Solving some overflow traffic models with changed serving intensities

摘要

This paper investigates specific systems with overflow traffic. A primary group with two Poisson traffics is considered whereupon the rejected calls from one traffic are directed to the alternative group with changed serving intensities. The generating function technique is used for analytical solving the model with secondary and ternary groups and the model that separately treated the channels in alternative groups. The obtained analytical solutions essentially reduce the constraints concerning the equation system size, convergence, and calculation time, which arise when numerically solving the steady-state system equations. For the case with single channels in the ternary group, explicit solutions for traffic parameters are obtained. Also, comparison with the model that has a unique serving intensity of overflow traffic is made.