Optimal Slotted ALOHA under Delivery Deadline Constraint for Multiple-Packet Reception

TL;DR

This paper optimizes the slotted ALOHA protocol for channels with multiple-packet reception, considering delivery deadlines, deriving optimal transmission probabilities, and proposing a distributed algorithm for dynamic environments.

Contribution

It derives the optimal transmission probability for maximizing successful delivery probability under delivery deadlines and develops a distributed algorithm for adaptive tuning in changing network sizes.

Findings

Optimal transmission probability derived for various M and D values.

Fixed-point iteration method for computing the optimal probability.

Distributed algorithm achieves near-optimal performance in dynamic scenarios.

Abstract

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.