A batch arrival unreliable server queue with two phases of service and Bernoulli vacation schedule under randomised vacation policy. (2016)

• Record Type: Journal Article
• Authors: Choudhury, Gautam; Deka, Mitali
• Is Part Of: International journal of services and operations management. Volume 24:Number 1(2016)
• Page Start: 33
• Page End: 72
• Publication Date: 2016
• Subjects: stationary queue size distribution -- breakdown -- repair time -- busy period -- batch arrivals -- unreliable server queues -- Bernoulli vacation schedule -- randomised vacation policy -- cost modelling; Production management -- Periodicals; 658.5005
• Languages: English
• ISSNs: 1744-2370

Abstract

This paper deals with an M X /G/1 Bernoulli vacation queue with two phases of service in which an unreliable server operates a randomised vacation policy with at most M consecutive vacations. If the system is empty by the end of the M th vacation, the server becomes idle in the system until at least one customer arrives at the queue. Assume that the server may meet an unpredictable breakdown according to a Poisson process and the repair time has a general distribution. For such a system, we derive the joint distribution of state of the server and queue size, the pgf of the stationary queue size distribution at a departure epoch, LST of busy period distribution and waiting time distribution along with some important performance measures of the model. Finally, we develop a cost model to determine optimal randomised policy along with some numerical illustration.