State diagrams and steady-state balance equations for open queuing network models

In this paper, the state diagrams and steady-state balance equations for two kinds of open queuing network models are presented. The first model comprises a network of single queues with single servers, while the second model comprises multiple servers for single queues. State diagrams are drawn for (2, 3) queuing networks with (i) single servers and (ii) multiple servers. Steady-state balance equations are derived from the state diagrams. The paper provides a method to solve open queuing networks by analyzing the stochastic process involved in the transition of states in a continuous time Markov chain which represents the state diagram of a queuing system.