  Multi-access edge computing (MEC) and network virtualization technologies are
important enablers for fifth-generation (5G) networks to deliver diverse
applications and services. Services are often provided as fully connected
virtual network functions (VNF)s, through service function chaining (SFC).
However, the problem of allocating SFC resources at the network edge still
faces many challenges related to the way VNFs are placed, chained and
scheduled. In this paper, to solve these problems, we propose a game
theory-based approach with the objective to reduce service latency in the
context of SFC at the network edge. The problem of allocating SFC resources can
be divided into two subproblems. 1) The VNF placement and routing subproblem,
and 2) the VNF scheduling subproblem. For the former subproblem, we formulate
it as a mean field game (MFG) in which VNFs are modeled as entities contending
over edge resources with the goal of reducing the resource consumption of MEC
nodes and reducing latency for users. We propose a on a reinforcement
learning-based technique, where the Ishikawa-Mann learning algorithm (IMLA) is
used. For the later subproblem we formulate it as a matching game between the
VFNs and an edge resources in order to find the execution order of the VNFs
while reducing the latency. To efficiently solve it, we propose a modified
version of the many-to-one deferred acceptance algorithm (DAA), called the
enhanced multi-step deferred acceptance algorithm (eMSDA). To illustrate the
performance of the proposed approaches, we perform extensive simulations. The
obtained results show that the proposed approaches outperform the benchmarks
other state-of-the-art methods.
