Application of nonparametric laws in queuing systems and renewal theory

Nonparametric survival distributions find, more and more, applications in a variety of field: reliability theory and survival analysis, queueing theory, maintenance, stock management, theory of the economy,... The purpose of this paper is to use lower and upper bounds, in term of average means of the reliability functions belonging to the following distributions classes: IFR, DFR, NBU and NWU, which are presented by Sengupta (1994), to bound some of characteristics. We use some of these laws to evaluate the mean stationnary waiting time in GI/GI/1 queueing system, by bringing up to date those bounds found by Stoyan (1983). As application to renewal theory and reliability, we use qualitative properties of time of repair to bound the mean of life system.