Some characteristics on a finite queue with normal partial and total failures

• Published in: Microelectronics and reliability 1996-02, Vol.36 (2), p.265-267
• Main Authors: Sridharan, V., Jayashree, P.J.
• Format: Article
• Language: English
• Subjects: Applied sciences; Exact sciences and technology; Operational research and scientific management; Operational research. Management science; Queuing theory. Traffic theory
• ISSN: 0026-2714; 1872-941X
• DOI: 10.1016/0026-2714(95)00088-J

In this paper we consider that units arrive at a service station in a Poisson fashion with rate λ and are served exponentially by a single server with rate μ in normal working condition, and with slower rate v ( v < μ) in the case of partial failure of the service channel. The total failure of a unit is repaired with repair rate β 1 and that of partial failure with repair rate β 2. The partial and total failure rates for the service channel are a 1 and a 2, respectively. The system will function even if a partial failure occurs. The waiting room is finite and the service discipline is a first come first served basis (FCFS). The purpose of this paper is to obtain a steady-state probability generating function for the number of customers present in the system for different states. The probability of various states, along with corresponding results for the particular cases of the system, has been derived.