Mathematical Model of Communication Delays in Wireless Networks

Abstract

Abstract-The paper presents a new conception of building probabilistic models of communication delays in wireless networks that basis on using a delta function sequence to describe retransmissions between a transmitter and a receiver. It is assumed that the access time of the transmitter is described by a probability density function and the communication channel established in the wireless medium is disturbed by passive or active factors which cause that the transmission can be not correct and the sent data have to be retransmitted. Theoretical considerations have been verified by measurement results obtained by using the experimental system developed for investigating delays caused by external disturbances influencing the wireless transmission. A method of identification of the proposed model parameters and verification of the identified values has been presented.

Sharing Location Information in Multi-UAV Systems by Common Channel Multi-Token Circulation Method in FANETs

“…The BER is calculated for all sent and overheard packets: Packet transmission time (PTT) is one of the most important parameters to determine system performance in the proposed token-based approach. In communication systems, transmission time is defined as the elapsed time between the start of sending a token and the arrival of the last bit of the token at the target node [27]. Two basic parameters are used to calculate the transmission time, i.e., packet size and bit transmission rate, as shown in (4).…”

Investigations of wireless transmission model based on delta function in indoor environment

“…A model of the total delay has to contain all possible values of the delays occurring in the described conditions [10]. If one takes into account that access procedures commonly used in wireless networks are of random character [1], the total delay should be described in probabilistic categories.…”

“…Such a description can be obtained by using the Dirac's delta [6] as a probability density function. The convolution of the probability density function g(τ ) with the delta function gives [10]:…”

“…The radio signal being the communication medium in wireless networks is exposed to many different disturbances both of passive and active nature [4,10]. The passive disturbances are caused by terrain obstacles, walls, etc.…”

“…This paper proposes a method of probabilistic description of delays mainly directed on wireless networks and based on using the delta function [2] for description of both constant delays introduced by network devices and communication delays appearing when Correspondence: beata.krupanek@polsl.pl retransmissions are performed. This model was described in details in reference [10].…”