Multiple delay capture probability and performance of DS-SS slotted ALOHA packet radio system

We address the throughput and delay performance of a direct sequence spread spectrum (DS-SS) slotted ALOHA packet radio system, where all users use a common spreading code to communicate with a central station. Unlike in previous works where packets are constrained to arrive on a finite set of discrete times, we consider in this paper that packet arrivals are continuously and uniformly distributed over an arbitrary uncertainty interval. We derive a closed form multi-packet capture probability and obtain the throughput and delay expressions for the DS-SS slotted ALOHA packet radio system. We use simulations to validate our analysis.