Sum Rate and Access Delay Optimization of Short-Packet Aloha

Shortening the packet length has been a consensus in wireless network design for supporting the ultra-low latency Internet of Things (IoT) applications. Yet, with short-packet transmission, the rate loss would occur, which further depends on the blocklength, making the network optimization notoriously difficult, especially for random access networks. This paper focuses on the representative random access network, i.e., Aloha, with short packet transmission, namely, short-packet Aloha. Specifically, we aim to optimize the sum rate and access delay of short-packet Aloha. By deriving the probability of successful transmissions of packets, both the network sum rate and the probability generating function of access delay are obtained as explicit functions of key system parameters. The maximum sum rate and the minimum mean access delay are further derived by jointly tuning the packet transmission probability and the blocklength of packets. The effect of system parameters on the optimal sum rate and access delay performance is investigated. It is shown that the maximum sum rate is insensitive to the retry limit
$M$
, while deteriorates as the information bits per packet
$k$
decreases. In contrast, the optimal delay performance can be improved with a small
$M$
or
$k$
. The reliability performance is also evaluated and shown to be enhanced with a large retry limit
$M$
. The analysis sheds important light on the access design of practical short-packet Aloha networks. By taking LTE-M as an example, it is found that to improve access delay performance, the information bits per packet
$k$
should not exceed an upperbound, which polynomially decreases as the network size increases.