An approximation scheme for solving non-product form queueing networks with multiple chains and state dependent service rates is described. Estimates of the steady state probability distribution are obtained using less computational requirements than the standard solution techniques. The approximation scheme is based on a property called chain conditional balance, which leads to a decomposition of the global balance equations into smaller sets of equations. A technique for combining conditional distributions is examined and used to combine the solutions of conditional balance equations into the final estimates. Expressions for the storage and computational requirements of the approximation algorithm are given and an example is provided. An error analysis is described in which the approximation is tested on a large number of randomly generated queueing networks. The experimental results indicate that the approximation yields good estimates of the steady state distribution, as well as several important performance measures of these networks. © 1985.
Agre, J. R., & Tripathi, S. K. (1985). Approximate solution to multichain queueing networks with state dependent service rates. Performance Evaluation, 5(1), 45–55. https://doi.org/10.1016/0166-5316(85)90005-7