Multi-stage semi-open queuing networks (SOQNs) are widely used to analyze the performance of multistage manufacturing systems and automated warehousing systems. While there are several methods available for solving single-stage SOQNs, solution methods for multi-stage SOQNs are limited. Decomposition of a multi-stage SOQN into single-stage SOQNs and evaluation of an individual singlestage SOQN is a possibility. However, the challenge lies in obtaining the job departure process information from an upstream single-stage SOQN to evaluate the performance of a downstream single-stage SOQN. In this paper, we propose a two-moment approximation approach for estimating the squared coefficient of variation of the job inter-departure time from a single-stage SOQN, which can serve as an input to link multi-stage SOQNs. Using numerical experiments, we test the robustness of the proposed approach for various input parameter settings for both single and multi-class jobs. We find that the proposed approach works quite well, particularly when the coefficient of variation of the job inter-arrival time is less than two. We demonstrate the efficacy of the proposed approach using a case study on a multi-tier shuttle-based compact storage system and benchmark our results with an existing approach. The results indicate that our approach yields more accurate estimates of the performance measures in comparison to the existing approach in the literature.

Semi-open queues, Job departure process, Approximation, Facility planning and design
hdl.handle.net/1765/135218
Computers & Operations Research
Department of Technology and Operations Management

Kumawat, G.L., & Roy, D. (2021). A new solution approach for multi-stage semi-open queuing networks: An application in shuttle-based compact storage systems. Computers & Operations Research, 125. Retrieved from http://hdl.handle.net/1765/135218