Performance analysis and capacity optimization for retrial queues with generally distributed retrial times

• Applicant: Professor Dr. Raik Stolletz
• Subject Area: Operations Management and Computer Science for Business Administration
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 522848863

With this project an important research gap in the analysis and optimization of retrial queues will be filled. This proposal focuses on queueing systems with generally distributed retrial times that occur due to impatient customers leaving the queue. Such retrials may influence the system's utilization and hence may positively impact the performance measures both from a customer’s point of view and from a service provider's point of view. The contributions of this research project are threefold: i) We will develop fast and accurate methods to approximate the performance measures of time-dependent queues with generally distributed retrial times. A new hybrid method for performance evaluation combines the advantages of two classes of approximation methods and will be able to analyze both underloaded and overloaded retrial queues. These methods will be used to derive managerial insights into the influence of generally distributed retrial times on the performance measures. The sensitivity of the distribution on demand smoothing effects will be investigated. ii) Based on the time-dependent methods for the performance analysis we will approximate stationary performance measures through a limit analysis. This will lead to closed-form approximations for stationary retrial queues with multiple servers and generally distributed retrial times which are not described in literature yet. iii) We will analyze and describe demand smoothing effects in retrial queues. Stylized models will be proposed and discussed to derive analytical insights into demand smoothing and how they depend on the distribution of the retrial times. We will develop and analyze methods to determine the optimal capacity in such queueing systems, i.e. optimizing the stationary and time-dependent number of servers. Those methods will be used to derive managerial insights on the structure of optimized staffing levels and the sensitivity of the retrial-time distribution on the optimal solutions. The contributions of our project are expected to be valuable and important from both a methodological point of view and a managerial point of view. Methodologically, we will develop new approximation methods and related staffing algorithms for stationary and time-dependent retrial queues with generally distributed retrial times. The new hybrid method for time-dependent performance evaluation combines the advantages of two classes of approximation methods and can be potentially applied to general time-dependent queueing models in further research. This project also addresses important managerial issues such as demand smoothing. It is essential to understand demand smoothing effects to improve the system performance depending on the distribution of retrial times. Based on the findings of this research project, future research can be devoted to influence the retrial behavior to optimally smooth the demand.

• DFG Programme: Research Grants
• International Connection: France
• Cooperation Partner: Professor Dr. Benjamin Legros