Stationary tail asymptotics of a tandem queue with feedback

Motivated by applications in computer networks, in this talk, we consider a tandem queue with feedback.In this model, both the interarrival time and the service time are exponential. Upon completion of the service at thesecond station, the customer either leaves the system with probability p or goes back together with all customersin the second queue to the first queue with probability 1-p. We demonstrate how to use alpha-positivity to studystationary tail asymptotics of the queue lengths.References [1] Haque, L., Liu, L. and Zhao, Y.Q. (2004). Sufficient Conditions for a Geometric Tail in a QBD Process withCountably Many Levels and Phases, accepted by Stochastic Models.[2] Miyazawa, M. and Zhao, Y.Q. (2004). The Stationary Tail Asymptotics in the GI/G/1 Type Queue withCountably Many Background States, Adv. in Appl. Probab., 36(4), 1231-1251.