The accuracy of call-congestion measurements for loss systems with renewal input

The concept of a generalized renewal process is used to derive an asymptotic approximation for the variance of the observed proportion of unsuccessful attempts on a trunk group during a given time-interval. Calls are assumed to arrive according to a general renewal process, and those which are blocked leave the system and do not return (loss system). As an application of our result we examine the special case of an overflow input–an important example from telephone networks with alternate routing. Comparison of our results with values obtained from simulation indicates that the approximation is quite accurate for telephone traffic-engineering purposes.