![](bg2.png)
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
m
× Q
m
square in-
put matrices A
m
and B
m
, i.e., C
m
= A
m
B
m
. 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
m
and B
m
both horizontally and
vertically such that:
WINSYS 2021 - 18th International Conference on Wireless Networks and Mobile Systems
108