A generic modeling framework for queueing-inventory systems with a single removable server

Abstract

In this article, we use a quasi-birth-and-death (QBD) modeling approach to model queueing-inventory systems with a single removable server. We consider both finite and infinite queueing capacities. Breakdowns and start-up times are also taken into account. All stochastic times are allowed to be general distributions except for the breakdown intervals, which are assumed to be exponential. The general distributions are approximated by phase type representations, resulting in the matrix-algebraic approach to derive the probability vector of the queue length. Some performance measures of interest are obtained by using both hybrid and standard procedures to solve the proposed QBD models. An optimal control policy based on a two-critical number approach using some convexity properties is proposed and its validity is verified through extensive numeric studies.

本研究針對可移除單一服務員佇列存貨系統提出包含有限及無限等候區兩種情境之通用分析架構 ， 模式中考慮機器當機及啟動時間因素 ， 假設當機間隔時間為指數分配 ， 其餘隨機過程不作假設 ， 意即允許為任意機率分配。 本研究使用相形分配去趨近任意機率分配 ， 使得所研究問題具備所謂的擬生死型式 ， 因此得以方便使用矩陣分析方法求解幾乎任何等候模型之佇列長度機率分配 ， 對於此特殊有限及無限擬生死模型 ， 我們分別提出對應之標準解法及混合解法 ， 進而得到一些可衡量系統績效的數學式 ， 最後藉由問題本身的凸函數特 性 ， 可迅速找出有最低成本之基本存貨量及啟動生產之累積訂單量這兩個控制參數 ， 經由大量實驗數據測試結果證明本研究所提方法論確實可行及有效。

(聯絡人: [email protected])

Keywords:

• queueing-inventory system
• removable server
• quasi-birth-and-death
• breakdown
• startup

Keywords:

• 關鍵詞 ： 佇列存貨系統 ， 可移除服務員 ， 擬生死 ， 機器當機 ， 啟動時間

Acknowledgement

This research is partially supported by National Science Council of Taiwan under grant NSC 98-2221E-164-016.

Notes

(聯絡人: [email protected])