Maximum Entropy Analysis of M/(G1,G2)/1 Retrial Queueing Model with Second Phase Optional Service and Bernoulli Vacation Schedule

In this paper, a bulk arrival retrial queueing model with two phases of service symbolically denoted by M/(G1,G2)/1 has been discussed under Bernoulli vacation schedule to explore main ly its steady state behaviour using maximum entropy principle (MEP). We consider that customers arrive in batches according to Poisson distribution and a single server of the system provides his services in two phases-first phase essential service (FPES) and the next second phase optional service (SPOS) with different service rates. As per classical retrial service policy,the server has an option to avail vacations to complete some additional work under Bernoulli schedule when the second phase optional service (SPOS) is not demanded by arriv ing customers and such type of vacation is referred as working vacation.By employ ing the maximum entropy approach, we have derivedthe approximate expected wait ing time in the orbit.Moreover, a comparative study between the exact waiting time and the approximate waiting time based on maximum entropy analysis has been carried out to validate the investigative results by way of numerical illustrations and sensitivity analysis.