What the Utility Score Is Really Ranking

Ada re-derives this chapter’s own numbers step by step, at full precision

foundations
math-foundations
calculation-audit
emerging-paradigms
Ada ADA · CALCULATION AUDIT

What the Utility Score Is Really Ranking

A smart-city air-quality node must hand its pollution alert to the better carrier: a delivery vehicle that passes city hall 3 times a day scores U = 0.405, against 0.334 for a pedestrian who passes once a week — a 21% edge that the weights 0.6, 0.3, and 0.1 are meant to justify. This audit re-runs the weighted score at full precision and asks what that reassuringly exact number is really ranking.

Companion to the chapter DTN Social Routing — every number here comes from that chapter.

Ada: Social routing lives or dies on one comparison — is a candidate carrier a better bet than the node already holding the bundle? This chapter scores a delivery vehicle at U = 0.405 against a once-a-week pedestrian and calls it a 21% advantage. The weights (alpha = 0.6, beta = 0.3, gamma = 0.1) and the freshness and battery inputs (0.8 and 0.9) are the chapter’s own; let me re-run the score and keep full precision on the weekly rate.

  • Vehicle encounter rate: P_daily = 3 / 24 = 0.125 per hour.
  • Vehicle utility: 0.6 x 0.125 + 0.3 x 0.8 + 0.1 x 0.9 = 0.075 + 0.24 + 0.09 = 0.405.
  • Pedestrian encounter rate: P_weekly = 1 / 168 = 0.00595238 per hour (not the rounded 0.006).
  • Pedestrian utility: 0.6 x 0.00595238 + 0.24 + 0.09 = 0.00357143 + 0.33 = 0.333571.
  • Advantage: 0.405 / 0.333571 = 1.2141, i.e. 21.4% — the chapter’s “21%” rounded down slightly.

The audit confirms the ranking and sharpens the lesson: almost the entire gap comes from the encounter term (0.075 versus 0.0036), because the mobility and resource terms are identical for both carriers. A utility function only discriminates on the input that actually differs, so this forwarding decision rests entirely on the quality of the colocation estimate — not on the reassuring precision of the weighted sum.

Every number above is taken from the chapter’s own material and re-derived step by step.