⚡ electrical engineering

Brief Announcement: Generative Markov Model for Distributed Computing Systems

This paper proposes a tractable generative Markov model framework that factorizes complex, heterogeneous distributed computing states to enable efficient simulation and optimization, demonstrating through a collaborative AI inference case study that distributed resource utilization significantly reduces latency and server load compared to centralized scheduling.

Original authors: Alfreds Lapkovskis, Ali Beikmohammadi, Sindri Magnússon, Praveen Kumar Donta

Published 2026-06-03

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CC BY 4.0

Original authors: Alfreds Lapkovskis, Ali Beikmohammadi, Sindri Magnússon, Praveen Kumar Donta

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are running a massive, high-stakes pizza delivery service. In the old days, you had one giant, super-fast kitchen (the Cloud) that made every single pizza from scratch. It worked great when you had a few orders, but as your city grew, that one kitchen became a bottleneck. The chefs were overwhelmed, the ovens were bursting, and the pizzas took forever to get to customers. Plus, building bigger kitchens is expensive and uses a lot of energy.

Now, imagine a new idea: The "Volunteer Kitchen" Network. Instead of just using your central kitchen, you ask your customers: "Hey, do you have a spare oven or a free hand? If you're not busy, can you help make a slice of pizza for your neighbor?"

This is the core idea of the paper: Distributed Computing. It's about using the idle power of millions of personal devices (like phones and laptops) to help solve big problems, rather than relying on just one giant server.

The Problem: It's Too Chaotic to Manage

The problem with this "Volunteer Kitchen" idea is that it's incredibly messy.

Some volunteers are online, some are offline.
Some have powerful ovens (fast computers), others have weak ones.
The demand changes randomly.

Trying to predict how this chaotic system behaves is like trying to predict the weather in a hurricane. Traditional math models are too simple to handle it, and trying to simulate every single possibility is computationally impossible (it would take a supercomputer a million years to figure out the best plan).

The Solution: The "Lego" Model

The authors propose a new way to model this chaos called a Generative Markov Model.

Think of this model as a giant, smart Lego set.

The Old Way: Trying to understand the whole system as one giant, solid block of plastic. If you want to change one piece, you have to melt down the whole block. It's too heavy and rigid.
The New Way (This Paper): Breaking the system down into tiny, individual Lego bricks (variables).
- One brick is "Is User A online?"
- Another is "How much memory does User B have?"
- Another is "Is the pizza dough ready?"

The magic trick is that these bricks are sparse. This means most bricks don't care about each other. User A's online status doesn't directly change User B's memory. They only interact with their immediate neighbors.

By building the model this way, the authors created a system that is tractable (manageable). They can simulate the whole chaotic pizza network by just snapping together these small, independent bricks. This allows them to run "what-if" scenarios instantly: What happens if 1,000 new users join? What if the internet slows down?

The Experiment: Centralized vs. Distributed

The authors tested their model with a specific scenario: Collaborative AI Inference.

The Setup: A central server tries to answer AI questions (like "What's in this photo?").
The Test: They compared two strategies:
1. Centralized: The server tries to do all the work itself.
2. Distributed: The server offloads parts of the work to the users' devices when it gets busy.

The Results:

The Bottleneck: As the number of users grew, the Centralized strategy crashed. The server became a traffic jam, and the wait times (latency) skyrocketed.
The Win: The Distributed strategy was like a well-oiled machine. By spreading the work out to the users' devices, the wait times stayed low, and the central server didn't have to work as hard.

The Big Takeaway

The paper shows that spreading the work out is better, but you can't just guess how to do it. You need a formal, mathematical map (the Generative Markov Model) to understand the system before you can optimize it.

Their model acts like a flight simulator for distributed computing. It lets engineers practice making decisions in a safe, virtual environment to find the best way to balance the load between the central server and the volunteer devices, saving money and making things faster for everyone.

In short: They built a smart, modular math model that turns a chaotic, unpredictable network of devices into a manageable system, proving that sharing the workload is the key to scaling up AI without breaking the bank.

Technical Summary: Generative Markov Model for Distributed Computing Systems

Problem Statement

Emerging distributed computing paradigms, such as the computing continuum, are characterized by inherent heterogeneity, stochasticity, and complexity. While cloud computing offers advantages like on-demand provisioning, scaling AI inference infrastructure to meet growing demand incurs significant costs and environmental burdens. Alternative paradigms like volunteer computing and the computing continuum (integrating user devices, edge, and cloud) offer potential efficiency gains. However, these systems struggle to provide stable Quality-of-Service (QoS) guarantees due to resource heterogeneity and intermittent user availability.

The core challenge identified is the lack of a unified formal model capable of accounting for resource heterogeneity, stochastic availability, and the high dimensionality of system states. Without such a model, reasoning about performance trade-offs and optimizing decision-making policies at scale remains difficult, hindering large-scale deployments.

Methodology

The authors propose a Generative Markov Model (GMM) framework to model distributed computing systems. The methodology relies on a structured, factorized representation of the system state to ensure tractability.

1. Theoretical Framework

The system state at time $t$ , denoted as $s_t$ , is defined as a tuple of $N$ high-dimensional variables. To manage the complexity of the joint distribution over state sequences, the model imposes the Markov property and utilizes a two-level sparse factorization:

Variable Factorization: The joint distribution $p(s_t | s_{t-1})$ is decomposed into conditional distributions (factors) for each high-level variable $v_t$ , conditioned on a specific subset of parent variables $Pa(v_t)$ from the current and previous states.
Element Factorization: Each high-dimensional variable $v_t$ is further factorized over its individual elements $v_t \in v_t$ . This exploits the sparse dependency structure inherent in distributed systems, where components (e.g., nodes, tasks) evolve based on local information rather than the global state.

This factorization yields a tractable model that enables simulation, inference, and policy learning over system states that would otherwise be computationally infeasible to handle.

2. Case Study: Collaborative Distributed AI Inference

The framework is instantiated for a collaborative AI inference scenario involving a dedicated server ( $v_0$ ) and a set of user nodes ( $I$ ).

System State: The state vector $s_t$ includes user availability ( $o_t$ ), request states ( $q_t$ ), resource allocations ( $a_t$ ), readiness states ( $x_t$ ), execution states ( $y_t$ ), resource consumption ( $c_t$ ), and duration variables ( $d_t$ ).
Dependencies: The model captures complex dependencies, such as resource autocorrelation (handled via history buffers) and the coupling of data transfer and execution phases.
Policies: Decision-making is governed by two policy factors:
- Scheduler ( $\pi$ ): Runs on the server, deciding subtask downloads and execution assignments.
- Executor ( $\varsigma$ ): Runs on each node, enforcing local resource constraints (e.g., aborts, pauses).
Optimization Problems:
- Scheduler Policy Optimization: Formulated as an average-reward Reinforcement Learning (RL) problem to maximize long-term QoS (minimizing latency).
- Dedicated Resource Optimization: A chance-constrained optimization problem to find the minimal nominal server resources required to meet specific latency thresholds for different task types, given fixed policies.

Key Contributions

Generative Markov Modeling: The paper introduces a framework modeling the entire distributed computing system as a generative Markov model. Unlike prior work that formulates specific decision problems as MDPs, this approach models the system dynamics themselves, bridging distributed computing with Markov chain theory and RL.
Novel Factorization Structure: The framework employs a novel two-level sparse factorization (variable and element levels) and a modular structure. This allows conditional distributions to be estimated independently using techniques suited to specific system variables, keeping the model tractable despite high dimensionality.
Practical Instantiation: The authors provide a concrete instantiation for collaborative AI inference, demonstrating how the model handles the interplay between dedicated server resources and volunteered user resources.

Results

The framework was evaluated through a simulation of a distributed inference system with up to 10,000 users and varying server capacities. Two scheduling policies were compared: Centralized (all subtasks on the server) and Distributed (subtasks uniformly distributed across the server and online users).

Latency Performance: As the user count increased, the centralized policy became a bottleneck, leading to significantly higher P99 latencies. In contrast, the distributed policy progressively outperformed the centralized approach, yielding lower latency even with naive distribution strategies.
Resource Efficiency: The distributed policy consistently achieved lower CPU and memory usage on the server compared to the centralized policy. Notably, at 1,000 users, both policies achieved comparable P99 latencies, but the distributed policy did so with considerably lower server resource consumption.
Scalability: The results indicate that distributing computation across user devices reduces both latency and server resource consumption, validating the efficacy of adaptive decision-making in such environments.

Significance and Claims

The paper claims that the proposed framework provides a necessary formal model for reasoning about performance trade-offs and optimizing decision-making in complex, heterogeneous distributed systems. By making the system state tractable through sparse factorization, the framework enables:

Simulation and Evaluation: The ability to simulate system behavior under varying conditions (e.g., load, resource availability) without requiring full-scale physical deployment.
Policy Optimization: A direct bridge to RL methods for learning optimal scheduling policies (as defined in the optimization problems).
Modularity: The capacity to extend the model to new resource types, task structures, or node behaviors without redesigning the entire framework.

The authors conclude that while centralized scheduling fails at scale, distributing computation across user devices offers significant efficiency gains. They emphasize that developing and optimizing such adaptive decision-making strategies is infeasible without the unified probabilistic structure provided by their framework. Future work is planned to focus on real-environment validation, scalability investigations, and further optimization of scheduler and resource allocation policies.