Heavy-traffic revenue maximization in parallel multiclass queues

Motivated by revenue maximization in server farms with admission control, we investigate the optimal scheduling in parallel processor-sharing queues. Incoming customers are distinguished in multiple classes and we define revenue as a weighted sum of class throughputs. Under these assumptions, we describe a heavy-traffic limit for the revenue maximization problem and study the asymptotic properties of the optimization model as the number of clients increases. Our main result is a simple heuristic that is able to provide tight guarantees on the optimality gap of its solutions. In the general case with M queues and R classes, we prove that our heuristic is (1+1M-1)-competitive in heavy-traffic. Experimental results indicate that the proposed heuristic is remarkably accurate, despite its negligible computational costs, both in random instances and using service rates of a web application measured on multiple cloud deployments

Exponential penalty function control of loss networks

We introduce penalty-function-based admission control policies to approximately maximize the expected reward rate in a loss network. These control policies are easy to implement and perform well both in the transient period as well as in steady state. A major advantage of the penalty approach is that it avoids solving the associated dynamic program. However, a disadvantage of this approach is that it requires the capacity requested by individual requests to be sufficiently small compared to total available capacity. We first solve a related deterministic linear program (LP) and then translate an optimal solution of the LP into an admission control policy for the loss network via an exponential penalty function. We show that the penalty policy is a target-tracking policy--it performs well because the optimal solution of the LP is a good target. We demonstrate that the penalty approach can be extended to track arbitrarily defined target sets. Results from preliminary simulation studies are included.Comment: Published at http://dx.doi.org/10.1214/105051604000000936 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A mathematical programming approach to stochastic and dynamic optimization problems

Includes bibliographical references (p. 46-50).Supported by a Presidential Young Investigator Award. DDM-9158118 Supported by matching funds from Draper Laboratory.Dimitris Bertsimas

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

The achievable region method in the optimal control of queueing systems : formulations, bounds and policies

Cover title.Includes bibliographical references (p. 44-48).Supported in part by a Presidential Young Investigator Award, with matching funds from Draper Laboratory. DDM-9158118Dimitris Bertsimas

The achievable region method in the optimal control of queueing systems : formulations, bounds and policies

Cover title.Includes bibliographical references (p. 44-48).Supported in part by a Presidential Young Investigator Award, with matching funds from Draper Laboratory. DDM-9158118Dimitris Bertsimas

Revenue Optimization for a Make-to-Order Queue in an Uncertain Market Environment

We consider a revenue-maximizing make-to-order manufacturer that serves a market of price- and delay-sensitive customers and operates in an environment in which the market size varies stochastically over time. A key feature of our analysis is that no model is assumed for the evolution of the market size. We analyze two main settings: (i) the size of the market is observable at any point in time; and (ii) the size of the market is not observable and hence cannot be used for decision making. We focus on high-volume systems that are characterized by large processing capacities and market sizes, and where the latter fluctuate on a slower timescale than that of the underlying production system dynamics. We develop an approach to tackle such problems that is based on an asymptotic analysis and that yields near-optimal policy recommendations for the original system via the solution of a stochastic fluid model