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Analysis of a Three-Queue Polling System with Probabilistic Routing

In this paper, we consider a three-queue polling system with probabilistic routing. The choice of the queue to be visited next may depend on the current state of the system through the polling probability. Using the embedded Markov chain technique, we derived expressions for the steady-state joint and marginal queue length distribution at the switch points, as well as the waiting time distribution at each queue. The relation between the queue length and waiting time distributions becomes inherent in the model, providing a platform for easily computing waiting time moments.