Two-layer queueing networks

A family of queueing networks with a two-layer configuration is proposed and analyzed in order to provide well structured hierarchy of network models for performance analysis of computer and/or communication systems. The upper layer describes the often-disregarded software behavior while the lower layer describes the usual hardware behavior. For the case in which the upper layer includes no outstanding queues, a product form equilibrium joint distribution is established assuming state-dependent arrival and state-dependent service rate functions with general service time distributions. The marginal distributions are derived for convenience in applying the results. For the case in which the upper layer does include outstanding queues, an approximation method is proposed, which generalizes the flow-equivalent methods.