  The TASEP is a paradigmatic model from non-equilibrium statistical physics,
which describes particles hopping along a lattice of discrete sites. The TASEP
is applicable to a broad range of different transport systems, but does not
consider the fact that in many such systems the availability of resources
required for the transport is limited. In this paper we extend the TASEP to
include the effect of a limited number of two different fundamental transport
resources: the hopping particles, and the "fuel carriers", which provide the
energy required to drive the system away from equilibrium. As as consequence,
the system's dynamics are substantially affected: a "limited resources" regime
emerges, where the current is limited by the rate of refuelling, and the usual
coexistence line between low and high particle density opens into a broad
region on the phase plane. Due to the combination of a limited amount of both
resources, multiple phase transitions are possible when increasing the exit
rate beta for a fixed entry rate alpha. This is a new feature that can only be
obtained by the inclusion of both kinds of limited resources. We also show that
the fluctuations in particle density in the LD and HD phases are unaffected by
fluctuations in the number of loaded fuel carriers, except by the fact that
when these fuel resources become limited, the particle hopping rate is severely
reduced.
