Diagonal Scaling: A Multi-Dimensional Resource Model and Optimization Framework for Distributed Databases

TL;DR

This work addresses the limitations of binary scale-out vs scale-up decisions in distributed databases by introducing the Scaling Plane, a two-dimensional model with $H$ (node count) and $V=(c,r,b,s)$ (per-node resources). It derives analytic surfaces for node latency $L_{ ext{node}}(V)$, coordination latency $L_{ ext{coord}}(H)$, total latency $L(H,V)$, throughput $T(H,V)$, coordination overhead $K(H,V)$, and cost $C(H,V)$, then formulates a multi-objective objective $F(H,V)=\alpha L(H,V)+\beta C(H,V)+\gamma K(H,V)$ subject to constraints on latency and throughput. The DiagonalScale algorithm performs a discrete local search over the $H$–$V$ plane, incorporating a rebalance penalty to bias toward stable trajectories and proving convergence to a local optimum. Empirical evaluation on synthetic surfaces and real systems (Distributed SQL and KV stores) demonstrates that diagonal scaling yields up to 40% lower $p95$ latency, up to 37% lower cost per query, and 2–5× fewer rebalances compared with axis-aligned autoscalers, validating the multi-dimensional approach and guiding next-generation cloud autoscaling.

Abstract

Modern cloud databases present scaling as a binary decision: scale-out by adding nodes or scale-up by increasing per-node resources. This one-dimensional view is limiting because database performance, cost, and coordination overhead emerge from the joint interaction of horizontal elasticity and per-node CPU, memory, network bandwidth, and storage IOPS. As a result, systems often overreact to load spikes, underreact to memory pressure, or oscillate between suboptimal states. We introduce the Scaling Plane, a two-dimensional model in which each distributed database configuration is represented as a point (H, V), with H denoting node count and V a vector of resources. Over this plane, we define smooth approximations of latency, throughput, coordination overhead, and monetary cost, providing a unified view of performance trade-offs. We show analytically and empirically that optimal scaling trajectories frequently lie along diagonal paths: sequences of joint horizontal and vertical adjustments that simultaneously exploit cluster parallelism and per-node improvements. To compute such actions, we propose DIAGONALSCALE, a discrete local-search algorithm that evaluates horizontal, vertical, and diagonal moves in the Scaling Plane and selects the configuration minimizing a multi-objective function subject to SLA constraints. Using synthetic surfaces, microbenchmarks, and experiments on distributed SQL and KV systems, we demonstrate that diagonal scaling reduces p95 latency by up to 40 percent, lowers cost-per-query by up to 37 percent, and reduces rebalancing by 2 to 5 times compared to horizontal-only and vertical-only autoscaling. Our results highlight the need for multi-dimensional scaling models and provide a foundation for next-generation autoscaling in cloud database systems.

Figures (7)

• Figure 1: The Scaling Plane, showing horizontal, vertical, and diagonal scaling paths. Diagonal paths traverse interior regions where many surfaces reach their minima.
• Figure 2: Synthetic latency surface $L(H,V)$ demonstrating reduced per-node latency with larger $V$ and increased coordination latency with larger $H$.
• Figure 3: Cost-per-query heatmap illustrating interior minima reachable by diagonal scaling.
• Figure 4: Autoscaling trajectories in the Scaling Plane. Horizontal-only and vertical-only strategies move along axis-aligned paths. DiagonalScale converges toward interior optima.
• Figure 5: Latency under a time-varying workload. DiagonalScale maintains lower and more stable tail latency.