Beyond Virtual Delay: Improving Packet Delay Bound in Network Calculus
2026-06-11 • Performance
PerformanceNetworking and Internet Architecture
AI summaryⓘ
The authors explain that the usual way to estimate the longest packet delay in a network is often too cautious because it is based on something called virtual delay. They prove that the actual packet delay is always less than or equal to this virtual delay, meaning the standard method can overestimate delays. Using this insight, they develop a new, improved way to calculate packet delays without extra assumptions. Their new method works better, especially in systems with specific traffic and service patterns, as shown in a real example related to time-sensitive networking.
network calculuspacket delayvirtual delayarrival curveservice curveleaky-bucketrate-latency service curvetime-sensitive networking (TSN)delay bound
Authors
Yuming Jiang
Abstract
In network calculus, a fundamental result is the classical delay bound given by the horizontal deviation between the arrival and service curves. While widely used, the classical bound is derived from the notion of virtual delay. In this work, we first show that the maximum packet delay is always upper-bounded by the maximum virtual delay, revealing inherent conservatism when applying the virtual-delay-based bound to packet delay. Motivated by this insight, we revisit packet delay analysis and derive a new packet delay bound that requires no assumptions beyond the arrival and service curves. Specializing the new bound to a system with leaky-bucket arrival curve and rate-latency service curve shows strict improvement over the classical bound, which is further demonstrated through a case study in time-sensitive networking (TSN).