Analysis of random walks with an absorbing barrier and chemical rule (Q1006024)

The paper considers continuous random walks with an absorbing barrier and chemical rule for transition rates. It means that transition rate from \(n\) to \(m\) equals either to \(\lambda \) if \(m = 2k + 1,\,n = 2k\) or \(m = 2k,\,n = 2k + 1\) or to \(\mu \) if \(m = 2k - 1,\,n = 2k\) or \(m = 2k,\,n = 2k - 1\). The paper derives explicit expressions for the first passage time and the transient state distributions. The derived formula for the transient state is free of Bessel functions or any integral forms. It is demonstrated that the busy period distribution of a non-empty \(M/M/1/\infty \) queueing model is a special case of the derived result.