We prove a stochastic decomposition formula for the number of customers in an M/G/∞ system with service speeds depending on 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.
Stochastic decomposition of the M/G/∞ queue in a random environment
D'Auria B.
2007
Abstract
We prove a stochastic decomposition formula for the number of customers in an M/G/∞ system with service speeds depending on 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.
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