  This paper considers the slotted ALOHA protocol in a communication channel
shared by N users. It is assumed that the channel has the multiple-packet
reception (MPR) capability that allows the correct reception of up to M ($1
\leq M < N$) time-overlapping packets. To evaluate the reliability in the
scenario that a packet needs to be transmitted within a strict delivery
deadline D ($D \geq 1$) (in unit of slot) since its arrival at the head of
queue, we consider the successful delivery probability (SDP) of a packet as
performance metric of interest. We derive the optimal transmission probability
that maximizes the SDP for any $1 \leq M < N$ and any $D \geq 1$, and show it
can be computed by a fixed-point iteration. In particular, the case for D = 1
(i.e., throughput maximization) is first completely addressed in this paper.
Based on these theoretical results, for real-life scenarios where N may be
unknown and changing, we develop a distributed algorithm that enables each user
to tune its transmission probability at runtime according to the estimate of N.
Simulation results show that the proposed algorithm is effective in dynamic
scenarios, with near-optimal performance.
