Abstract

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 a J \Theta J matrix G, known as the workload contents matrix, has a spectral radius less than unity, where J represents the number of service stations. The (j; `)th component of matrix G can be interpreted as the amount of future work for station j that is embodied in per unit of immediate work at station ` at time t. This class includes Rybko-Stolyar network with FIFO service discipline as a special case. The result extends existing diffusion limiting theorems to non-feedforward multiclass queueing networks. In establishing the diffusion limit theorem, a new approach is taken. 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: f...

Citations