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Pure threshold strategies for a two-node tandem network under partial information

In a two node tandem network, customers decide to join or balk by maximizing a given profit function whose costs are proportional to the sojourn time they spend at each queue. Assuming that their choices are taken without knowing the complete state of the system, we show that a pure threshold equilibrium policy exists. In particular we analyze the case when the partial information consists in informing the arrival customers of the total number of users in the network.