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, G-queue, 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.

In this study, computing on the cloud is important to current technologies. CC (Cloud Computing) significantly emphasizes task scheduling as one of its most critical components, we examine an M/G/1 queueing system with two service categories and a Bernoulli vacation subject to the active breakdown. On occurrence of a breakdown , the repair on the service channel starts instantly. Furthermore, the nature of the customer is considered as reneging and balking. Significant performance measures for this queueing model are examined in steady-state using the supplementary variable technique and have also discussed a few special cases of this model. This technique handles each task using a Non-Markovian process before its real allocation to cloud resources. This step comes before the actual assignment of tasks. Numerical illustrations of the effects of various parameters on system performance have also been presented.