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Queueing Theory & Slack

Tom Geraghty · Complexity & Systems, Organisational Design

Uses queueing theory to make a quantitative case for slack (spare, non-committed capacity) as a resilience investment rather than waste. The core relationship, a simplified stand-in for Kingman's Formula, is that expected wait time for unplanned work is proportional to %utilised divided by %free: at 50% utilisation the wait-time proxy is 1, at 80% it's 4, at 90% it's 9, and at 99% it's 99 — a curve that stays flat for most of its range and then turns sharply upward, with the inflection sitting around 80% utilisation. Past that point, small increases in how 'busy' a team is produce disproportionate, then exponential, increases in how long unplanned work waits to be picked up, which is why teams running near capacity can tip from busy to overwhelmed with little warning. The piece frames this against a persistent management bias, quoting Wears (2017) on how the 'measure and manage' orthodoxy of Lean, Six Sigma and TQI treats unutilised time as costly waste and rewards managers for visibly raising utilisation, while the resilience bought by spare capacity is much harder to measure and rarely rewarded — so organisations tend to erode their own buffer even though doing so, especially in complex or variable environments, ultimately harms them. Slack time is not idle time: as long as what fills it is interruptible, it can be used for experimentation, learning and support work without compromising the team's ability to respond to the unexpected. Google's '20% time' is offered as the clearest illustration — its real function isn't the bonus side-project time itself but the fact that it's interruptible, meaning capacity can be reclaimed instantly when something urgent lands. Where psychological safety is also present, slack time additionally gives people room to think more deeply, surface concerns, and propose fixes before they become incidents. The argument is bounded, not universal: in stable, low-variance environments with little unplanned work, running close to full utilisation carries little cost, and the real danger is believing an environment is stable and predictable when it isn't. Traces queueing theory's origins to Erlang's modelling of the Copenhagen telephone exchange and its subsequent use in traffic, computing (the utilisation/wait-time relationship is, per the piece, the only chart to appear in Gene Kim's The Phoenix Project), industrial engineering (Goldratt's The Goal), and healthcare, and points toward Kingman's Formula, Little's Theorem and Kendall's notation for readers wanting the fuller mathematical treatment.

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