A batch arrival unreliable server delaying repair queue with two phases of service and Bernoulli vacation under multiple vacation policy

作者：Choudhury Gautam^*; Deka Mitali

来源：Quality Technology and Quantitative Management, 2018, 15(2): 157-186.

DOI：10.1080/16843703.2016.1208934

• Stationary queue size distribution
• random breakdown
• repair time
• delay time
• Bernoulli vacation
• multiple vacation and reliability index

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 lambda. 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.

• 出版日期2018