A queueing-inventory system with two classes of customers |
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| Authors: | Ning Zhao Zhaotong Lian |
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| Institution: | 1. Faculty of Science, Kunming University of Science and Technology, China;2. Faculty of Business Administration, University of Macau, Macau SAR, China;1. Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 136-701, Republic of Korea;2. Department of Mathematics Education, Chungbuk National University, 1 Chungdae-ro, Seowon-gu, Cheongju, Chungbuk, 362-763, Republic of Korea;1. School of Economics and Management, Yanshan University, Qinhuangdao 066004, China;2. Liren College, Yanshan University, Qinhuangdao 066004, China;1. Dept. of Mathematics, Cochin University of Science & Technology, Kochi 682 022, India;2. Dept. of Mathematics, Govt. Engg. College, Thrissur 680 009, India;1. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai 600 005, India;2. Department of Food Trade and Business Management, College of Food and Dairy Technology, TANUVAS, Chennai, India;3. Department of Mathematics with Computer Applications, Ethiraj College for Women, Chennai, India;4. Madras School of Economics, Chennai, India |
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| Abstract: | We consider a queueing-inventory system with two classes of customers. Customers arrive at a service facility according to Poisson processes. Service times follow exponential distributions. Each service uses one item in the attached inventory supplied by an outside supplier with exponentially distributed lead time. We find a priority service rule to minimize the long-run expected waiting cost by dynamic programming method and obtain the necessary and sufficient condition for the priority queueing-inventory system being stable. Formulating the model as a level-dependent quasi-birth-and-death (QBD) process, we can compute the steady state probability distribution by Bright–Taylor algorithm. Useful analytical properties for the cost function are identified and extensive computations are conducted to examine the impact of different parameters to the system performance measures. |
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