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An M/M/c queue with customer interjections and balking

WU Wenqing1  HE Gang2  TANG Yinghui3,*  YU Miaomiao4   

  1. 1. School of Science, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China; 2. School of Computer Science and Technology, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China; 3. School of Mathematics Science, Sichuan Normal University, Chengdu 610066, China; 4. School of Science, Sichuan University of Science and Engineering, Zigong 643000, Sichuan, China
  • Received:2017-11-15 Online:2018-12-15 Published:2018-12-15

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Abstract:

This paper studies an M/M/c queueing system with customer interjections and balking. Arriving customers are divided into normal customers and interjecting customers, in which the normal customers join the queue at the end, and the interjecting customers try to cut in the queue and occupy a position as close to the head of the queue as possible. The behavior of the interjecting customers is described by the percentage of customers interjecting and the tolerance level of interjection by individual customer. By using the theory of the exponential distributions, the Laplace-Stieltjes transform and the formula of the total probability, we obtain the waiting time of a customer in position n, the waiting time of a normal customer, and the waiting time of an interjecting customer. Furthermore, we discuss the influence of system parameters on the system performance measures.

Key words: M/M/c queueing system, customer interjections, balking, waiting time