In this research, we examine a two-stage retrial tandem queueing model with working vacation strategies. A consumer arrives utilizing a compound Markovian arrival process (MAP). The server serves consumers based on a single service, and service time follows an exponential distribution. A retrial tandem queue with working vacation is a queuing system that includes two sequential queues, where customers arrive, and if they are not serviced immediately, they can either retry later (retrial) or go into a “working vacation” state before returning for service. When a task fails due to transient issues such as network errors, resource unavailability, or temporary system glitches, it is moved to the retrial queue. Working vacation means that while customers are on vacation, they can still receive service if a server is available. This research is dedicated to exploring innovative strategies to enhance the quality of service (QoS) in the context of Internet and web services, focusing on the implementation of tandem queuing systems with retrial and working vacation techniques .The suggested model employs the matrix analytic method to determine the probability generating function of queue size at any chosen departure epoch in steady state. Several performance indices are obtained, including mean queue length, mean client waiting time in the queue, busy period analysis, and so on. To validate the analytical technique, we calculate numerical results.