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標題: Mx/M/1排隊系統含有第二選擇服務之最佳管理
Optimal management of an Mx/M/1 queue with second optional service
作者: 陳楷
Chen, Kai
關鍵字: First essential service
second optional service
batch arrival queue
Newton-Quasi method
出版社: 應用數學系所
引用: 1. J. Al-Jararha and K. C. Madan, An M/G/1 queue with second optional service with general service time distribution. Information and Management Sciences, 14 (2003) 47-56. 2. Y. Baba, On the Mx/G/1 queue with vacation time. Operations Research Letters, 5(1986) 93-98. 3. G. Briere and M.L. Chaudhry, Computational analysis of single-server bulk arrival queues, Mx/G/1 . Computers and Operations Research, 15 (1988) 283-292. 4. G. Choudhury, Some aspects of an M/G/1 queueing system with optional service. Top, 11 (2003) 141-150. 5. G. Choudhury and M. Paul, A batch arrival queue with a second optional service channel under N-policy. Stochastic Analysis and Applications, 24 (2006) 1-21. 6. M. V. Cromie, M. L. Chaudhry and W. K. Grassmann, Further results for the queueing system Mx/M/c . Journal of the Operational Research Society, 30 (1979) 755-763. 7. J.-C. Ke, Batch arrival queues under vacation policies with server breakdowns and startup/closedown times. Applied Mathematical Modelling, 31 (2007) 1282-1292. 8. K. C. Madan, An M/G/1 queue with second optional service. Queueing Systems. 34 (2000) 37-46. 9. J. Medhi, A single server Poisson input queue with a second optional channel. Queueing Systems, 42 (2002) 239-242. 10. J. Wang, An M/G/1 queue with second optional service and server breakdowns. Computers and Mathematics with Applications, 47 (2004) 1713-1723.
摘要: 此篇論文主要在研究一個建立在穩態條件下Mx/M/1排隊系統擁有第二選擇性服務。而此模型的第一選擇服務的服務時間服從指數分配參數mu1,以及第二選擇服務的服務時間服從指數分配參數mu2。當正在接受完第一個選擇性服務的顧客,這個顧客可能有theta的機率會離開這個系統或者是有機率1-theta的可能去接受第二選擇性服務,而每一批顧客的到達時間會服從一個混合性的普瓦松過程。首先我們先分析此模型系統性能測量的結果;接著我們建立一個每單位時間內每位顧客消耗的總期望成本函數,而且此函數限制在一個穩定的條件裡;最後我們運用數學上牛頓極值方法,直到滿足一個穩定的限制條件後,我們才能得到此函數全面性的極小值。
This paper studies an Mx/M/1 queue with second optional service under steady-state conditions. The service time of first essential service follows exponential distribution with parameter mu1 and that of second optional service follows exponential distribution with parameter mu2. As soon as first essential service of a customer is completed, a customer may leave the system with probability theta or may opt for second optional service with probability 1-theta. Arrival times of each batch size follow a compound Poisson process. We develop the analytic results of system performance measures. We construct the total expected cost function per customer per unit time and impose a constraint on the stability condition. Applying the Newton-Quasi method, we obtain the global minimum value until a stability condition constraint is satisfied.
其他識別: U0005-2306200822000100
Appears in Collections:應用數學系所



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