Semi-open queuing networks: a review of stochastic models, solution methods and new research areas

Abstract

Capturing the waiting times (at an external queue) for a customer to access a movable resource is an important step towards measuring customer service and system performance in manufacturing, logistics, communication and health care systems. Such waiting time measures are typically used for sizing resource and buffer capacities, and thereby minimising customer waiting time probabilities. In this regard, semi-open queuing networks (SOQNs), which decouple the arriving customers/transactions from the network resources using a synchronisation station (also known as a semaphore queue), can potentially capture the customer/transaction waiting times/costs more precisely and provide a rich network modelling construct. Hence, modelling manufacturing or service systems using SOQNs is an important step towards measuring customer flow times (sojourn times) wherein the customer waiting times at an external queue are a critical component. In this paper, we present several stochastic models for manufacturing and service systems using SOQNs and also discuss the potential applications of SOQNs. We then review the solution methods for SOQNs and also compare the numerical accuracies for three promising methods. Finally, we include the potential research areas in SOQNs.

Keywords:

• semi-open queuing networks
• semaphore/match/synchronisation/fork-join queues
• stochastic models
• solution methods

Acknowledgements

The author would like to thank Prof. Ivo Adan for discussing the problem of orderlies movement in hospitals. I would also like to acknowledge Mr. Akash Gupta for performing the numerical experiments to compare the performance of different solution methods. Finally, I would thank the anonymous reviewers for their comments on improving the exposition of this paper.

Notes

No potential conflict of interest was reported by the author.