to split their CDC tasks

and distribute the CDC subtasks to the edge servers

for computations. Then, based on the requirements of

the vehicles, the double auction mechanism matches

the vehicles and edge servers as well as determines

the payment prices of the vehicles and selling prices

of the edge servers. For our future work, we can con-

sider different types of distributed computation tasks,

e.g., gradient descent, convolution and Fourier Trans-

form.

ACKNOWLEDGEMENTS

This research is supported, in part, by Alibaba

Group through Alibaba Innovative Research (AIR)

Program and Alibaba-NTU Singapore Joint Re-

search Institute (JRI), and Singapore Energy Market

Authority (EMA), Energy Resilience, under Grant

NRF2017EWT-EP003-041. This research is also

supported by WASP/NTU grant M4082187 (4080)

and Singapore Ministry of Education (MOE) Tier 1

(RG16/20).

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