Properties and Analysis of Queueing Network Models with Finite Capacities

A b s t r a c t Queueing network models with finite capacity queues and blocking are used to represent systems with finite capacity resources and with resource constraints, such as production, communication and computer systems. Various blocking mechanisms have been defined in literature to represent the various behaviours of real systems with limited resources. Queueing networks with finite capacity queues and blocking, their properties and the exact and approximate analytical solution methods for their analysis are surveyed. The class of product-form networks with finite capacities is described, including both homogeneous and non-homogeneous models, i.e., models of systems in which different resources work under either the same or different blocking mechanisms. Nonhomogeneous network models can be used to represent complex systems, such as integrated computer-communication systems. Exact solution algorithms to evaluate the passage time distribution of queueing networks with finite capacity are discussed, as well as some recent results on the arrival time queue length distribution and its relation to the random time queue length distribution. This result provides an extension of the arrival theorem to a class of product-form networks with finite capacity. Properties of queueing network models with blocking are presented. These include insensitivity properties and equivalencies between models with and without blocking, between models with both homogeneous and non-homogeneous blocking types, and relationships between open and closed queueing network models with blocking. Although properties of queueing networks with blocking have been mainly derived for the queue length distribution and average performance indices, we shall also present some equivalence properties in terms of passage time distribution in closed models.