Learning Service Slowdown using Observational Data

TL;DR

The paper tackles learning service slowdowns from observational congestion data in multi-server systems with adaptive congestion control. It shows that marginal congestion statistics can fail under diffusion-scale balancing and introduces a robust potential-action statistic, with theoretical guarantees: under maximally stable policies and heavy traffic, reliable slowdown detection is achievable via a relative-threshold rule; a central-limit theorem enables finite-time confidence, and normal-approximation bounds provide practical reliability estimates. Numerical results illustrate that potential-action signals closely track slowdown magnitudes and outperform marginal statistics, especially at moderate-to-high loads. The work suggests practitioners should combine multiple orthogonal statistics for reliable slowdown detection in complex, adaptive systems, with actionable online monitoring guidance.

Abstract

Being able to identify service slowdowns is crucial to many operational problems. We study how to use observational congestion data to learn service slowdown in a multi-server system that uses adaptive congestion control mechanisms. We show that a commonly used summary statistic that relies on the marginal congestion measured at individual servers can be highly inaccurate in the presence of adaptive congestion control. We propose a new statistic based on potential routing actions, and show it provides a much more robust signal for server slowdown in these settings. Unlike the marginal statistic, potential action aims to detect changes in the routing actions, and is able to uncover slowdowns even when they do not reflect in marginal congestion. Our results highlight the complexity in performing observational statistical analysis for service systems in the presence of adaptive congestion control. They also suggest that practitioners may want to combine multiple, orthogonal statistics to achieve reliable slowdown detection.

Figures (8)

• Figure 1: An illustration of the parallel multi-server system. Incoming jobs are sent to various servers by the dispatcher upon arrival. A slowdown refers to the event when the processing speed of the server, nominally at $\mu$, drops to $\alpha\mu$ for some $\alpha \in (0,1)$.
• Figure 2: An illustration of the format of observational congestion data. Each column represents the queue lengths at the various servers at a particular point in time. The data set consists of $N$ such samples collected at different points in time.
• Figure 3: An illustration of potential action versus marginal congestion summary statistics when applied to the same congestion data measured across 9 consecutive time periods. The system contains 30 servers and a dispatcher using the join-the-shortest-queue policy, and runs at a 95% load. The x-axis is the identity of the server, and y-axis the value of the corresponding statistic. The potential action statistic shows the empirical distribution of the potential actions across the servers, and marginal congestion the empirical average queue lengths. One can easily identify, using the potential action statistic, that server 15 experienced a slowdown starting from window 4, whereas it is very difficult to tell that from the marginal congestion statistic, which is considerably noisier and visually indistinguishable from one window to the next.
• Figure 4: An operator's dashboard, indicating whether there is a slowdown (y-axis values around 1) in a system with 10 servers for different loads ($\rho$) and a slowdown of $60\%$ ($\alpha=0.4$) at sample time 5000.
• Figure 5: The absolute error between the estimated $\pi^R_1/\pi^R_2$ ratio and the actual slowdown factor $\alpha$, for different number of servers and loads. The error is relatively small for moderate to high loads in all cases, suggesting that potential action based statistics can be beneficial not only to detect slowdowns, but also provide information on the slowdown magnitude.

Theorems & Definitions (25)

• Definition 1: Summary Statistic
• Definition 2: Decision Rule
• Definition 3: Index-Plus Decision Space
• Definition 4: Relative Threshold Rule
• Remark 1
• Definition 5: One-Server Failure with Known Slowdown Rate
• Definition 6: Reliability
• Remark 2
• Definition 7: Marginal Summary Statistic
• Theorem 1