A batch arrival unreliable server delaying repair queue with two phases of service and Bernoulli vacation under multiple vacation policy. Issue 2 (4th March 2018)

• Record Type: Journal Article
• Authors: Choudhury, Gautam; Deka, Mitali
• Is Part Of: Quality technology & quantitative management. Volume 15:Issue 2(2018)
• Page Start: 157
• Page End: 186
• Publication Date: 2018-03-04
• Subjects: Stationary queue size distribution -- random breakdown -- repair time -- delay time -- Bernoulli vacation -- multiple vacation and reliability index; Quality control -- Periodicals; Quality control -- Statistical methods -- Periodicals; Industrial management -- Periodicals; Industrial management; Management -- Research -- Methodology -- Periodicals; Qualitative research -- Periodicals; Management; Quality control; Quality control -- Statistical methods; Periodicals; 658.00721
• DOI: 10.1080/16843703.2016.1208934
• Languages: English
• ISSNs: 1684-3703

Abstract

Abstract: This paper deals with an M X / G /1 unreliable queue with two phases of service and Bernoulli vacation schedule under multiple vacation policy, where after each vacation completion or service completion, the server takes sequence of vacations until a batch of new customer arrive. Further concept of the delay time is also introduced. We assume that customers arrive to the system according to a Poisson process with rate . While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. After completion of both phases of service, the server either goes for a vacation with probability p (0 ≤ p ≤ 1) or may continue to serve the next unit, if any, with probability q (= 1 – p ). Otherwise; it remains in the system until a customer arrives. For this model, we derive queue size distributions at various epochs, busy period distribution, waiting time distribution under the steady-state condition. Next, we derive reliability function and related reliability indices of this model. Finally, some numerical examples are presented for illustrative purpose.