  In this paper, we consider the service caching and the computing resource
allocation in edge computing (EC) enabled networks. We introduce a random
service caching design considering multiple types of latency sensitive services
and the base stations (BSs)' service caching storage. We then derive a
successful service probability (SSP). We also formulate a SSP maximization
problem subject to the service caching distribution and the computing resource
allocation. Then, we show that the optimization problem is nonconvex and
develop a novel algorithm to obtain the stationary point of the SSP
maximization problem by adopting the parallel successive convex approximation
(SCA). Moreover, to further reduce the computational complexity, we also
provide a low complex algorithm that can obtain the near-optimal solution of
the SSP maximization problem in high computing capability region. Finally, from
numerical simulations, we show that proposed solutions achieve higher SSP than
baseline schemes. Moreover, we show that the near-optimal solution achieves
reliable performance in the high computing capability region. We also explore
the impacts of target delays, a BSs' service cache size, and an EC servers'
computing capability on the SSP.
