Delay Bounds under Arbitrary Multiplexing: When Network Calculus Leaves You in the Lurch...

Network calculus has proven as a valuable and versatile methodology for worst-case analysis of communication networks. One issue in which it is still lacking is the treatment of aggregate multiplexing, in particular if the FIFO property cannot be assumed when flows are merged. In this paper, we address the problem of bounding the delay of individual traffic flows in feed-forward networks under arbitrary multiplexing. Somewhat surprisingly, we find that direct application of network calculus results in loose bounds even in seemingly simple scenarios. The reasons for this "failure" of network calculus are discussed in detail and a method to arrive at tight delay bounds for arbitrary (aggregate) multiplexing is presented. This method is based on the solution of an optimization problem. For the special case of sink-tree networks this optimization problem is solved explicitly, thus arriving at a closed-form expression for the delay bound. Numerical experiments illustrate that in sink-tree networks the improvement over bounds based on direct application of network calculus can be considerable.