Exact Worst-Case Delay in FIFO-Multiplexing Feed-Forward Networks

• Published in: IEEE/ACM transactions on networking Vol. 23; no. 5; pp. 1387 - 1400
• Main Authors: Bouillard, Anne, Stea, Giovanni
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); IEEE/ACM
• Series: IEEE/ACM Transactions on Networking
• Subjects: Aggregates; Approximation; Arrivals; Calculus; Computation; Computer Science; Convolution; Delay; Delays; Discrete Mathematics; First-in-first-out (FIFO) multiplexing; IEEE transactions; Linear programming; Mathematical models; Mixed integer; Multiplexing; network calculus; Networking and Internet Architecture; Networks; Upper bound; worst-case delay; Network Calculus; Worst-case Delay; FIFO multiplexing
• ISSN: 1063-6692; 1558-2566
• DOI: 10.1109/TNET.2014.2332071

In this paper, we compute the actual worst-case end-to-end delay for a flow in a feed-forward network of first-in-first-out (FIFO)-multiplexing service curve nodes, where flows are shaped by piecewise-affine concave arrival curves, and service curves are piecewise affine and convex. We show that the worst-case delay problem can be formulated as a mixed integer linear programming problem, whose size grows exponentially with the number of nodes involved. Furthermore, we present approximate solution schemes to find upper and lower delay bounds on the worst-case delay. Both only require to solve just one linear programming problem and yield bounds that are generally more accurate than those found in the previous work, which are computed under more restrictive assumptions.