Analysis of the Optimal Resource Allocation for a Tandem Queueing System

TL;DR

This paper analyzes a controllable tandem queueing system with two nodes, focusing on optimal resource allocation to minimize long-term costs using Markov decision processes and dynamic programming.

Contribution

It derives the structure, monotonicity, and uniqueness conditions of the optimal resource allocation policy, including bang-bang control properties.

Findings

Optimal policies are monotonic with respect to queue lengths.

Conditions for the uniqueness of the optimal policy are established.

Bang-bang control policy property is characterized under certain conditions.

Abstract

In this paper, we study a controllable tandem queueing system consisting of two nodes and a controller, in which customers arrive according to a Poisson process and must receive service at both nodes before leaving the system. A decision maker dynamically allocates the number of service resource to each node facility according to the number of customers in each node. In the model, the objective is to minimize the long-run average costs. We cast these problems as Markov decision problems by dynamic programming approach and derive the monotonicity of the optimal allocation policy and the relationship between the two nodes' optimal policy. Furthermore, we get the conditions under which the optimal policy is unique and has the bang-bang control policy property.