Spatial Composition of Metrics
updated by
- rfc-6248 — RFC 4148 and the IP Performance Metrics (IPPM) Registry of Metrics Are Obsolete
Extracted elements (27)
Histogram bins of 1 ms were chosen for PDV composition under an implicit accuracy requirement that errors of a few milliseconds are acceptable when assessing a composed distribution quantile; very tight distributions with ranges on the order of a few milliseconds are not accurately represented at this resolution.
If any sub-path delay distribution is multi-modal, the measured means may not be stable and the mean statistic will not reliably describe the complete-path delay distribution, making the composition conjecture fail.
Spatial composition is needed because end-to-end measurement is sometimes impractical: paths may cross independent domains with conflicting policies, tools, and timing, so each domain measures its own sub-path and results are combined to estimate complete-path performance.
The Finite-One-way-Delay approach handles lost packets by reducing the event space to packets that actually arrive, computing conditional statistics rather than assigning infinite delay to losses. This avoids undefined outcomes while enabling valid mean calculations.
Correlated loss root causes (e.g., shared physical routes, a single catastrophic event) can invalidate the independence assumption required by the packet-loss composition function; measurements before and after such events must not be combined.
Sub-path measurement packets (addressed to sub-path edge nodes) may traverse different physical paths through ECMP or bundled links than packets addressed to the complete-path endpoints, causing composed performance estimates to differ from actual complete-path performance.
The Type-P-One-way-pdv-refmin metric is equivalent to the IP Packet Delay Variation parameter defined in ITU-T Y.1540, enabling cross-standard interoperability for delay variation reporting.
In the PDV selection function F, the current packet MUST have a valid Type-P-Finite-One-way-Delay less than Tmax and MUST have been transmitted during [T, Tf]; the min-delay reference packet MUST be the one with the minimum valid finite delay.
Poisson and/or Periodic streams are RECOMMENDED for sub-path measurements used in spatial composition.
The assumption of sub-path independence with regard to the metric being composed is REQUIRED for the composition functions defined in this memo.
The measurement methodology SHOULD have synchronized measurement time intervals across all sub-paths, but largely overlapping intervals MAY suffice.
The set of sub-path measurements SHOULD cover all critical network elements in the complete path; exchange points or other elements omitted from sub-path coverage introduce error.
When a composed metric requires sub-path measurements from paths A, B, and C, and one or more sub-path results are undefined, then the composed metric SHOULD also be recorded as undefined.
When measurements cannot be initiated on a sub-path during a test interval, the entire test result SHOULD be recorded as 'undefined', distinct from the case where all packets were sent but declared lost.
When multiple packets share the minimum Type-P-Finite-One-way-Delay value, the value for the earliest arriving packet SHOULD be used as the PDV reference.
PDV statistics defined include MeanPDV (arithmetic mean over N packets), VarPDV (sample variance), SkewPDV (normalized third central moment), and a quantile (fraction of singletons below the given value). All are defined in Section 6.1.4.
The Approximate Convolution composition function derives the complete-path PDV quantile by convolving 1-ms-bin histograms of the sub-path one-way delay distributions using the relation P(X+Y+Z <= a) = integral of P(X <= a-y-z)*P(Y=y)*P(Z=z) dy dz.
The Normal Power Approximation (NPA) composition function estimates the complete-path PDV quantile by combining sub-path summary statistics using the procedure defined in ITU-T Y.1541 Clause 8 and Appendix X.
Type-P-Composite-One-way-Packet-Loss-Empirical-Probability (CompEp) is computed as CompEp = 1 - product over all S sub-paths of (1 - Eps), combining the empirical loss probabilities of each sub-path under independence assumptions.
Type-P-Finite-Composite-One-way-Delay-Mean (CompMeanDelay) is computed as the sum of the mean delays of all S constituent sub-paths: CompMeanDelay = sum over s=1..S of MeanDelay[s].
Type-P-Finite-Composite-One-way-Delay-Minimum (CompMinDelay) is computed as the sum of the minimum delays of all S constituent sub-paths: CompMinDelay = sum over s=1..S of MinDelay[s].
Type-P-Finite-One-way-Delay-<Sample>-Stream is defined as FiniteDelay[i] = TstampDst - TstampSrc, restricted to packets with finite (non-undefined) one-way delay. It is the foundational element for all delay composition metrics.
Type-P-One-way-pdv-refmin-<Sample>-Stream defines packet delay variation (PDV) as PDV[n] = FiniteDelay[n] - MinDelay, where MinDelay is the minimum finite one-way delay observed in the stream. This normalizes all variation to the minimum-delay reference.
RFC 6049 registers 13 metrics in the IANA-IPPM-METRICS-REGISTRY-MIB (ianaIppmMetrics 71–83), covering finite one-way delay stream and mean (71–72), composite delay mean and minimum (73–75), packet loss empirical probability (76–77), and PDV refmin stream, mean, variance, skewness, quantile, and NPA (78–83).
An adversary that identifies measurement packets can manipulate their processing (inflating or deflating delay) or inject spurious packets into the sample; cryptographic hash-based packet integrity checks are recommended to discourage such interference.
Passive measurement MUST restrict attention to packet headers of interest. If user payloads are temporarily stored for length analysis, suitable precautions MUST be taken to maintain confidentiality; a hashing function is recommended for payload comparisons.
The measurement stream methodology can be abused for denial-of-service attacks against the destination or intervening networks; bilateral or multilateral agreements on timing, size, and frequency of measurement traffic should be established before use.