Computation and Tightness Assessment of End-to-end Delay Bounds in FIFO-multiplexing Tandems

1 Part of the content of this report has appeared as [1] and [2]. ABSTRACT This paper addresses the problem of estimating the worst-case endto-end delay for a flow in a tandem of FIFO multiplexing nodes, following up our previous work [14]. We consider the state-of-theart method for computing delay bounds, i.e. upper bounds on the worst-case delay, called the Least Upper Delay Bound (LUDB) methodology, and we describe efficient numerical techniques to compute the LUDB. The latter allow good delay bounds to be computed for tandems of several tens of nodes within minutes of computation time. Furthermore, we show that, unlike what happens in some specific sub-classes of FIFO tandems analyzed in the previous work, the LUDB may actually be larger than the worst-case delay, even when end-to-end analysis is possible. Therefore, in order to assess how close the derived bounds are to the actual, still unknown, worst-case delays, we devise a method to compute lower bounds on the worst-case delay. Our analysis shows that the gap between the upper and lower bounds is reasonably small, at least when end-to-end analysis is possible, which implicitly validates the upper bounds themselves. Keywords