Optimal control of stochastic networks of M/M/∞ queues with linear costs

2025/09/10 by Giovanni Pugliese Carratelli, Carratelli, Giovanni Pugliese, Ioannis Lestas +1
Business, Management and Accounting · Computer Science · Engineering · #60J27 #60K25 #93E20 #Advanced Queuing Theory Analysis #Advanced Wireless Network Optimization #Age of Information Optimization #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2509.08572

openalex publication_date 2025/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an arbitrary network of M/M/∞ queues with controlled transitions between queues. We consider optimal control problems where the costs are linear functions of the state and inputs over a finite or infinite horizon. We provide in both cases an explicit characterization of the optimal control policies. We also show that these do not involve state feedback, but they depend on the network topology and system parameters. The results are also illustrated with various examples.

Citations

• Exact Dynamic Programming for Positive Systems with Linear Optimal Cost
• An Overview for Markov Decision Processes in Queues and Networks
• The Value of Service Rate Flexibility in an M/M/1 Queue with Admission Control

Related

• Explicit solution for a network control problem in the large deviation regime
• Optimal control of a stochastic network driven by a fractional Brownian motion input
• Construction of Asymptotically Optimal Control for a Stochastic Network from a Free Boundary Problem
• Model-Predictive Control for Discrete-Time Queueing Networks with Varying Topology
• Optimal Control of Linear Cost Networks