Pair formation in a Markovian arrival process with two event labels

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ID: 272716
2004
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Abstract
The stochastic process resulting when pairs of events are formed from two point processes is a rich source of questions. When the two point processes have different rates, the resulting stochastic process has a mean drift towards either -∞ or +∞. However, when the two processes have equal rates, we end up with a null-recurrent Markov chain and this has interesting behavior. We study this process for both discrete and continuous times and consider special cases with applications in communications networks. One interesting result for applications is the waiting time of a packet waiting for a token, a special case of this pair-formation process. Pair formation by two independent Poisson processes of equal rates results in a point process that is asymptotically a Poisson process of the same rate.
Reference Key
alfa2004journalpair Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Marcel F. Neuts,Attahiru Sule Alfa;Marcel F. Neuts;Attahiru Sule Alfa;
Journal journal of applied probability
Year 2004
DOI
10.1239/jap/1101840557
URL
https://sciprofiles.com/publication/view/f78e1c14c1cf7c7cb049a1ab496185af
Keywords
map algorithmic probability point process pair formation null recurrence

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