Abstract
An age-dependent branching process where disasters occur as a renewal process leading to annihilation or survival ofall 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 timet 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 timet (ii) the total sojourn time of all cells in the system upto timet and (iii) the number of living cells at timet. Some of the existing results are deduced as special cases for related processes.
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Kumar, B.K., Vijayakumar, A. The sojourn time and related characteristics of the age-dependent branching process. JAMC 14, 157–172 (2004). https://doi.org/10.1007/BF02936105
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DOI: https://doi.org/10.1007/BF02936105