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Mathematical Model of Communication Delays in Wireless Networks

Krupanek B., Bogacz R.

International Journal of Electronics and Telecommunications

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2016

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Vol. 62, No. 1

61--64

EN

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.

2

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

Jakubiec J., Krupanek B.

Measurement Automation Monitoring

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2015

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Vol. 61, No. 9

426-429

EN

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.

3

Application of delta function in probabilistic modeling of communication delays in wireless networks – measurement identification and application of the delay model

Jakubiec J., Krupanek B.

Measurement Automation Monitoring

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2015

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Vol. 61, No. 11

498--502

EN

The paper is the second part of the publication [1] which presents the mathematical fundamentals of a new probabilistic model of communication delays in wireless networks. This model is based on a delta function sequence used to describe retransmissions between a transmitter and a receiver [2], [3] which occur when external disturbances influence a wireless transmission. In the paper, there are described a method of identification of the proposed model parameters on the basis of measurements results of delays and verification of the identified values. The model application for describing delays in multi-node wireless networks is presented and illustrated by examples.

4

The delta function and the composition of distributions

Fisher B.

Demonstratio Mathematica

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2002

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Vol. 35, nr 1

117-123

EN

Let F be a distribution and let / be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {Fn{f)}, where Fn(x) = F(x) * 6n{x) and {6n(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function 6(x). The distribution 6(s)(xlamba+) is evaluated for lambda > 0 and s=0,1,2,....