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STOCHASTIC DECOMPOSITION OF THE M/G/∞ QUEUE IN A RANDOM ENVIRONMENT

We prove a stochastic decomposition formula for the number of customers in an M/G/∞ system with service speeds depending on the state of an independent random environment. In addition, we present a new technique to analyze this kind of queues and apply it to solve some examples of M/M/∞ queues in random environment.