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Unified killing mechanism in a single server queue with renewal input

  • Nitin KumarEmail author
  • F. P. Barbhuiya
  • U. C. Gupta
Application Article


Queueing systems experienced in real-life situations are very often influenced by negative arrivals which are independent of service process and cause the elimination of jobs from the system. Such a scenario occurs in computer network and telecommunication systems where an attack by a malicious virus results in the removal of some or all data files from the system. Along this direction many authors have proposed various killing processes in the past. This paper unifies different killing mechanisms into the classical single server queue having infinite capacity, where arrival occurs as renewal process with exponential service time distribution. The system is assumed to be affected by negative customers as well as disasters. The model is investigated in steady-state in a very simple and elegant way by means of supplementary variable and difference equation technique. The distribution of system-content for the positive customers is derived in an explicit form at pre-arrival and random epochs. The influence of different parameters on the system performance are also examined.


Negative customers Positive customers Disasters Supplementary variable technique Renewal input 

Mathematics Subject Classification

60K25 68M20 



Nitin Kumar and F. P. Barbhuiya are grateful to Indian Institute of Technology Kharagpur, India for the financial support. The authors are thankful to the editor and two anonymous referees for their valuable remarks and suggestions which led to the paper in current form.


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Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of TechnologyKharagpurIndia

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