Proofing Markov Memory-less Processes Mathematically

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Discussion Overview

The discussion revolves around the mathematical proof of whether an arrival process, specifically the arrival of people at a bus stop, can be classified as a Markov process and potentially a Poisson process. The scope includes theoretical aspects of stochastic processes and statistical testing.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant suggests that to prove a process is Markovian, one must show it satisfies the definition of a Markov Process, noting that the approach depends on the specifics of the arrival process.
  • Another participant mentions the assumption of a memoryless system to facilitate the application of queueing theory and stochastic processes, indicating that it is mathematically permissible to assume the system is Markovian.
  • A participant reiterates the need to prove the Markovian nature of the arrival process and raises the question of what statistical tests could be used to evaluate the hypothesis that the arrival process is Poisson, clarifying that statistical tests do not constitute "proof."

Areas of Agreement / Disagreement

Participants express differing views on the approach to proving the Markovian nature of the process and the role of statistical tests, indicating that multiple competing views remain without consensus on the best method to establish proof.

Contextual Notes

There are limitations regarding the specific definitions and assumptions related to the arrival process and the statistical methods applicable for testing the hypothesis of a Poisson process.

Mark J.
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How to mathematically proof that an arrival process is Markov ,memory-less ?
 
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That general, all you can say is "show that it satisfies the definition of "Markov Process". How you would do that, of course, depends upon exactly what the arrival process is.
 
The process is people arrival at the bus stop.
I have time arrivals and now I need to proof that is indeed markovian process and maybe poisson
 
Surely one would assume a memoryless system to allow for the theory of queues and stochastic processes can be applied to your queueing system?

I am sure it is mathematically allowed to assume (wlog) that your system is Markovian.
 
Mark J. said:
The process is people arrival at the bus stop.
I have time arrivals and now I need to proof that is indeed markovian process and maybe poisson

Perhaps a clear statement of your question is: "I have data for the arrival times of people at a bus stop. What statistical tests can I use to test the hypothesis that the arrival process is Poission?". (Statistical tests aren't "proof".)
 

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