The optimal management of a queueing system with controlling arrivals

Abstract

This article considers the optimal management problem of a finite capacity M/H₂/1 queueing system, in which the unreliable server operates the F-policy. When the number of customers in the system reaches its capacity K (), no further arriving customers are allowed to enter the system until a certain number of customers who are already in the system have been served so that the number of customers in the system decreases to a predetermined threshold F (). At that time, the server needs to take an exponential startup time and allow customers to enter the system. The F-policy investigates the most common issue of controlling arrival to a queueing system and a startup time is required before allowing customers to enter the system. This system is useful in many potential applications for wireless communication networks, transportation service systems, and production systems. Some important performance measures are derived. A cost model, developed to determine the optimal capacity K, the optimal threshold F, the optimal setup rate, and the optimal repair rate at a minimum cost, is also studied.

摘要

本論文討論一個有限容量M/H₂/1排隊系統的最佳化問題 ， 其中服務者為不可信度且操作F方策。 當顧客數達到系統容量K()時 ， 此時系統不再准許顧客進入 ， 直到等待服務的顧客數小於一個預先設定的門檻值F() ， 才允許顧客進入系統要求服務。 在這個狀況下 ， 系統需要先執行一個指數分布的起動時間 ， 才開始提供服務。 這系統可應用於無線通信的應用上 ， 運輸管控或生產管理。 我們推導系統的效能測度 ， 發展一個成本模式 ， 在最低成本下 ， 尋找到最佳化的K與F值 ， 最佳化的啟動率及最佳化的修理率。

(*聯絡人: [email protected])

Keywords:

• birth and death process
• control
• F-policy
• server startup
• server breakdown
• quasi-Newton method

Keywords:

• 關鍵詞： 生死過程 ， 控制 ， F-方策 ， 故障 ， 準牛頓方法

Acknowledgments

The authors thank the referees and editors for their constructive remarks and comments, which helped them to improve the clarity of the article. The second author acknowledges the support by the National Science Council of Taiwan, under Contract no. 96-2628-E-025-001-MY3.

Notes

(*聯絡人: [email protected])