Unified killing mechanism in a single server queue with renewal input

• Published in: Opsearch Vol. 57; no. 1; pp. 246 - 259
• Main Authors: Kumar, Nitin, Barbhuiya, F. P., Gupta, U. C.
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.03.2020; Springer Nature B.V
• Subjects: Application Article; Business and Management; Computer networks; Computer viruses; Customers; Difference equations; Disasters; Electric communication systems; Management; Markov analysis; Mathematics; Operations research; Operations Research/Decision Theory; Queues; Queuing theory; Disasters; Positive customers; Renewal input; Supplementary variable technique; 68M20; Negative customers; 60K25
• ISSN: 0030-3887; 0975-0320
• DOI: 10.1007/s12597-019-00408-w

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.