Before revision:  Assume that each queue of type  r is replicated k times and consider the set of policies that are periodic with period k \sum_r p_r and such that exactly p_r jobs are sent in a period to each queue of type  r.
After revision:  Assume that each queue of type r is replicated ~k times, we consider a set of policies that are periodic with period k \sum_r p_r and such that exactly p_r jobs are sent in a period to each queue of type r.