Bounds on the stability of the stationary distribution of the number of busy channels in the system GI\(| GI| \infty\) (Q912496)

For the GI/GI/\(\infty\) system the stability problem of the time stationary distribution of the number of busy channels is treated. Bounds are derived for the total variation and the Kantorovich-Rubinshtein distances of the distributions of the original and a perturbed system in terms of the Lévy-Prokhorov or Kantorovich-Rubinshtein distances, respectively, of their interarrival time and service time distributions. Under the condition of starting the idle systems a uniform bound for all t of the total variation distance of the time dependent distributions is given.