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Zhanyou Ma [1] and Yalin Guo [1] and Pengcheng Wang [1] and Yumei Hou [2]

Academic Editor: Yuji Liu

, 1, , College of Science, , Yanshan University, , Qinhuangdao 066004, , China, , ysu.edu.cn,

, 2, , School of Economics & Management, , Yanshan University, , Qinhuangdao 066004, , China, , ysu.edu.cn,

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

In recent years, queueing system with negative arrivals (G-queue) has become a research hotspot. Those studied models have been used to simulate computer communication system and the manufacturing system et al. The appropriate killing strategy must be determined in the queueing system with negative arrivals. Gelenbe et al. [1] investigated a single-sever G-queue system with the RCE and RCH killing strategies. Jain and Sigman [2] considered the effect of disaster on M/G/1 queueing system. Based on the model of the literature [2], Boucherie and Boxma [3] made a promotion and established a new killing strategy to allow a negative arrival for removing a random amount of positive customers which made the killing strategy tend to generalization.

Continuous time queueing systems with negative customers have been discussed extensively in the past years (see the literature [2–4]). In recent years, scholars pay more attention to the study of the discrete-time queueing systems with negative arrivals and obtain some significant results. Atencia and Moreno [5] adopted two different types of killing strategies (RCH and disaster) to analyze the Geo/Geo/1 queueing model with negative arrivals and obtained the stationary probability generating function of the queue length by solving balance equation in the system. Wang and Zhang [6] introduced negative customers into the retrial queue and deduced the stochastic decomposition law on discrete-time retrial G-queue. Jia and Chen [7] analyzed a Geom/Geom/1 queue with negative customers and single working vacation and derived the probabilities of the server in idle and busy period. Su and Ma [8] dealt with a Geom/Geom/1 Bernoulli feedback queue with single vacation, and the stationary distribution for the number of customers in the system and the stochastic decomposition were obtained. Chae et al. [9] extended the Geo/Geo/1 queue, with negative and...

      

      

   

                              

          

  

      

 

  

   

                             

   

  

                 

 

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