Delay analysis in static poisson network

We investigate the delay of the discrete-time slotted ALOHA network where the sources are distributed as a Poisson point process. Each of the sources is paired with a destination at a given distance and a buffer of infinite capacity. The network is assumed to be static, i.e., the sources and the destinations are generated at first and remain static during all the time slots. Employing tools from queueing theory as well as point process theory, we obtain upper bounds and lower bounds for the cumulative distribution function (cdf) of the conditional mean delay. Numerical results show that the gap between the upper and lower bounds is small, and the results also reveal how these bounds vary with system parameters.