An open exponential queuing network with limited waiting spaces and losses: A method of approximate analysis

Open exponential queuing networks are considered where each node in a network represents several exponential servers with a joint waiting space (a buffer) of limited capacity. A customer arriving to a node with fully occupied buffer is lost. An assumption is made that the input flow to each node formed as a mixture of the external Poisson flow and the flows coming from other nodes is a Poisson flow. Under this assumption, a method of computing network parameters is presented which is based on solving iteratively a system of nonlinear equations for the unknown nodal flow rates. A method based on Markov chain techniques is presented to find the approximate value of the average conditional sojourn time in the network for customers which completed their service process in the network and for customers which were lost eventually. It is demonstrated for two types of a network (a complete 5-node graph and a 5-node tandem-type system) that the network parameters obtained by the derived analytic method are close to those obtained by the Monte Carlo simulation method.