Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE SOJOURN TIME AND RELATED CHARACTERISTICS OF THE AGE-DEPENDENT BRANCHING PROCESS

  • Kumar, B.-Krishba (School of Mathematics, Anna University) ;
  • Vijayakumar, A. (School of Mathematics, Anna University)
  • Published : 2004.01.01

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Abstract

An age-dependent branching process where disasters occur as a renewal process leading to annihilation or survival of all the cells, is considered. For such a process, the total mean sojourn time of all the cells in the system is analysed using the regeneration point technique. The mean number of cells which die in time t and its asymptotic behaviour are discussed. When the disasters arrival as a Poisson process and the lifetime of the cells follows exponential distribution, elegant inter- relationships are found among the means of (i) the total number of cells which die in time t (ii) the total sojourn time of all cells in the system upto time t and (iii) the number of living cells at time t. Some of the existing results are deduced as special cases for related processes.

Keywords

References

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