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A queueing system with two stages of heterogeneous services, multiple vacations, and closedown upon server failure is considered in this study for MX/Ga,b data. Two different services must be provided to a group of customers one at a time. At time C, the server finishes its shut-down procedures following the conclusion of each SPS. A server that has a queue length shorter than a takes numerous, different-duration vacations. Upon returning from vacation, if the server detects that there are less than a customers in the queue, they will continue to serve the following batch if the server determines that there are at least a customers waiting for service. During the server’s first phase of operation, the service channels will momentarily fail with a probability of (π1) at any time, and during the server’s second phase of operation, the service channels will fail with a probability of (π2) at any time.
Palaniammal et al. (Sun,) studied this question.