  In this paper, we analyze the problem of how to adapt the concept of priority
to situations where several perfectly divisible resources have to be allocated
among certain set of agents that have exactly one claim which is used for all
resources. In particular, we introduce constrained sequential priority rules
and two constrained random arrival rules, which extend the classical sequential
priority rules and the random arrival rule to these situations. Moreover, we
provide an axiomatic analysis of these rules.
