Abstract: In this paper are explored Partial Differential Equations models of multi-class queue and buffer systems. Models of basic rules like FIFO (first in - first out) and LIFO (last in - first out) and shared processor are given. They lead to a family of nonclassical systems of conservation laws with time-varying propagation velocity. The numerical analysis of convenient discretization schemes is also performed. We special interest for queue bound preservation at the numerical point of view. Numerical results show the efficiency of the approach. These models are especially good candidates for heavy traffic flow networks simulation.
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