caa a22 4500 44584213X CHVBK 20180317145347.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00245-011-9144-y doi (NATIONALLICENCE)springer-10.1007/s00245-011-9144-y Day Martin Department of Mathematics, Virginia Tech, 24061, Blacksburg, VA, USA aut Weak Convergence and Fluid Limits in Optimal Time-to-Empty Queueing Control Problems [Elektronische Daten] [Martin Day] 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. Springer Science+Business Media, LLC, 2011 Queueing nationallicence Fluid limit nationallicence Optimal control nationallicence Relaxed controls nationallicence Applied Mathematics & Optimization Springer-Verlag 64/3(2011-12-01), 339-362 0095-4616 64:3<339 2011 64 245 https://doi.org/10.1007/s00245-011-9144-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00245-011-9144-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Day Martin Department of Mathematics, Virginia Tech, 24061, Blacksburg, VA, USA aut NATIONALLICENCE 773 0- Applied Mathematics & Optimization Springer-Verlag 64/3(2011-12-01), 339-362 0095-4616 64:3<339 2011 64 245 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer