# Dynamic scheduling in a partially fluid, partially lossy queueing system

## TL;DR

This paper analyzes a single server queue with two job classes under dynamic scheduling policies in a fluid limit, revealing a pseudo-conservation law and characterizing Pareto-optimal performance trade-offs.

## Contribution

It introduces a fluid limit analysis for a partially fluid, partially lossy queueing system, establishing a pseudo-conservation law and identifying Pareto-complete scheduling policies.

## Key findings

- Performance of each class is characterized under dynamic policies.
- A pseudo-conservation law links class performances to eager class blocking probabilities.
- The Pareto frontier of performance vectors is characterized, with a class of Pareto-complete policies identified.

## Abstract

We consider a single server queueing system with two classes of jobs: eager jobs with small sizes that require service to begin almost immediately upon arrival, and tolerant jobs with larger sizes that can wait for service. While blocking probability is the relevant performance metric for the eager class, the tolerant class seeks to minimize its mean sojourn time. In this paper, we discuss the performance of each class under dynamic scheduling policies, where the scheduling of both classes depends on the instantaneous state of the system. This analysis is carried out under a certain fluid limit, where the arrival rate and service rate of the eager class are scaled to infinity, holding the offered load constant. Our performance characterizations reveal a (dynamic) pseudo-conservation law that ties the performance of both the classes to the standalone blocking probabilities of the eager class. Further, the performance is robust to other specifics of the scheduling policies. We also characterize the Pareto frontier of the achievable region of performance vectors under the same fluid limit, and identify a (two-parameter) class of Pareto-complete scheduling policies.