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GEOM/GEOM[A]/1/ queue with late arrival system with delayed access and delayed multiple working vacations

This paper considers a discrete-time bulk-service queue with infinite buffer space and delay multiple working vacations. Considering a late arrival system with delayed access (LAS-AD), it is assumed that the inter-arrival times, service times, vacation times are all geometrically distributed. | Yugoslav Journal of Operations Research 24 (2014) Number 1, 127-143 DOI: 10.2298/YJOR120627014C GEOM/GEOM[A]/1/ QUEUE WITH LATE ARRIVAL SYSTEM WITH DELAYED ACCESS AND DELAYED MULTIPLE WORKING VACATIONS Jiang CHENG School of Mathematics &Software Science, Sichuan Normal University, Chengdu, Sichuan, 610066, China. College of Computer Science and Technology, Southwest University for Nationalities, Chengdu,Sichuan, 610041, China, jiangcheng_uestc@163.com Yinghui TANG1 School of Mathematics &Software Science, Sichuan Normal University, Chengdu, Sichuan, 610066, China. tangyh@uestc.edu.cn Miaomiao YU School of Science, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000,China mmyu75@163.com Received: June 2012 / Accepted: April 2013 Abstract: This paper considers a discrete-time bulk-service queue with infinite buffer space and delay multiple working vacations. Considering a late arrival system with delayed access (LAS-AD), it is assumed that the inter-arrival times, service times, vacation times are all geometrically distributed. The server does not take a vacation immediately at service complete epoch but keeps idle period. According to a bulk-service rule, at least one customer is needed to start a service with a maximum serving capacity ' a ' . Using probability analysis method and displacement operator method, the queue length and the probability generating function of waiting time at pre-arrival epochs are 1 This work is supported by the National Natural Science Foundation of China (No.71171138) and the Talent Introduction Foundation of Sichuan University of Science & Engineering (2012RC23). Corresponding authors: Jiang CHENG & Yinghui TANG. 128 J. Cheng, Y. Tang, M. Yu / GEOM/GEOM[a]/1/ obtained. Furthermore, the outside observer’s observation epoch queue length distributions are given. Finally, computational examples with numerical results in the form of graphs and tables are discussed. Keywords: Discrete time, bulk-service, working .