  To make better use of file diversity provided by random caching and improve
the successful transmission probability (STP) of a file, we consider
retransmissions with random discontinuous transmission (DTX) in a large-scale
cache-enabled heterogeneous wireless network (HetNet) employing random caching.
We analyze and optimize the STP in two mobility scenarios, i.e., the high
mobility scenario and the static scenario. First, in each scenario, by using
tools from stochastic geometry, we obtain the closed-form expressions for the
STP in the general and low signal-to-interference ratio (SIR) threshold
regimes, respectively. The analysis shows that a larger caching probability
corresponds to a higher STP in both scenarios; random DTX can improve the STP
in the static scenario and its benefit gradually diminishes when mobility
increases. Then, in each scenario, we consider the maximization of the STP with
respect to the caching probability and the BS activity probability, which is a
challenging non-convex optimization problem. In particular, in the high
mobility scenario, we obtain a globally optimal solution using interior point
method. In the static scenario, we develop a low-complexity iterative algorithm
to obtain a stationary point using alternating optimization. Finally, numerical
results show that the proposed solutions achieve significant gains over
existing baseline schemes and can well adapt to the changes of the system
parameters to wisely utilize storage resources and transmission opportunities.
