Asymptotic optimality of the Round–Robin policy in multipath routing with resequencing |
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Authors: | Konstantinos P Tsoukatos Armand M Makowski |
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Institution: | (1) Communications and Computer Engineering Department, University of Thessaly, Greece;(2) Department of Electrical and Computer Engineering, and Institute for Systems Research, University of Maryland, College Park, MD, 20742 |
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Abstract: | We consider a model of a multipath routing system where arriving customers are routed to a set of identical, parallel, single
server queues according to balancing policies operating without state information. After completion of service, customers
are required to leave the system in their order of arrival, thus incurring an additional resequencing delay. We are interested
in minimizing the end-to-end delay (including time at the resequencing buffer) experienced by arriving customers. To that
end we establish the optimality of the Round–Robin routing assignment in two asymptotic regimes, namely heavy and light traffic:
In heavy traffic, the Round–Robin customer assignment is shown to achieve the smallest (in the increasing convex stochastic
ordering) end-to-end delay amongst all routing policies operating without queue state information. In light traffic, and for
the special case of Poisson arrivals, we show that Round–Robin is again an optimal (in the strong stochastic ordering) routing
policy. We illustrate the stochastic comparison results by several simulation examples.
The work of the first author was supported through an ARCHIMEDES grant by the Greek Ministry of Education.
The work of the second author was prepared through collaborative participation in the Communications and Networks Consortium
sponsored by the U.S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement
DAAD19-01-2-0011. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding
any copyright notation thereon. The views and conclusions contained in this document are those of the authors and should not
be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the
U.S. Government. |
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Keywords: | Heavy and light traffic Multipath routing Round– Robin policy Parallel queues Resequencing |
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