Problem: Given a Direct Graph G (as shown in Fig Below). Each vertex represent a sensor node (have a limited battery). A link -> has a weight (represents the probability that will send the data packet to ). This weight will be fixed for a t seconds and then will be changed after that, as the battery of the nodes will be consumed per time. For example, as shown in Figure below, say we have node , pr( -> )=0.3; pr( -> )=0.5; pr( -> )=0.2; ; after a time t, this probability distribution will be changed ( according to the energy level of the battery ).
please see the link or the attached file.
please see the problem here:
http://staff.ustc.edu.cn/~anmande/problems/johndcook.htm
It's may be
http://www.rle.mit.edu/rgallager/documents/6.262-4vaw.pdf
http://www.columbia.edu/~ks20/4703-Sigman/4703-07-Notes-MC.pdf
https://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter11.pdf
@Himadri Nath Saha
THANK YOU. i had a problem with Markov heh. the probability is changed per time while Markov required the probability is fixed ( i meant the initial transaction matrix of markov)
@Ammar Hawbani
Do you mean that Markov chain should have only one transaction matrix and that is why it is not applicable in your case?
Time-inhomogeneous Markov chain that its transaction matrix is a random variable described by time-inhomogenous Poisson Process.
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