  In this paper, with the aid of the mathematical tool of stochastic geometry,
we introduce analytical and computational frameworks for the distribution of
three different definitions of delay, i.e., the time that it takes for a user
to successfully receive a data packet, in large-scale cellular networks. We
also provide an asymptotic analysis of one of the delay distributions, which
can be regarded as the packet loss probability of a given network. To mitigate
the inherent computational difficulties of the obtained analytical formulations
in some cases, we propose efficient numerical approximations based on the
numerical inversion method, the Riemann sum, and the Beta distribution.
Finally, we demonstrate the accuracy of the obtained analytical formulations
and the corresponding approximations against Monte Carlo simulation results,
and unveil insights on the delay performance with respect to several design
parameters, such as the decoding threshold, the transmit power, and the
deployment density of the base stations. The proposed methods can facilitate
the analysis and optimization of cellular networks subject to reliability
constraints on the network packet delay that are not restricted to the local
(average) delay, e.g., in the context of delay sensitive applications.
