A system with dynamically varying mixed priorities and an unreliable server (Q1124523)

At a service station with a single server H classes of calls arrive in simple streams with rates \(\lambda_ 1,...,\lambda_ H\). The service times of the calls are exponentially distributed with means \(b_ 1,...,b_ H\). The queue discipline with mixed priorities is described by a priority matrix \((q_{ik})\) where the element \(q_{ik}\) represents the priority of the calls of class i with respect to the calls of class k (without priority, relative priority, absolute priority). The calls are selected for service according to a linear priority function of the form \(\beta_ k\tau_ k\) for a call of class k where \(\tau_ k\) is the sojourn time of this call in the system and \(\beta_ k\) is a proportionality factor. The server can fail, the instants of failure are described by a simple stream, the repair times of the server are exponentially distributed. A representation of the stationary average waiting time of calls of class k \((k=1,...,H)\) is given.