Publication: Closed queueing networks under congestion: non-bottleneck independence and bottleneck convergence
Loading...
Identifiers
Publication date
2012-06
Defense date
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Impact
Export
Abstract
We analyze the behavior of closed product-form queueing networks when the number
of customers grows to infinity and remains proportionate on each route (or class). First,
we focus on the stationary behavior and prove the conjecture that the stationary
distribution at non-bottleneck queues converges weakly to the stationary distribution of
an ergodic, open product-form queueing network. This open network is obtained by
replacing bottleneck queues with per-route Poissonian sources whose rates are
determined by the solution of a strictly concave optimization problem. Then, we focus
on the transient behavior of the network and use fluid limits to prove that the amount of
fluid, or customers, on each route eventually concentrates on the bottleneck queues
only, and that the long-term proportions of fluid in each route and in each queue solve
the dual of the concave optimization problem that determines the throughputs of the
previous open network.
Description
Keywords
Closed queueing networks, Product-form, Asymptotic independence, Fluid limit, Large population