2 that apart from the above worst-case ratio an additive performance guarantee for WSEPT can be derived as well.
Moreover, with some additional conditions on weights and expected processing times of the jobs, we obtain asymptotic optimality for the performance of the WSEPT rule.
Note that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the optimum value for a single machine problem, since the optimum policy on a single machine is WSEPT [Rothkopf 1966]; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the optimum value on n machines.
With assumptions on the input parameters of the problem which assure that the right-hand side remains bounded, Weiss  has thus proved asymptotic optimality of WSEPT for a wide class of processing time distributions.
In the single machine case, the proof of optimality for WSEPT dates back to 1966.
Their work is based on approximate conservation laws for the performance of Klimov's index rule (which corresponds to the WSEPT rule for the model we consider here).
Note that in this case the performance of WSEPT can be arbitrarily bad.