A note on solutions of a functional equation arising in a queuing model for a LAN gateway

Abstract

We discuss some issues concerning solutions of the functional equation (Formula Presented) in the class of analytic functions P mapping D¯ 2(D¯ stands for the closure of the unit disc D in the complex plane C) into C. Here rj, sj∈ (0 , 1) for j= 1 , 2 are fixed, ξj= rjsj, (Formula Presented) for every q∈ R and (Formula Presented). The equation arises in a two-dimensional queueing model for a LAN gateway.