# Anonymity Mixes as (Partial) Assembly Queues: Modeling and Analysis

## TL;DR

This paper models batch mix anonymity networks using queueing theory, analyzing delay and anonymity trade-offs, and proposes a randomized strategy that improves delay but impacts anonymity.

## Contribution

It introduces a queueing model for batch mixes, analyzes delay growth, and proposes a randomized mixing strategy balancing delay and anonymity.

## Key findings

- Delay grows rapidly as batch size approaches number of senders
- Randomized batching improves delay scaling
- Randomization reduces anonymity capabilities

## Abstract

Anonymity platforms route the traffic over a network of special routers that are known as mixes and implement various traffic disruption techniques to hide the communicating users' identities. Batch mixes in particular anonymize communicating peers by allowing message exchange to take place only after a sufficient number of messages (a batch) accumulate, thus introducing delay. We introduce a queueing model for batch mix and study its delay properties. Our analysis shows that delay of a batch mix grows quickly as the batch size gets close to the number of senders connected to the mix. We then propose a randomized batch mixing strategy and show that it achieves much better delay scaling in terms of the batch size. However, randomization is shown to reduce the anonymity preserving capabilities of the mix. We also observe that queueing models are particularly useful to study anonymity metrics that are more practically relevant such as the time-to-deanonymize metric.