  Previous works on the queuing model introduced by Barab\'asi to account for
the heavy tailed distributions of the temporal patterns found in many human
activities mainly concentrate on the extremal dynamics case and on lists of
only two items. Here we obtain exact results for the general case with
arbitrary values of the list length $L$ and of the degree of randomness that
interpolates between the deterministic and purely random limits. The
statistically fundamental quantities are extracted from the solution of master
equations. From this analysis, new scaling features of the model are uncovered.
