A Note on Time and Space Methods in Network Calculus

We model some lossless queuing systems arising in guaranteed service networks as non-linear min-plus systems that can be bounded by linear systems. We introduce the distinction between space and time methods for such systems. Space methods are related to min-plus system theory, while time methods borrow from dynamic programming and exploit the causality of the operators. We apply this to the window ow control problem previously studied by: Cruz and Okino; Chang; Agrawal and Rajan. We explain the existing bounds by the combination of the space and time methods, and derive a reened, tighter bound.