ON THE GUARANTEED THROUGHPUT AND EFFICIENCY OF CLOSED REENTRANT LINES

A closed network is said to be ''guaranteed efficient'' if the through put converges under all non-idling policies to the capacity of the bot tlenecks in the network, as the number of trapped customers increases to infinity. We obtain a necessary condition for guaranteed efficiency of closed re-entrant lines. For balanced two-station systems, this ne cessary condition is almost sufficient, differing from it only by the strictness of an inequality. This near characterization is obtained by studying a special type of virtual station called ''alternating visit virtual station''. These special virtual stations allow us to relate the necessary condition to certain indices arising in heavy traffic st udies using a Brownian network approximation, as well as to certain po licies proposed as being extremal with respect to the asymptotic loss in the throughput. Using the near characterization of guaranteed effic iency we also answer the often pondered question of whether an open ne twork or its closed counterpart has greater throughput - the answer is that neither can assure a greater guaranteed throughput.