On the guaranteed throughput and efficiency of closed re-entrant lines |
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Authors: | Morrison James R Kumar PR |
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Institution: | (1) Department of Electrical and Computer Engineering, and Coordinated Science Laboratory, University of Illinois, Urbana-Champaign CSL, 1308 West Main Street, Urbana, IL 61801, USA |
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Abstract: | A closed network is said to be “guaranteed efficient” if the throughput converges under all non-idling policies to the capacity
of the bottlenecks 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 necessary 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 studies using a Brownian network approximation, as well
as to certain policies proposed as being extremal with respect to the asymptotic loss in the throughput. Using the near characterization
of guaranteed efficiency we also answer the often pondered question of whether an open network or its closed counterpart has
greater throughput - the answer is that neither can assure a greater guaranteed throughput.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | queueing networks throughput closed networks efficiency stability |
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