A Riemann-Hilbert boundary value problem for single-server systems with two queues for blocked and feedback customers

摘要

We analyze a novel Markovian single-server system with two queues for call-back option and feedback. If upon arrival the server is busy, the job registers to be called back later by the server. A job that completes its service may request another round of service. Registered jobs and feedback jobs are said to be in two separated queues from which they are called by the server. We investigate stability conditions and obtain the generating function of the joint queue length distribution as a solution of a homogeneous Riemann-Hilbert boundary value problem.