Weak Convergence and Fluid Limits in Optimal Time-to-Empty Queueing Control Problems

Weak Convergence and Fluid Limits in Optimal Time-to-Empty Queueing Control Problems We consider a class of controlled queue length processes, in which the control allocates each server’s effort among the several classes of customers requiring its service. Served customers are routed through the network according to (prescribed) routing probabilities. In the fluid rescaling, $X^{n}(t)=\frac{1}{n} X(nt)$ , we consider the optimal control problem of minimizing the integral of an undiscounted positive running cost until the first time that X n =0. Our main result uses weak convergence ideas to show that the optimal value functions V n of the stochastic control problems for X n ( t ) converge (as n →∞) to the optimal value V of a control problem for the limiting fluid process. This requires certain equicontinuity and boundedness hypotheses on { V n }. We observe that these are essentially the same hypotheses that would be needed for the Barles-Perthame approach in terms of semicontinuous viscosity solutions. Sufficient conditions for these equicontinuity and boundedness properties are briefly discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Weak Convergence and Fluid Limits in Optimal Time-to-Empty Queueing Control Problems

Loading next page...
Copyright © 2011 by Springer Science+Business Media, LLC
Mathematics; Calculus of Variations and Optimal Control; Optimization; Theoretical, Mathematical and Computational Physics; Numerical and Computational Physics; Mathematical Methods in Physics; Systems Theory, Control
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial