Application of delta function to probabilistic modeling of communication delays in wireless networks – introduction and mathematical basis

The paper presents the mathematical basis of a new method for building probabilistic models of communication delays in wireless networks in the case if the sent data are not correct and have to be retransmitted. The method is based on using a delta function sequence to describe delays in retransmissions between a transmitter and a receiver [1, 2] under assumption that the access time of the transmitter is taken as random and described by a probability density function. The retransmissions are caused by passive or active external disturbances influencing the communication channel established in the wireless medium [3, 4, 5]. Theoretical considerations are illustrated by examples using both measured and simulated data.