Instability of nonhomogeneous queueing networks (Q1850765)

The author studies strong and weak instability for an open queueing network with multi-server nonhomogeneous stations. The traffic intensity \(\rho\) of the network is defined to be the maximum of the traffic intensities of the stations. Let \(\Omega (t)\) and \(\nu_t\) be the total workload and the number of customers in the system at time \(t\), respectively. It is shown that \(\rho > 1\) implies that \(\liminf_{t\to \infty} \Omega(t)/t > 0\) and \(\liminf_{t\to \infty} \nu_t/t > 0\). For \(\rho = 1\) the main results are that the network has infinite expected regeneration time and that \(\Omega(t) \to \infty\) stochastically. Analogous results are proved for corresponding networks with several classes of customers and Markovian switching between these classes.