Idle and inter-arrival time statistics in public access mobile radio (PAMR) systems

The statistics of the message arrivals to a PAMR trunked system are investigated. The tools used to perform the statistical analysis have been previously used in similar works and are extremely simple. First, the probability density functions are fitted to the channel idle time (time between the end of a message and the beginning of the next one on the same channel). To characterise the population that generates the offered traffic it is more important to know the time between call attempts. This is a difficult measure as it needs to be deduced from other measures: attempts are not seen when they really occur, but when the system allocates a radio-channel to them. Two methods used to obtain the coefficient of variation of the time between call attempts are presented. Based on the proposed procedures we show that in our system the infinite population assumption is far from the true situation. The measures presented show that the time between call attempts follows a probability distribution that is smoother than the exponential distribution and that models such as finite population or unbalanced multipopulation should be considered.