Abstract :
A transmission policy for slotted ALOHA is studied in terms of new packet generation rate, number of retransmission attempts and number of power levels. The retransmission cut-off is not required for stable operation of slotted ALOHA if the new packet generation rate is less than a critical limit. Results show that the magnitude of this critical limit of the new packet generation rate is 0.36 for single power level, 0.53 for two power levels, 0.62 for three power levels, etc., and one for a very large number of power levels. The system attains maximum throughput for a given number of power levels, when the new packet generation rate exceeds the corresponding critical limit, by adjusting the number of retransmission attempts. A complete analysis for the new packet generation rate with the proper adjustment of the number of retransmission attempts for any number of power levels that provides both stable operation and maximum throughput is executed. The system becomes unstable even without any retransmission attempts, if the new packet generation rate is equivalent to or greater than another critical limit we refer to as unstable critical limit. Results show that the magnitude of this unstable critical limit of the new packet generation rate is one for single power level, 1.63 for two power levels, 2.10 for three power levels, etc. The stable operating regions with and without retransmission cut-off are presented in terms of the new packet generation rate and the number of power levels. Furthermore, an unstable operating region is also discussed.
