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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;第一個選擇性服務;second optional service;batch arrival queue;Newton-Quasi method;第二個選擇性服務;群體到達排隊系統;牛頓法
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.

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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