# Routing and Scheduling of Network Flows with Deadlines and Discrete Capacity Allocation

## TL;DR

This paper addresses the complex problem of joint routing and scheduling of data flows with deadlines in communication networks, incorporating discrete capacity units, and proposes novel algorithms with proven effectiveness.

## Contribution

It introduces a new formulation for flow routing with deadlines using time slicing and develops a column generation algorithm and a Max-Flow based algorithm for efficient solutions.

## Key findings

- The problem is proven to be computationally complex.
- The TSA formulation effectively models deadline constraints.
- The proposed algorithms perform well across various scenarios.

## Abstract

Joint scheduling and routing of data flows with deadline constraints in communication networks has been attracting research interest. This type of problem distinguishes from conventional multicommodity flows due to the presence of the time dimension. In this paper, we address a flow routing and scheduling problem with delivery deadline, where the assignment of link capacity occurs in discrete units. Discrete capacity allocation is motivated by applications in communication systems, where it is common to have a base unit of capacity (e.g., wavelength channel in optical communications). We present and prove complexity results of the problem. Next, we give an optimization formulation based on a time slicing approach (TSA), which amounts to a discretization of the time into time slices to enable to formulate the deadline constraints. We then derive an effective reformulation of the problem, via which a column generation algorithm (CGA) is developed. In addition, we propose a simple and fast Max-Flow based Algorithm (MFA). We use a number of network and traffic scenarios to study various performance aspects of the algorithms.