HBH: Theoretical transmissions/receptions for a L-limited Hop by...

In hopbyhop: Transmissions and Receptions in a Hop by Hop Network

Description

This function computes the expected value of the number of transmissions/receptions for Hop by hop model with L-limited retransmissions per packet.

Usage

HBH(p1, p2, L, N)

Arguments

p1	Data success probability
p2	ACK success probability
L	Maximum number of retransmissions.
N	Number of Hops

Details

When there is no limitation, L value must be set as L=Inf.

Value

The ouput is a matrix containing the following values for each hop and total:

1	Success Probability
2	Expected Data Transmissions
3	Expected ACK Transmissions
4	Expected Total Transmissions
5	Expected Data Receptions
6	Expected ACK Receptions
7	Expected Total Receptions

Author(s)

Christian E. Galarza and Jonathan M. Olate

References

Palma, J.M.O.; Carvalho, L.D.P.; Goncalves, A.P.C.; Galarza, C.E.; De Oliveira, A.M., "Application of Control Theory Markov Systems to Minimize the Number of Transmissions in a Multi-hop Network," in Computer Aided System Engineering (APCASE), 2015 Asia-Pacific Conference on , vol., no., pp.296-301, 14-16 July 2015 <DOI:10.1109/APCASE.2015.59>

Olate, Jonathan Matias Palma, et al. "Networked control systems application: Minimization of the global number of interactions, transmissions and receptions in multi-hop network using discrete-time markovian jump linear systems." IEEE Latin America Transactions 14.6 (2016): 2675-2680.

See Also

MCHBH,stochastic_HBH

Examples

#An N=5 Hop by hop system with limited L=7 retransmission per hop
HBH(p1=0.65,p2=0.4,L=7,N=5)

#An ilimited N=5 Hop by hop system
HBH(p1=0.65,p2=0.4,L=Inf,N=5)

Example output

    
########################################### 
HOP BY HOP - THEORETICAL RESULTS 
########################################### 
    
Data success probability         p1 =  0.65 
ACK success probability          p2 =  0.4 
Maximum number of transmissions  L  =  7 
Number of Hops                   N  =  5 
    
                             Hop 1/5 Hop 2/5 Hop 3/5 Hop 4/5 Hop 5/5  Total
Success Probability            0.999   0.999   0.998   0.997   0.997  0.997
Expected Data Transmissions    3.379   3.377   3.374   3.372   3.370 16.872
Expected ACK Transmissions     2.196   2.195   2.193   2.192   2.191 10.967
Expected Total Transmissions   5.575   5.571   5.568   5.564   5.561 27.839
Expected Data Receptions       2.196   2.195   2.193   2.192   2.191 10.967
Expected ACK Receptions        0.878   0.878   0.877   0.877   0.876  4.387
Expected Total Receptions      3.075   3.073   3.071   3.069   3.067 15.354
    
########################################### 
HOP BY HOP - THEORETICAL RESULTS 
########################################### 
    
Data success probability         p1 =  0.65 
ACK success probability          p2 =  0.4 
Maximum number of transmissions  L  =  Inf 
Number of Hops                   N  =  5 
    
                             Hop 1/5 Hop 2/5 Hop 3/5 Hop 4/5 Hop 5/5  Total
Success Probability            1.000   1.000   1.000   1.000   1.000  1.000
Expected Data Transmissions    3.846   3.846   3.846   3.846   3.846 19.231
Expected ACK Transmissions     2.500   2.500   2.500   2.500   2.500 12.500
Expected Total Transmissions   6.346   6.346   6.346   6.346   6.346 31.731
Expected Data Receptions       2.500   2.500   2.500   2.500   2.500 12.500
Expected ACK Receptions        1.000   1.000   1.000   1.000   1.000  5.000
Expected Total Receptions      3.500   3.500   3.500   3.500   3.500 17.500

hopbyhop documentation built on July 7, 2019, 1:03 a.m.