Retrial G-queue with precipitous breakdown and non-tenacious customers

Abstract

We perform an analysis on an M/G/1 system that has bulk arrival Poisson process as well as instantaneous service, Precipitous breakdown and random repair, Gqueue, and operation under an MBV (Modified Bernoulli vacation) policy. The positive outcome of a customer retrial is lost when an Anti-positive customer arrives during a positive (good) customer’s assistance period. If a new customer enters and notices that the server is currently undergoing repairs or on vacation, they may renege or balk from the system. To obtain a wide variety of additional outcomes, we use the details provided by the supplementary variable method regarding the rates at which different events occur and it is possible to determine the probability-generating functions of queue length distributions as well as the explicit formulations of important performance metrics. The numerical data confirm the analytical findings about the major performance metrics.

Keywords

• retrial queue
• bulk arrival
• non-tenacious customers
• precipitous breakdown
• modified bernoulli vacation