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<p>We study a Birth–death process (BDP), in which the death process is triggered only by the accumulation of the population size to a specific size, <i>N</i>. We also assume that immigration takes place when and only when the population size remains at zero and that ONLY one unit immigrates into the system. The birth and death rates are assumed to depend on the population size. Motivation for such processes comes from specific populations, such as tumors, start decaying after it has grown to some size. A transient analysis of the above BDP is conducted using the generating function method. This leads to a Volterra Integral equation involving a crucial system probability. The above equation is solved numerically to obtain various system performance measures. A numerical comparison of the average population size in the new model and the Kendall BDP has been conducted.</p>

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A Birth–Death Process with Immigration and N-Policy for the Death Process

  • 期刊论文

  • 发表日期：

    2025年4月15日

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  • A. Shimna,
  • Viswanath C. Narayanan

摘要

We study a Birth–death process (BDP), in which the death process is triggered only by the accumulation of the population size to a specific size, N. We also assume that immigration takes place when and only when the population size remains at zero and that ONLY one unit immigrates into the system. The birth and death rates are assumed to depend on the population size. Motivation for such processes comes from specific populations, such as tumors, start decaying after it has grown to some size. A transient analysis of the above BDP is conducted using the generating function method. This leads to a Volterra Integral equation involving a crucial system probability. The above equation is solved numerically to obtain various system performance measures. A numerical comparison of the average population size in the new model and the Kendall BDP has been conducted.