The Congestion Time Limit Distribution for a Fully Available Group of Trunks

Abstract

A fully available group of n trunks is considered under the assumption that a Poisson stream of calls with constant intensity $\lambda $ is serviced. The complete availability group is a loss-system. The holding time is independent of the stream of calls and has an exponential distribution with a mean holding time equal to 1.Let $\xi (t) = \{ \xi _0 (t),\xi _1 (t), \cdots ,\xi _n (t)\} $ be a random vector, where $\xi _\alpha (t)$ is the life time of the system in its $\alpha $ state, $\alpha = 0,1, \cdots ,n$, during the time interval $[0,t]$. The second moments of the random vector $\xi (t)$ are determined as rational functions of $\lambda $. These results make it possible to apply integral and local limit theorems for practical purposes.