Mean and Variance of Overflow Traffic for Time Dependent Inputs

Telecommunications networks have been designed to maintain predetermined service levels for time-varying traffic loads. This inevitably causes redundant investments, and thus, there are possibilities for further economization by adaptively controlling the systems. In order to establish the optimum strategy of controlling telecommunications networks, it is essential to study time dependent traffic characteristics. This paper analyzes a system in which a time-dependent Poisson input is offered to a finite primary trunk group, and the overflow traffic is carried by an infinite secondary trunk group. Methods for calculating the mean and variance of the overflow traffic (the number of calls existing in the secondary group) are proposed, including an approximate evaluation for which accuracy is examined. Calculated examples are given for various time dependent inputs, and properties of the overflow traffic are discussed. The methods and results presented will be useful for analysis and optimum design of the network systems with time dependent traffic.