ON HEAVY TRAFFIC APPROXIMATIONS FOR TRANSIENT CHARACTERISTICS OF M M/INFINITY QUEUES/

In this paper, transient characteristics related to excursions of the occupation process of M/M/infinity queues are studied, when the excurs ion level is large and close to the mean offered load. We show that th e classical diffusion approximation by an Ornstein-Uhlen-beck (OU) pro cess captures well the average values of the transient variables consi dered, while the asymptotic distributions of these variables depart fr om those corresponding to the OU process. They exhibit, however equiva lent tail behaviour at infinity and numerical evidence shows that they are amazingly close to each other over the whole half-line.