Proofing Markov Memory-less Processes Mathematically

  • Thread starter Thread starter Mark J.
  • Start date Start date
AI Thread Summary
To prove that an arrival process is Markovian and memory-less, one must demonstrate that it satisfies the definition of a Markov Process, which depends on the specific characteristics of the arrival process. In the context of people arriving at a bus stop, it is suggested to assume the system is Markovian for the application of queueing theory and stochastic processes. The discussion highlights the need for statistical tests to evaluate the hypothesis that the arrival process follows a Poisson distribution, noting that statistical tests do not constitute mathematical proof. Ultimately, clear identification of the arrival data and appropriate statistical methods are crucial for validating the Markovian nature of the process. Understanding these concepts is essential for effectively analyzing arrival patterns in queueing systems.
Mark J.
Messages
81
Reaction score
0
How to mathematically proof that an arrival process is Markov ,memory-less ?
 
Mathematics news on Phys.org
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".)
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Similar threads

B Proof that pattern recognition is unending?
Replies
12
Views
2K
I Markov Processes: Estimating Transition Probabilities
Replies
6
Views
2K
Solve the given problem involving conditional probability
Replies
32
Views
2K
I Monumental Proof Settles Geometric Langlands Conjecture
Replies
1
Views
2K
Markov processes (Weight Suspended equally by n Cables)
Replies
4
Views
1K
I Markov Process: How to Tell Reversibility & Eigenvalues=1
Replies
12
Views
2K
I Standard way of expressing 'no proof given'?
Replies
11
Views
2K
Insights How to Write a Math Proof and Their Structure
Replies
2
Views
2K
Understanding Markov Chains: Deriving and Solving Probabilities
Replies
1
Views
2K
Mathematical proofs, physics and time management
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top