The dwell time τ between steps is the time to go once round the cycle: phase-type, PH(α, T), with T the cycle's sub-generator (stage i is left at rate kᵢ). With the resolvent 𝓡₀ = (−T)⁻¹, the page computes E τ = α𝓡₀𝟏, E τ² = 2α𝓡₀²𝟏, the speed v = d / E τ and r = E τ²/(E τ)² − 1 by solving the linear systems, and the density α eTt t₀ by uniformisation. Renewal theory gives Var x(t) ≈ r·d·v·t for the motors' positions, so r can be read from noise alone; Aldous and Shepp (1987) give n ≥ 1/r for any phase-type time with n stages, with equality only for equal stages in a line (Erlang).
ADP, the product, competes with ATP for the empty front head: if ADP binds first the head is stuck until it leaves, a loop in the cycle. The dwell time is still phase-type, now with a route that can repeat, so T is no longer a simple chain and the linear solves do real work. The speed falls as for a competitive inhibitor (the top speed is unchanged; more ATP is needed to reach half of it), and the loop makes the waits more variable: r rises and the stage count read from the noise falls, though no stage was removed. The bound n ≥ 1/r still holds (here n counts the ADP state too); it just gets weaker.
Illustrative, not fitted: an 8 nm step; ATP binds at 2 per µM per second; ADP binds at 0.5 per µM per second and leaves at 25 per second (40 ms stuck, an inhibition constant of 50 µM); the hidden stages together take 10 ms (so the top speed is 800 nm/s and half of it is reached at 50 µM of ATP without ADP); unequal stages have rates in the ratio 1 : 2 : 3 : …. The real kinesin cycle has more structure (two heads, back-steps, load); this is the counting argument, not a model of the molecule.