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Simultaneous Success-Run Chains

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  • Jozef L. Teugels

    (University of Louvain, Heverlee, Belgium)

Abstract

If every element from a source of identical particles has to perform a certain fixed success-run Markov chain with n + 2 states, and if the particles are put into the initial state one at a time, they act independently and reach the absorbing state n + 2 after n + 2 steps or they return to the source. This sequence of simultaneous success-run chains can be analysed by using a “basic” Markov chain with 2 n different states that is studied in great detail. Among others, we derive the transition matrix and the stationary distribution. It further turns out that, for m ≧ n the basic Markov chain already behaves in a stationary way , so that it is easy to find the distribution of the number of absorbed particles at a certain instant, as well as the number of particles that return to the source. The proofs of the main theorems are based on mathematical induction and matrix methods.

Suggested Citation

  • Jozef L. Teugels, 1970. "Simultaneous Success-Run Chains," Operations Research, INFORMS, vol. 18(1), pages 132-144, February.
    • Handle: RePEc:inm:oropre:v:18:y:1970:i:1:p:132-144
    DOI: 10.1287/opre.18.1.132
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