We analyse the radio light curves of the blazars 1308+326, 2223−052 and 2251+158 using University of Michigan Radio Observatory and Metsähovi Radio Observatory multifrequency monitoring data combined with high-resolution very long baseline interferometry (VLBI) observations in order to extract the properties of prominent outbursts. The outbursts are classified as ‘core’ and ‘jet’ events according to their behaviour at different frequencies and their associations with features appearing in the VLBI jet. We define the activity cycle for each blazar as the time interval between successive ‘core’ outbursts. The durations of the activity cycle derived in this way are ≥14 yr for 1308+326, ∼12 yr for 2223−052 and 12.4 ± 0.6 yr for 2251+158. We find an unusual frequency dependence for the time profiles for a major flare in 1308+326, which may provide evidence for acceleration or bending of the jet flow in the optically thick part of the emission region. Analysis of these activity cycles, combined with our earlier results, leads us to suggest that more luminous blazars possess shorter activity cycles, consistent with the accretion rates being higher in more powerful sources (relative to the Eddington rate).