Existence Condition for the Diffusion Approximations of Multiclass Priority Queueing Networks
Queueing Systems: Theory and Applications
Diffusion Approximation in Overloaded Switching Queueing Models
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Multiserver Loss Systems with Subscribers
Mathematics of Operations Research
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The diffusion approximation is proved for a class of multiclass queueing networks under FIFO service disciplines. In addition to the usual assumptions for a heavy traffic limit theorem, a key condition that characterizes this class is that aJ x J matrixG, known as the workload contents matrix, has a spectral radius less than unity, whereJ represents the number of service stations. The ( j,l)th component of matrixG can be interpreted as the long-run average amount of future work for stationj that is embodied in a unit of immediate work at stationl. This class includes, as a special case, the feedforward multiclass queueing network and the Rybko-Stolyar network under FIFO service discipline.A new approach is taken in establishing the diffusion limit theorem. The traditional approach is based on an oblique reflection mapping, but such a mapping is not well defined for the network under consideration. Our approach takes two steps: Arst establishing theC-tightness of the scaled queueing processes, and then completing the proof for the convergence of the scaled queueing processes by invoking the weak uniqueness for the limiting processes, which are semimartingale reflecting Brownian motions.