Matlab Code for the Distribution of Age of Information in Status Update Systems with Heterogeneous Information Sources

INSTRUCTIONS:

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The single .zip file (codes.zip) shall be extracted into a single folder which will be consisting of five MATLAB .m files: a script "numericalExample.m" and four functions "Bufferless.m", "GAW.m", "RA_SB.m" and "generateRvCov.m".

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1) DESCRIPTION OF CONTENTS:

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a) Script "numericalExample.m": 

This example obtains per-source mean Peak-AoI (PAoI) and AoI values as well as per-source PAoI and AoI violation probabilities for the following four servers consisting of N sources:

 - Non-preemptive Bufferless server,

 - Probabilistic Generate-at-will (GAW) server,

 - Last-come First-serve with Preemption Only in Waiting (LCFS-W) server,

 - Random Arrival with Single Buffer (RA-SB) server.

b) Functions "Bufferless.m", "GAW.m" and "RA_SB.m":

These functions construct and solve analytical models for Non-preemptive Bufferless, Probabilistic Generate-at-will (GAW) and Random Arrival with Single Buffer (RA-SB) servers using the theory of absorbing Markov Chains. In particular, they obtain per-source PAoI/AoI distributions where the sources may have different (i) general phase-type service time distributions, (ii) packet error probabilities and (iii) arrival rates. These three functions are used to obtain the performance metrics studied in the script "numericalExample.m". For detailed input-output descriptions of each function, we refer the user to the .m files:

- "Bufferless.m": Non-preemptive Bufferless server

- "GAW.m": Probabilistic GAW server

- "RA_SB.m": RA-SB server

c) Function "generateRvCov.m":

This function constructs a phase type random variable with given coefficient of variation. In particular, if the given coefficient is between 0 and 1, it uses mixture of erlang random variables whereas if the given coefficient is higher than 1, it uses hyperexponential distribution.

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2) INPUT PARAMETERS OF THE SCRIPT "numericalExample.m":

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User specifies the following inputs in "INPUT PARAMETERS" code block:

- Input 1: Arrival rates as 1xN vector.

- Input 2: Average service rates as 1xN vector.

- Input 3: Squared coefficient of variations as 1xN vector.

- Input 4: Packet error probabilities as 1xN vector.

- Input 5: Age threshold value as a scalar which will be used for calculating PAoI and  AoI violation probabilities for each source.

- Input 6: For RA-SB server, cross replacement probabilities as NxN matrix.

- Input 7: For GAW server, source selection probabilities as 1xN vector.

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