Tbe Least Positive Root of the Characteristic Equation z=K{z)
Prakash Narayan · Journal of Information and Optimization Sciences · 2013
In the study of the theory of queues many results of interest are reported in terms of the least positive root ζ of z=K(z), where K(z) is a probability generating function. In branching processes this rootζ is called the extinction probability. In this paper we give some bounds for this root ζ when the p.g.f. is negative binomia or poisson. These bounds are better than those reported earlier. We also give a[ more efficient algorithm for computing this root ζ to a given accuracy.