  Network slicing is a promising approach for enabling low latency computation
offloading in edge computing systems. In this paper, we consider an edge
computing system under network slicing in which the wireless devices generate
latency sensitive computational tasks. We address the problem of joint dynamic
assignment of computational tasks to slices, management of radio resources
across slices and management of radio and computing resources within slices. We
formulate the Joint Slice Selection and Edge Resource Management(JSS-ERM)
problem as a mixed-integer problem with the objective to minimize the
completion time of computational tasks. We show that the JSS-ERM problem is
NP-hard and develop an approximation algorithm with bounded approximation ratio
based on a game theoretic treatment of the problem. We provide extensive
simulation results to show that network slicing can improve the system
performance compared to no slicing and that the proposed solution can achieve
significant gains compared to the equal slicing policy. Our results also show
that the computational complexity of the proposed algorithm is approximately
linear in the number of devices.
