---
type: claim
domain: internet-finance
description: "Higher variance-to-mean ratio requires more capacity to maintain same congestion level"
confidence: proven
source: "Liu et al. (NC State), 'Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes' (2019)"
created: 2026-03-11
sourced_from:
- inbox/archive/internet-finance/2019-00-00-liu-modeling-nonstationary-non-poisson-arrival-processes.md
---

# Arrival process burstiness increases required capacity for fixed service level

Congestion measures (queue length, wait time, utilization) are increasing functions of arrival process variability. For a fixed average arrival rate and service rate, a bursty arrival process requires more capacity than a smooth (Poisson) arrival process to maintain the same service level.

This means that modeling arrivals as Poisson when they are actually bursty (higher variance-to-mean ratio) will systematically underestimate required capacity, leading to service degradation.

## Evidence

Liu et al. establish that "congestion measures are increasing functions of arrival process variability — more bursty = more capacity needed." This is a fundamental result in queueing theory: variance in the arrival process translates directly to variance in system state, which manifests as congestion.

The CIATA method explicitly models the "asymptotic variance-to-mean (dispersion) ratio" as a separate parameter from the rate function, recognizing that burstiness is a first-order determinant of system performance, not a second-order correction.

## Application to Research Pipeline Capacity

For pipelines processing research sources that arrive in bursts:

1. A Poisson model with the same average rate will underestimate queue lengths and wait times
2. Capacity sized for Poisson arrivals will experience congestion during burst periods
3. The dispersion ratio (variance/mean) must be measured and incorporated into capacity planning

The MMPP framework provides a tractable way to model this: the state-switching structure naturally generates higher variance than Poisson while remaining analytically tractable for capacity calculations.

---

Relevant Notes:
- domains/internet-finance/_map

Topics:
- core/mechanisms/_map