  Time-sensitive services (TSSs) have been widely envisioned for future sixth
generation (6G) wireless communication networks. Due to its inherent
low-latency advantage, mobile edge computing (MEC) will be an indispensable
enabler for TSSs. The random characteristics of the delay experienced by users
are key metrics reflecting the quality of service (QoS) of TSSs. Most existing
studies on MEC have focused on the average delay. Only a few research efforts
have been devoted to other random delay characteristics, such as the delay
bound violation probability and the probability distribution of the delay, by
decoupling the transmission and computation processes of MEC. However, if these
two processes could not be decoupled, the coupling will bring new challenges to
analyzing the random delay characteristics. In this paper, an MEC system with a
limited computation buffer at the edge server is considered. In this system,
the transmission process and computation process form a feedback loop and could
not be decoupled. We formulate a discrete-time two-stage tandem queueing
system. Then, by using the matrix-geometric method, we obtain the estimation
methods for the random delay characteristics, including the probability
distribution of the delay, the delay bound violation probability, the average
delay and the delay standard deviation. The estimation methods are verified by
simulations. The random delay characteristics are analyzed by numerical
experiments, which unveil the coupling relationship between the transmission
process and computation process for MEC. These results will largely facilitate
elaborate allocation of communication and computation resources to improve the
QoS of TSSs.
