Stability and bounds for single server queues in random environment

We consider a single server queue where the speed of the server is a function of a random environment. The only assumptions concerning the arrival process (arrival dates and service requirements) and the speed process are stationarity and ergodicity. A general expression is given for the stability condition. In the case where the two processes are independent, we show that the workload in this queue is larger for convex ordering than the workload in a queue with the same arrival process but fixed deterministic speed taken as the average of the speed process. On leave from INRIA : the work of this author was supported through a grant from the Minta Martin Aeronautical Research Fund. College of Engineering, University of Maryland at College Park, U.S.A. The work of this author was supported partially through N.S.F. grant; ECS-83-51386 and partially through a grant from the Minta Martin Aeronautical Research Fund, College of Engineering, University of Maryland at College Park, U.S.A. On leave from INRIA : the work of this author was supported through a grant from the Minta Martin Aeronautical Research Fund. College of Engineering, University of Maryland at College Park, U.S.A. The work of this author was supported partially through N.S.F. grant; ECS-83-51386 and partially through a grant from the Minta Martin Aeronautical Research Fund, College of Engineering, University of Maryland at College Park, U.S.A. Notes On leave from INRIA : the work of this author was supported through a grant from the Minta Martin Aeronautical Research Fund. College of Engineering, University of Maryland at College Park, U.S.A. The work of this author was supported partially through N.S.F. grant; ECS-83-51386 and partially through a grant from the Minta Martin Aeronautical Research Fund, College of Engineering, University of Maryland at College Park, U.S.A.