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

@article{Bertsimas1995TheAR, title={The achievable region method in the optimal control of queueing systems; formulations, bounds and policies}, author={Dimitris Bertsimas}, journal={Queueing Systems}, year={1995}, volume={21}, pages={337-389} }

We survey a new approach that the author and his co-workers have developed to formulate stochastic control problems (predominantly queueing systems) asmathematical programming problems. The central idea is to characterize the region of achievable performance in a stochastic control problem, i.e., find linear or nonlinear constraints on the performance vectors that all policies satisfy. We present linear and nonlinear relaxations of the performance space for the following problems: Indexable…

## 47 Citations

### Optimization of Multiclass Queueing Networks with Changeover Times Via the Achievable Region Approach: Part I, the Single-Station Case

- 1999

Computer Science

This approach seeks to obtain performance bounds and scheduling policies from the solution of a mathematical program over a relaxation of the system's performance region to address the performance optimization problem in a single-station multiclass queueing network with changeover times.

### Optimization of Multiclass Queueing Networks with Changeover Times Via the Achievable Region Method: Part Ii, the Multi-Station Case

- 1998

Computer Science

We address the problem of scheduling a multi-station multiclass queueing network (MQNET) with server changeover times to minimize steady-state mean job holding costs. We present new lower bounds on…

### Strongly asymptotically optimal design and control of production and service systems

- 2000

Computer Science

A formal definition of strong asymptotic optimality in the context of design and control of queueing systems that can be modeled as single or multiple stage queueing networks is provided.

### The achievable region approach to the optimal control of stochastic systems

- 1999

Computer Science

The achievable region approach seeks solutions to stochastic optimization problems by characterizing the space of all possible performances (the achievable region) of the system of interest and…

### A linear programming approach to stability , optimisation and performance analysis for Markovian multiclass queueing networks ★

- 1999

Business

Our object of study is a multiclass queueing network (MQNET) which consists of a collection of (connected) single-server stations. Exogenous arrivals into the system form independent Poisson streams,…

### Performance Bounds in Queueing Networks

- 2011

Computer Science

This paper surveys computable performance bounds for sequencing and scheduling control in open networks to minimize the long run average number of customers, or a weighted average over different customer classes.

### Delay and Power-Optimal Control in Multi-Class Queueing Systems

- 2011

Computer Science, Mathematics

ArXiv

The proposed unified framework provides a new set of tools for stochastic optimization and control over multi-class queueing systems with time average constraints and implement weighted priority policies in every busy period.

### Solving convex optimization with side constraints in a multi-class queue by adaptive $$c\mu $$cμ rule

- 2014

Computer Science

Queueing Syst. Theory Appl.

Combining the achievable region approach in queueing systems and the Lyapunov drift theory suitable to optimize renewal systems with time-average constraints, this paper shows that convex optimization problems can be solved by variants of adaptive $$c\mu $$cμ rules.

### Threshold control policies for heterogeneous server systems

- 2002

Mathematics, Computer Science

Math. Methods Oper. Res.

It is shown that any optimal, nonpreemptive policy is of threshold type, i.e., it assigns a customer to server Si, if this server is the fastest server available and the number of customers in the queue is mi or more.

### A linear programming approach to stability, optimisationand performance analysis for Markovian multiclassqueueing networks

- 1999

Business

Ann. Oper. Res.

A primal‐dual approachexploits the fact that the system satisfies (approximate) conservation laws to yield perform-ance guarantees for a natural index‐based scheduling heuristic, and is able to analyse the performance of an arbitrary priority policy.

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