Rate-Constrained Delay Optimization for Slotted Aloha

Slotted Aloha provides a simple way for accommodating the massive access of Machine-to-Machine (M2M) communications. Yet, the delay performance of slotted Aloha has long been observed to significantly deteriorate as the network size grows. It is therefore important to study how to optimize the delay performance of slotted Aloha in a large-scale network. This paper focuses on the optimization of access delay of a buffered slotted Aloha network, where n nodes transmit to a common receiver in fading channels. Specifically, by deriving the closed-form expressions of the network steady-state points in both unsaturated and saturated conditions, the first and second moments of access delay of each packet are obtained as explicit functions of system parameters, and minimized by optimizing the transmission probability of each node. The analysis shows that to achieve the minimum mean access delay, the transmission probability of each node should be reduced as the network size increases, leading to a diminishing node data rate unless the information encoding rate is jointly optimized. The minimum mean access delay for a given data rate requirement is further characterized, and effects of key parameters such as the minimum required data rate for each node, the mean received signal-to-noise ratio of each packet and the number of nodes on the rate-constrained minimum mean access delay are discussed. The practical insights of the analysis are also demonstrated by taking the example of an LTE-M system with smart grid applications.