  We introduce a multispecies exclusion model where length-conserving
probabilistic fusion and fission of the hard rods are allowed. Although all
rods enter the system with the same initial length ${\ell}=1$, their length can
keep changing, because of fusion and fission, as they move in a step-by-step
manner towards the exit. Two neighboring hard rods of lengths ${\ell}_{1}$ and
${\ell}_{2}$ can fuse into a single rod of longer length
${\ell}={\ell}_{1}+{\ell}_{2}$ provided ${\ell} \leq N$. Similarly,
length-conserving fission of a rod of length ${\ell}' \leq N$ results in two
shorter daughter rods. Based on the extremum current hypothesis, we plot the
phase diagram of the model under open boundary conditions utilizing the results
derived for the same model under periodic boundary condition using mean-field
approximation. The density profile and the flux profile of rods are in
excellent agreement with computer simulations. Although the fusion and fission
of the rods are motivated by similar phenomena observed in Intraflagellar
Transport (IFT) in eukaryotic flagella, this exclusion model is too simple to
account for the quantitative experimental data for any specific organism.
Nevertheless, the concepts of `flux profile' and `transition zone' that emerge
from the interplay of fusion and fission in this model are likely to have
important implications for IFT and for other similar transport phenomena in
long cell protrusions.
