Neurofilaments are transported along axons in the slow component of axonal transport. The average rate of movement is generally quoted as several millimeters or tenths of a millimeter per day, but this rate is known to decrease while the neurofilaments are in transit due to spatial and temporal factors that are not understood. We have previously presented a stochastic model for neurofilament movement in vivo based on the transport kinetics of single neurofilaments observed by time-lapse fluorescence imaging in cultured neurons. The model took into account multiple velocity states and was only accessible through computational simulations. In simulations of the movement of a pulse of radiolabeled neurofilaments, this model generated a Gaussian wave which closely matched the experimental data. Here we present a simpler model with only three velocity states which is more amenable to analytical approaches. We show that the transport wave can be fully described by the mean and variance and we present analytical solutions for these cumulants in terms of the kinetic parameters of the model. We use the resulting expressions to examine the slowing of neurofilament transport in the mouse sciatic nerve. We show that the slowing is accompanied by an increase in the spread of the wave and that these changes are most readily explained by a change in the rate at which neurofilaments reverse their direction of movement. This suggests that the directionality of neurofilament transport in axons may be under spatial and/or temporal control and that alterations in the directionality of neurofilament transport could provide a mechanism for regulating the transport and distribution of these cytoskeletal polymers along axons.