# PIF: A PI-based AQM that ensures performance isolation in multi tenant cloud data centers

Ahmed Ben Ali, Yann Labit, Kokouvi Benoit Nougnanke

► To cite this version:

Ahmed Ben Ali, Yann Labit, Kokouvi Benoit Nougnanke. PIF: A PI-based AQM that ensures performance isolation in multi tenant cloud data centers. IEEE NOMS 2025, IEEE, May 2025, Honolulu, United States. 10.1109/NOMS57970.2025.11073731. hal-04995732

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# PIF: A PI-based AQM that ensures performance isolation in multi tenant cloud data centers

Ahmed Ben Ali

Université de Toulouse
LAAS-CNRS

Toulouse, France

Email: abenali@laas.fr

Yann Labit

Université de Toulouse
LAAS-CNRS

Toulouse, France

Email: ylabit@laas.fr

Benoit Nougnanke

Télécom SudParis
Institut Polytechnique de Paris
Palaiseau, France

Email: kokouvi-benoit.nougnanke@telecom-sudparis.eu

***Abstract***—Managing fairness and performance isolation in multi-tenant cloud data centers is challenging using traditional flow-based methods like pure TCP settings without AQMs, which do not account for tenants generating multiple-flow traffic. Motivated by this observation, we explore PID (Proportional-Integral-Derivative) based AQMs and address this issue by first identifying and validating the system model through theoretical Analysis and simulations. We then implement a standard PI controller-based AQM and evaluate its performance, finding it insufficient in handling aggressive multi-flow tenant workloads. To improve this, we introduce a Modified PI Controller (PIF)-based AQM with adaptive mechanisms tailored for multi-tenant environments. Simulations show that the PIF controller significantly enhances fairness and isolation compared to default settings without AQM control, offering a robust solution for effective resource management in complex cloud data centers.

***Index Terms***—Multi-tenant environment, Cloud Data Center, Control theory, AQM, Fairness, Performance isolation.

## I. INTRODUCTION

In multi-tenant cloud data centers, tenants share physical infrastructure, posing challenges in fair resource allocation and performance isolation [1]–[3]. Traffic varies dynamically across tenants, and containerized microservices exacerbate fluctuations, degrading service quality without proper resource management. Traditional congestion control, such as TCP [4], struggles to ensure consistent tenant performance in such environments.

*Active Queue Management (AQM)* [5] mitigates congestion by managing queue lengths at network routers. Techniques like *Random Early Detection (RED)* [6] and *Controlled Delay (CoDel)* [7] preemptively drop packets based on queue size or delay. However, RED requires precise tuning and is unsuitable for dynamic workloads, while CoDel focuses on latency but overlooks tenant fairness, leading to uneven resource allocation.

Advanced AQMs like Proportional Integral Controller Enhanced (PIE) [8] dynamically adjust packet drop rates using control-theoretic principles for improved stability under fluctuating conditions. Yet, they lack tenant-specific fairness, leaving "noisy neighbors"—tenants with bursty traffic—able to disrupt others. Similarly, Model-Free Control (MFC) [9], while adaptable, does not cater to fairness requirements, making it less effective for multi-tenant scenarios.

To overcome these limitations, we propose *Proportional Integral Fairness (PIF)*, an AQM tailored to multi-tenant environments. PIF extends traditional PI controllers [10] with

adaptive mechanisms aligned with Service Level Objectives (SLOs) and Service Level Agreements (SLAs), ensuring equitable resource distribution amidst traffic fluctuations. It dynamically adjusts control parameters in real-time, promoting fairness across tenants and isolating disruptive traffic.

This work addresses two main objectives: (1) fair resource allocation among tenants and (2) enhanced performance isolation in multi-tenant data centers. Extensive ns-3 simulations validate PIF's superiority over RED, CoDel, and PIE, demonstrating improved fairness and consistent performance isolation in high-variability scenarios.

## II. STATE OF THE ART

AQM techniques are vital for managing congestion and performance in multi-tenant cloud data centers (MTCDCs), where tenants—users, applications, or organizations—share infrastructure and generate multiple flows. These environments require fair resource allocation and performance isolation. While traditional AQMs, control-theoretic methods, and QoS mechanisms address congestion, they often lack comprehensive solutions for tenant-based fairness and adaptive traffic management in dynamic cloud settings.

### A. Traditional AQM Approaches

*Random Early Detection (RED)* [6] prevents congestion by probabilistically dropping packets as queue length increases. However, its effectiveness relies heavily on parameter tuning, which is challenging in MTCDCs with highly variable traffic patterns. Additionally, RED lacks fairness mechanisms, making it unsuitable for equitable tenant resource allocation.

*Controlled Delay (CoDel)* [7] mitigates bufferbloat by dropping packets when queuing delay surpasses a threshold, effectively reducing latency. However, it does not ensure fairness among tenants or flows, potentially causing performance degradation in multi-tenant environments.

*Proportional Integral Controller Enhanced (PIE)* [8] uses control theory to adaptively adjust packet drop rates based on queue delay. While more adaptive than RED and CoDel, PIE still lacks explicit tenant-level fairness mechanisms, limiting its suitability for multi-tenant scenarios.

### B. Control-Theoretic Approaches for Resource Allocation

Control theory has been applied to network congestion management with various methods to improve queue stability
and responsiveness. Hollot et al. [11] introduced PI controllers for AQM, focusing on flow-level control rather than tenant-specific fairness. Ariba et al. [12] used state-feedback control for heterogeneous delays but lacked tenant-level fairness. Sonnet [13] and Skynet [14] optimize resource allocation and bandwidth management but do not explicitly address tenant fairness. Recent work [9] leverages Model-Free Control (MFC) [15] for adaptive congestion management, improving robustness but still omitting tenant-level fairness mechanisms.

### C. Quality of Service (QoS) Mechanisms and AI-Enhanced Techniques

Quality of Service (QoS) mechanisms, such as *Differentiated Services (DiffServ)*, provide congestion management and traffic prioritization using policies like *Weighted Random Early Detection (WRED)* and *Class-Based Weighted Fair Queueing (CBWFQ)* [16]. These methods ensure appropriate service levels for different traffic types. However, these approaches primarily target traffic classes rather than specific tenants or flows, lacking explicit tenant-level fairness. To address these limitations, adaptive methods like *SRQ-PI* [17] employ self-tuning PI controllers to dynamically adjust parameters for improved queue stability and responsiveness, while *machine learning-based techniques*, including *deep reinforcement learning*, are explored to predict traffic patterns and optimize AQM settings [18]. Despite their potential to enhance network performance, both QoS mechanisms and adaptive control techniques still face challenges in delivering explicit tenant-level fairness within multi-tenant cloud data centers.

### D. Proposed Contribution: Proportional Integral Fairness (PIF)

The proposed Proportional Integral Fairness (PIF) distinguishes itself from traditional AQM techniques by prioritizing fairness in multi-tenant environments. PIF distinguishes itself by incorporating adaptive mechanisms to dynamically adjust control parameters and resource allocation based on tenant-specific demands, ensuring equitable distribution during traffic fluctuations. This real-time adaptability allows PIF to effectively address "noisy neighbor" issues, enhancing performance isolation and maintaining fairness across tenants and flows.

### E. Comparative Summary

The following table provides a comparison of traditional AQMs, control-theoretic approaches, QoS mechanisms, and the proposed PIF method, with a focus on how they address fairness at the tenant or flow level.

## III. ARCHITECTURE

### A. Setup and Scenario

The leaf-spine architecture is a network topology commonly used in modern multi-tenant cloud data centers to provide high bandwidth and low latency across the network. It consists of two main layers: the spine layer and the leaf layer. Fig. 2 illustrates the general architecture, including the leaf-spine topology as the managed element within the multi-tenant cloud data center network.

**Scenario.** For this study and without loss of generality, we consider the simplified corresponding dumbbell topology using two tenants. We define a tenant as a Server-Client Couple of machines that are linked with 2 switches which themselves are linked by a bottleneck link as shown in Figure 1. We

<figure><img src="image_2.png" /><figcaption>Fig. 1. Topology of the simplified system that we will use in the rest of the paper</figcaption></figure>

will be using TCP for the transport protocol and different AQMs for comparison of a simple FIFO and our PID-Based AQM. We will vary the number of flows used by tenants to manipulate their workloads. To evaluate our control, we will use the fairness metric defined in the following section.

### B. Overview of the Architecture

To effectively handle performance isolation in multi-tenant data center networks through fair resource sharing complying with service level objectives (SLO), we propose a MAPE-K inspired framework [19] as depicted in Fig. 2. It incorporates a *Measuring Module* responsible for extracting metrics like latency and bandwidth from applications, supported by *Estimation Module* employing machine learning or statistical models to estimate relevant factors affecting system performance (not discussed in this paper). A *Classifier of system State* is introduced to categorize the current state of the system based on estimated variables, guiding a *Classifier of System State* to adapt the level of resource isolation. Further, a *Policy Maker* implements dynamic policies, adjusting resource allocations, and triggering actions such as auto-scaling. A continuous Feedback Loop ensures real-time adaptation and updates to the system based on the evolving conditions, creating a robust and adaptive architecture for effective SLO assurance.

Implementing this architecture requires a structured approach. First, we thoroughly identify the MTCDC model. Next, we evaluate system controllability and assess traditional PI controllers. Finally, we adapt and enhance the PI controller to handle a wider range of conditions.

## IV. BASICS IN IDENTIFICATION FOR MTCDC DYNAMICAL MODEL

We consider the MTCDC topology as a SISO (Single Input, Single Output) black box model given by the right side of the figure 2. Fundamental concepts such as causality, time invariance, linearity, and additivity play a pivotal role in the identification and modeling of system behaviors. Understanding these principles enables the development of models and control laws. In this section, we explore these foundational
<table><caption>TABLE I COMPARISON OF AQM APPROACHES</caption><thead><tr><th>Name</th><th>Approach</th><th>Multi-terminal/Multi-flow Support</th><th>Fairness</th><th>Control Strategy</th><th>Resource Focused</th><th>Performance Under Heavy Load</th></tr></thead><tbody><tr><td>RED [6]</td><td>Probability-based early drops</td><td>No explicit support</td><td>Non-explicit</td><td>Requires tuning of drop probabilities</td><td>Bandwidth</td><td>Good, but tuning-sensitive</td></tr><tr><td>CoDel [7]</td><td>Delay-based packet dropping</td><td>No explicit support</td><td>Non-explicit</td><td>Self-configuring, delay-based</td><td>Latency and delay</td><td>Good for low-latency environments</td></tr><tr><td>PIE [8]</td><td>Proportional-Integral controller</td><td>No explicit support</td><td>Non-explicit</td><td>Self-configuring, delay-based</td><td>Latency and queue length</td><td>Good, adapts to dynamic traffic</td></tr><tr><td>AQM MFC [9]</td><td>Model-Free Control and intelligent controllers</td><td>Real-time adjustment</td><td>Non-explicit</td><td>MFC-based, adaptable control</td><td>Queue length, stability, and adaptation</td><td>Robust under varying network conditions</td></tr><tr><td>Sonnet [13]</td><td>Feedback-based resource allocation</td><td>Dynamic resource allocation, not multi-tenant</td><td>Non-explicit</td><td>Control-theory-based, system-wide feedback</td><td>CPU and memory</td><td>Optimized for dynamic workloads</td></tr><tr><td>Skynet [14]</td><td>Control-theoretic feedback control</td><td>Yes, supports multiple terminals</td><td>Non-explicit</td><td>Centralized control, system-wide feedback</td><td>Bandwidth and resource allocation</td><td>Scales well with large-scale environments</td></tr><tr><td>Hollot and al. [11]</td><td>PI controller for congestion control</td><td>Supports multiple flows</td><td>Flow</td><td>Control-theory approach for queue regulation</td><td>Queue length and stability</td><td>Stabilizes network performance</td></tr><tr><td>Ariba and al. [12]</td><td>State-feedback control for TCP/AQM networks</td><td>Handles multiple time delays in the network</td><td>Flow</td><td>Robust control with delay compensation</td><td>Latency, queue management, and stability</td><td>Maintains stability under varying delays</td></tr><tr><td>QoS (DiffServ) [16]</td><td>Traffic prioritization with marking</td><td>No tenant-level isolation</td><td>Non-explicit</td><td>Configuration-based policy management</td><td>Traffic classification and prioritization</td><td>Scales well with varying traffic classes</td></tr><tr><td>SRQ-PI (Self-tuning) [17]</td><td>Adaptive PI-based</td><td>Adapts to multi-flow conditions</td><td>Flow</td><td>Adaptive control based on feedback</td><td>Bandwidth and latency optimization</td><td>Handles variations well</td></tr><tr><td>PIF (Fairness + Multi-tenant)</td><td>PI-based, adaptive control</td><td>Direct support for multi-tenant environments with multiple flows</td><td>Tenant</td><td>Adaptive PI-based with fairness guarantees</td><td>Bandwidth and flow allocation with tenant-level fairness</td><td>Maintains fairness across multiple tenants and flows</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>Fig. 2. General Overview of the Architecture</figcaption></figure>

concepts and provide a comprehensive framework for their application in Multi-Tenant Cloud Data Centers. The evaluation (Section VI) will complete the validation of the MTCDC model.

## A. Causality

### Definition 1:

A system is causal [20] if the output at any time $t$ depends only on the input at the present time $t$ and possibly on past inputs. This is explained by

$$y(t) = f(x(t), u(t-1), u(t-2), \dots) \quad (1)$$

where $t \in \mathbb{R}$ and $u(t), y(t) \in \mathbb{R}$.

**Remark 1:** In MTCDC, numerous tenants share resources, leading to complex interactions. The behavior of one tenant's workload can affect others, making it difficult to isolate: this is one of our challenges. One of these shared resources is the network bandwidth, which could introduce latency. If we manage performance isolation, delays could be minimized. Therefore, we propose the following hypotheses.

**Theorem 1:** If a system is causal, based on the first definition it will remain causal no matter what the isolation performance is.

**Proof 1:** The output $y_i(t)$ for tenant $i$ depends on the control
<table><caption>TABLE II
VARIABLES AND DESCRIPTIONS FOR MULTI-TENANT NETWORK CONTROL</caption><thead><tr><td>Variable</td><td>Description</td><td>Unit</td></tr></thead><tbody><tr><td>y(t)</td><td>Satisfied demand for a tenant at time t.</td><td>Mbps</td></tr><tr><td>u(t)</td><td>Control input to satisfy the demand or the SLO at time t.</td><td>Packets/second</td></tr><tr><td>SLO</td><td>Service Level Objective for a tenant (bandwidth).</td><td>Mbps</td></tr><tr><td>ε(t)</td><td>Difference to reduce to meet the SLO, defined as SLO - y(t).</td><td>Mbps</td></tr><tr><td>J(t)</td><td>Performance isolation fairness index at time t.</td><td>Dimensionless</td></tr><tr><td>K<sub>p</sub></td><td>Proportional gain in the control system, influencing the response to ε(t).</td><td>Dimensionless</td></tr><tr><td>K<sub>i</sub></td><td>Integral gain in the control system, addressing accumulated errors over time.</td><td>1/second</td></tr><tr><td>K<sub>d</sub></td><td>Derivative gain in the control system, responding to the rate of change of ε(t).</td><td>second</td></tr></tbody></table>

input $u_i(t)$, current and past measurements such as queue lengths, bandwidth usage, and predefined SLOs:

$$y_i(t) = f(u_i(t), u_i(t-1), \dots)$$

Since future inputs are not used, the system meets the definition of causality. Tenant isolation, while important, does not affect this definition.

## B. Time Invariance

**Definition 2:** A system is time-invariant [20] if a time shift $\tau$ in the input signal results in an identical time shift in the output signal. Mathematically, if $y(t)$ is the output due to input $u(t)$, then the output due to input $u(t-\tau)$ is $y(t-\tau)$.

$$y(t-\tau) = f(u(t-\tau)) \quad (2)$$

where $t, \tau \in \mathbb{R}$ and $u(t), y(t) \in \mathbb{R}$.

## C. Linearity

A system is linear [20] if it satisfies the properties of additivity and homogeneity.

**Definition 3:**

If an input $u(t)$ produces an output $y(t)$, then for any scalar $a$, the input $au(t)$ produces an output $ay(t)$. Mathematically,

$$f(ax(t)) = afx(t) = ay(t) \quad (3)$$

**Definition 4:**

If an input $u_1(t)$ produces an output $y_1(t)$ and another input $u_2(t)$ produces an output $y_2(t)$, then the combined input $u_1(t)+u_2(t)$ produces an output $y_1(t)+y_2(t)$. Mathematically:

$$f(u_1(t) + u_2(t)) = f(u_1(t)) + f(u_2(t)) \quad (4)$$

where $u_1(t), u_2(t), u(t), y(t) \in \mathbb{R}$ and $a \in \mathbb{R}$.

**Remark 2:** Definitions 3 and 4 establish the superposition theorem. This theorem states that for a linear system, the response (output) caused by two or more inputs is the sum of the responses that would have been caused by each input individually. Thus, the MTCDC environment under the performance isolation hypothesis is a linear time-invariant (LTI) model.

## D. α-Class model

Based on the LTI model, we now consider the precision performance for a closed-loop model.

**Definition 5:**

A linear model of Class $\alpha$ [20], in the context of control theory, refers to a dynamic system where the direct chain contains $\alpha$ pure integrators. This means that the system has poles at 0 with a multiplicity of $\alpha$. In other words, there are $\frac{1}{s}$ terms (where $s$ is the Laplace variable) in the transfer function of the direct chain.

More generally, if we have a linear differential equation describing the system and its corresponding transfer function is:

$$H(s) = \frac{b_m s^m + b_{m-1} s^{m-1} + \dots + b_1 s + b_0}{a_n s^n + a_{n-1} s^{n-1} + \dots + a_1 s + a_0} = \frac{N(s)}{D(s)} \quad (5)$$

where $N(s)$ and $D(s)$ are polynomials in $s$. For a Class 0 model, $a_0 \neq 0$, which means that $D(s)$ has no roots at 0.

**Remark 3:** There is a link between the class of a system (the number of pure integrators in the direct chain) and the precision of the closed-loop system [20]. The class of the system influences its ability to follow a reference or reject disturbances. To improve closed-loop precision, it is common to increase the class of the system by adding integrators in the direct chain.

We observe (see Section VI) that only a Proportional-Integral (PI) control law has an impact (for the precision) on the model, therefore, we deduce that our MTCDC environment is of Class 0.

## V. CONTROL LAWS DESIGN

A closed-loop control system, or feedback control system, continuously adjusts its inputs based on output feedback to maintain a desired outcome. A controller compares sensor feedback to the setpoint (desired value) and uses actuators to correct any discrepancies. For example, a thermostat-controlled heating system adjusts heating to maintain a consistent room temperature. This feedback mechanism ensures greater accuracy and responsiveness than open-loop systems.

<figure><img src="image_4.png" /><figcaption>Fig. 3. Closed-loop MTCDC environment</figcaption></figure>

For the rest of the document, we define:

* $y(t)$: satisfied demand for a tenant.

* $u(t)$: control input to satisfy the demand or the SLO.

* SLO: the SLO for a tenant. Bandwidth is the main shared resource in this case.

* $\epsilon(t)$: the difference to reduce to respect the SLO. Mathematically,

$$\epsilon(t) = \text{SLO} - y(t)$$
• $J(t)$: the performance isolation fairness index.

## A. PID Controller

A Proportional-Integral-Derivative (PID) controller is a widely used control loop feedback mechanism in industrial control systems. It continuously calculates an error value as the difference between a desired setpoint and a measured process variable and applies a correction based on proportional, integral, and derivative terms, hence the name PID.

The PID controller equation in continuous form is given by:

$$u(t) = K_p \epsilon(t) + K_i \int_{0}^{t} \epsilon(\tau) d\tau + K_d \frac{d\epsilon(t)}{dt} \quad (6)$$

where:

* $K_p$ is the proportional gain, a tuning parameter.

* $K_i$ is the integral gain, a tuning parameter.

* $K_d$ is the derivative gain, a tuning parameter.

## VI. EVALUATION

The evaluation procedure will consist of two phases. First, we will verify the characteristics identified during the system identification process. Then, we will assess the performance of our system in a multi-tenant environment, based on the previously described scenario. The evaluation procedures for each part and its objective are summarized in VI. To measure our system's effectiveness, we will use the following index: **Fairness Measure.** To measure fairness in multi-tenant environments, we use a modified version of Jain's fairness index that accounts for Service Level Objectives (SLOs) of each tenant. This index aggregates flows per tenant and evaluates fairness based on the ratio of observed throughput to each tenant's SLO:

$$J(x_1, \dots, x_n, SLO_1, \dots, SLO_n) = \frac{\left(\sum_{i=1}^{n} \frac{x_i}{SLO_i}\right)^2}{n \cdot \sum_{i=1}^{n} \left(\frac{x_i}{SLO_i}\right)^2} \quad (7)$$

where:

* $n$: Number of tenants.

* $x_i$: Total throughput used by the $i$-th tenant's flows.

* $SLO_i$: Service Level Objective of the $i$-th tenant.

This metric ranges from 0.5 to 1, with values closer to 1 indicating better fairness.

We will try to validate the specified theoretical results that we specified in the previous sections with NS-3 [21] simulations using the scenario described in Section II with the topology shown in Fig. 1.

## A. First results based on Control Theory Theorems

To confirm that the initial model (it means the MTCDC environment) is linear time-invariant (LTI) and contains no pure integrators, we use a PI controller and observe the closed-loop system behavior. The superposition principle is fundamental for LTI systems. By this way, we can exploit three assertions:

<table><caption>TABLE III
IDENTIFICATION AND CONTROL LAWS RESULTS OVERVIEW</caption><thead><tr><th colspan="3">Identification Results</th></tr><tr><th>Objective</th><th>Summary</th><th>Figure</th></tr></thead><tbody><tr><td>Linearity Verification</td><td>SLO scaling produced identical outputs, confirming linearity.</td><td>Fig. 4</td></tr><tr><td>Time Invariance Check</td><td>Same system behavior observed at different start times.</td><td>Fig. 4</td></tr><tr><td>Superposition Principle</td><td>System's linearity validated through response superposition.</td><td>Fig. 4</td></tr><tr><td>Class 0 System</td><td>Only PI parameters influenced performance, indicating Class 0.</td><td>Fig. 4</td></tr></tbody><thead><tr><th colspan="3">Control Laws Results</th></tr><tr><th>Method</th><th>Summary</th><th>Figure</th></tr></thead><tbody><tr><td>PI Controller</td><td>Achieved 0.99 fairness under low load; dropped to 0.81 in saturation.</td><td>Fig. 5, Fig. 6</td></tr><tr><td>Adaptive PI Controller</td><td>Fairness improved to 0.90 in high load with dynamic adjustments.</td><td>Fig. 7</td></tr></tbody></table>

1) If a system is LTI, it obeys the principle of superposition.

2) If a PI controller, defined by the transfer function $C(s) = K_p + \frac{K_i}{s}$, is applied to the system and the closed-loop system remains LTI, it implies the initial system $G(s)$ is also LTI.

3) If the closed-loop system shows a finite steady-state error for a step input, the initial model contains no pure integrators (0-Class model).

In summary, the following identification steps allow us to observe LTI behavior in a closed-loop system with a PI controller and 0-Class precision.

## B. Identification results

To verify the criteria, we conducted various simulations under different circumstances. We will proceed in the same order as the previously mentioned characteristics. First, we will address linearity. To confirm this criterion, we conducted the same simulation with SLO=4 and SLO=2. Then we multiplied the result of SLO = 2 by 2 and verified if it matched the SLO=4 result. This is observable in the following graph, let a=2, where the green and blue graphs are exactly the same.

According to Section IV.C. Remark 2, we have also verified the superposition principle.

<figure><img src="image_5.png" /><figcaption>Fig. 4. System Validation</figcaption></figure>

In the same graph, we have also addressed time invariance. To demonstrate this, we conducted one simulation starting at 0 s and another starting at 20 units of time. We then observed whether both simulations exhibited the same behavior, which is clearly shown in Figure 4.

Finally, to verify that the system is Class 0, we analyzed the impact of each parameter on the PID controller. If performance is not affected by the D factor, it confirms that the system
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