Modeling and optimization analysis of a retrial system with partial servers synchronous vacation and customer geometric loss

Abstract

In many actual issues, such as call center and cloud service computing center, retrial systems have been widely applied to derive the performance measures. This study takes up a multi-server retrial system with partial servers synchronous vacation and customer geometric loss. An arriving customer finding no servers available either enters a retrial group according to first-in-first-serve discipline or balks. In the retrial group, only the first customer can retry for his service. A customer from the retrial group finding all servers unavailable decides either balks or reenters the retrial group. Partial servers may be on vacation simultaneously when they become idle at the moment of service completion and system conditions satisfy the administrative policy. This retrial system is analyzed as a quasi-birth-death process, and some general descriptors are developed. Optimization problems, including single-objective and bi-objective, are constructed to help the manager’s decision-making. Numerical results are displayed tabularly and graphically. A potential application in which the proposed model can be applied is provided.

Keywords:

• Bi-objective analysis
• Geometric
• Loss
• Retrial system
• Synchronous vacation

Acknowledgments

The author world like to thank anonymous referees for their valuable comments and suggestions which greatly enhanced the clarity of the paper. All their comments were incorporated directly in the text. This research was supported by the National Science and Technology Council of Taiwan under Grant MOST 111-2221-E-025-002-MY3.