A note on time and space methods in network calculus

We model some lossless queueing 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 flow control problem previously studied by Cruz and Okino (1996); Chang (1997); Agrawal and Rajan (1996). We explain the existing bounds by the combination of space and time methods, and derive another bound that can be tighter.