The M/M\1 queue in a heavy‐tailed random environment

O. J. Boxma and I. A. Kurkova

Statistica Neerlandica, 2000, vol. 54, issue 2, 221-236

Abstract: We consider an M/M/1 queue with the special feature that the speed of the server alternates between two constant values sL and sH>sL. The high‐speed periods are exponentially distributed, and the low‐speed periods have a regularly varying distribution. We obtain explicit asymptotics for the tail of the workload distribution. The two cases in which the offered traffic load is smaller respectively larger than the low service speed are shown to result in completely different asymptotics.

Date: 2000
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