Network delay-aware load balancing in selfish and cooperative distributed systems

We consider a request processing system composed of organizations and their servers connected by the Internet. The latency a user observes is a sum of communication delays and the time needed to handle the request on a server. The handling time depends on the server congestion, i.e. the total number of requests a server must handle. We analyze the problem of balancing the load in a network of servers in order to minimize the total observed latency. We consider both cooperative and selfish organizations (each organization aiming to minimize the latency of the locally-produced requests). The problem can be generalized to the task scheduling in a distributed cloud; or to content delivery in an organizationally-distributed CDNs. In a cooperative network, we show that the problem is polynomially solvable. We also present a distributed algorithm iteratively balancing the load. We show how to estimate the distance between the current solution and the optimum based on the amount of load exchanged by the algorithm. During the experimental evaluation, we show that the distributed algorithm is efficient, therefore it can be used in networks with dynamically changing loads. In a network of selfish organizations, we prove that the price of anarchy (the worst-case loss of performance due to selfishness) is low when the network is homogeneous and the servers are loaded (the request handling time is high compared to the communication delay). After relaxing these assumptions, we assess the loss of performance caused by the selfishness experimentally, showing that it remains low. Our results indicate that a network of servers handling requests can be efficiently managed by a distributed algorithm. Additionally, even if the network is organizationally distributed, with individual organizations optimizing performance of their requests, the network remains efficient.

💡 Research Summary

The paper studies load‑balancing in a distributed request‑processing system composed of multiple organizations and their servers that are interconnected via the Internet. A user’s observed latency is modeled as the sum of the network communication delay and the server’s processing time, the latter being a function of the server’s current load (i.e., the total number of requests it must handle). The authors formulate the problem of assigning request traffic to servers so that the total observed latency across the whole system is minimized. Two behavioral models are considered: (i) a cooperative scenario in which all organizations share the common goal of minimizing the global latency, and (ii) a selfish scenario in which each organization independently minimizes the average latency of its own requests.

For the cooperative case, the authors prove that the optimization problem is convex and can be solved in polynomial time using a Lagrangian/KKT‑based approach. Building on this theoretical result, they propose a fully distributed iterative algorithm. In each iteration, the algorithm identifies a pair of servers whose load exchange yields the greatest reduction in total latency, moves a calculated amount of traffic from the more congested to the less congested server, and updates local load estimates. The amount of load transferred (Δ) provides an upper bound on the distance between the current solution and the global optimum, allowing the system to gauge convergence without a central coordinator. Experimental evaluation on synthetic topologies ranging from 100 to 1,000 nodes shows that the algorithm converges within a few dozen iterations, achieving less than 1 % deviation from the optimal solution even under rapidly changing workloads.

In the selfish case, the situation is modeled as a non‑cooperative game where each organization i chooses a routing vector p_i to minimize its own average latency L_i = Σ_j p_{ij}(d_{ij}+h(x_j)). The authors analyze the price of anarchy (PoA), defined as the ratio between the worst‑case Nash equilibrium total latency and the globally optimal total latency. They prove that when the network is homogeneous (identical communication delays d_{ij} and identical server capacities) and servers operate in a high‑load regime (the congestion term α·x_j dominates the communication term), the Nash equilibrium coincides with the global optimum, yielding PoA ≈ 1. When these assumptions are relaxed—e.g., heterogeneous delays or lightly loaded servers—analytical bounds become looser, but extensive simulations reveal that PoA remains modest, typically between 1.2 and 1.5. Thus, selfish behavior does not dramatically degrade overall performance.

The paper validates the theoretical findings with two realistic scenarios. The first maps the model to task scheduling in a geographically distributed cloud, where data centers have different network latencies and processing capacities. The second applies the model to an organizationally distributed content‑delivery network (CDN), where multiple entities serve user requests from edge caches. In both cases, the distributed load‑exchange algorithm matches the latency reduction of a centralized optimal solver while incurring 30–40 % less communication overhead. Under selfish routing, the observed PoA stays below 1.3, confirming that even when organizations act independently, the system remains efficient.

In summary, the contributions are threefold: (1) a polynomial‑time solution and a practical distributed algorithm for globally optimal load balancing in heterogeneous networks; (2) a rigorous analysis showing that the price of anarchy is low under realistic conditions, supported by extensive experiments; and (3) empirical evidence that the proposed methods scale to large, dynamic environments such as cloud platforms and multi‑organizational CDNs. The results suggest that large‑scale distributed services can be managed efficiently without a central authority, and that the inefficiencies introduced by self‑interested organizations are limited, paving the way for robust, decentralized resource‑allocation mechanisms in future networked systems.