Before revision:  In this article, we investigate the limiting behavior, as N goes to infinity, of the equilibrium at a queue when the service discipline is FIFO and the service time distribution has a power law with a given exponent -\beta, for \beta > 1. We show under the above ansatz that, as N goes to infinity , the tail of the equilibrium queue size exhibits a wide range of behavior depending on the relationship between \beta and D.
After revision:  In this article, we investigate the limiting behavior, as N goes to infinity, of the equilibrium at a queue when the service discipline is FIFO and the service time distribution has a power law with a given exponent -\beta, for \beta > 1. We show under the above ansatz that, as N \rightarrow\infty , the tail of the equilibrium queue size exhibits a wide range of behavior depending on the relationship between \beta and D.