Priority queuing systems with parameters dependent on queue length (Q2266664)

There arrive n Markov flows of demands at a one-line priority queuing system. If the queue length of class k demands at instant t is i, the parameter of the k-th flow is \(\lambda_{ki}\), and the servicing speed of these demands is \(\alpha_{ki}\). The duration of the amount of work that then has to be done has distribution function \(H_{ki}(t)\). The serviced demand also enters into the queue length. The queues are ordered in priority, demands of class k having priority over those of class m if \(k<m\). The system is assumed free at the initial instant. We determine the distributions of the occupation periods and of the queue lengths.