服務系統中服務人員動態控制之研究

本論文考慮一個沒有等候空間的服務系統，將顧客分成兩個等級，優先權高的顧客稱為VIP顧客，優先權低的顧客稱為一般顧客，因系統中的服務人員對兩種顧客皆可提供服務，故稱此系統為彈性服務系統，為了降低VIP顧客的流失率，在服務人員之中保留 r 數量的服務人員只對VIP顧客提供服務。系統有空閒的服務人員時，顧客可直接進入系統接受服務，若系統中空閒的服務人員數目小於或等於 r 時，一般顧客會因為剩餘的服務人員需保留給VIP顧客而流失。VIP顧客一但發現有剩餘的服務人員即享有進入系統接受服務的權利，若所有的服務人員在VIP顧客到達時處於忙碌的狀態，則也造成VIP顧客的流失。 VIP顧客及一般顧客的流失率訂為系統的服務水準，為使服務水準最高之下決定最少預留的服務人員數目為本論文所要討論的主要問題。以等候線理論定義服務系統的狀態，用隨機動態規劃的方法分析一些特性，藉由當有顧客佔用一空閒服務人員或有顧客被服務完而釋放一服務人員時，控制保留服務人員數目該增加、減少或是不做任何變化，再利用 Markov Decision Process 求解各狀態的保留策略，證明在成本函數滿足某些條件之下，最佳保留策略的存在。關鍵詞: 彈性服務系統，等候控制，Markov Decision Process，最佳策略。

關鍵字

彈性服務系統；等候控制； Markov Decision Process ；最佳策略

並列摘要

Queueing systems are useful to model manufacturing systems, telecommunication systems and service systems. On the other hand, control models take into account the possibility of dynamically varying some of the parameters of the system, such as the arrival or service rates, or the rules used to determine the routing of jobs or the processing order. In general, dynamic rules for setting such parameters offer the possibility of the improved performance, as compared to static rules. For the service system, two control problems are usually considered: how to decide whether to accept or reject an arriving customer, and how many resources should be allocated, for example, how to reserve the servers for higher priority customers. In this thesis, we consider a basic service system, in which there are two classes of customers: ordinary customers and priority customers (VIP customers), and serval flexible servers who can serve both classes of customers. A coming ordinary customer can enter the system if the free servers are greater than the number of reserved servers and a coming VIP customer can enter the system if there is a free server. Our objective is to minimize the expected total discounted cost by adding an additional reserved server or keeping the reserved servers (among total flexible servers) during the arrival process, and by keeping the reserved servers or reducing a reserved server during the departure process. We model the system by Markov decision process and study the monotonic properties of the optimal policy. According to these properties we have a switching curve of the system. The optimal control policy shows that we have a constant control level. Some numerical examples are provided to illustrate the results. Keyword: Flexible Service System, Queueing Control, Markov Decision Process, Threshold Policy.

並列關鍵字

Flexible Service System ； Queueing Control ； Markov Decision Process ； Threshold Policy

參考文獻

[1] E. G. Altman, G. Koole, and T. Jim´enez, On Optimal Call Admission Control in a Resource-sharing System, IEEE Transactions on Communications, 49, 1659-

1668, 2001.

[2] P. P. Belobaba, Application of a Probabilistic Decision Model to Airline Seat Inventory Control, Operations Research, 37, 183-197, 1989.

[3] D. Bertsekas, Dynamic Programming, Deterministic and Stochastic Models,

[4] G. R. Bitran and S. M. Gilbert, Managing Hotel Reservation with Uncertain

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服務系統中服務人員動態控制之研究

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