Lifecycle-Optimal Tokenization: Vocabulary Size as a Deployment-Regime-Dependent Infrastructure Parameter

Tokenizer vocabulary size is a foundational design choice in large language model (LLM) infrastructure, yet it is typically fixed at training time based on convention rather than deployment analysis. We show that the cost-optimal vocabulary is not a constant but a function of the serving regime. We formalize total deployment cost as $C_{lifecycle}(V) = C_{train}(V) + λ\cdot C_{infer}(V, B)$, where $λ$ is inference volume and $B$ is the serving batch size. Through controlled experiments on two GPU families spanning the memory-bound to compute-bound regimes (A10G, ridge $\approx$ 117 FLOP/byte; A100, ridge $\approx$ 183 FLOP/byte), we demonstrate: (1) the inference-optimal vocabulary shifts 16x with serving batch, from 32k at $B=1$ to 524k at $B=64+$, driven by amortization of the $V \times d$ unembedding matrix read; (2) at 1.3-2.3B model scale, quality (bits per byte, BPB) is optimized at $V=65$k, confirming scale-dependent vocabulary preference; (3) the lifecycle-optimal vocabulary diverges from training-optimal by up to 16x for production deployments. Quality is approximately invariant across the optimal range ($<$2% BPB spread), making vocabulary a pure systems optimization with no quality penalty in the measured range. Our results provide actionable capacity planning guidance: on-device deployments ($B=1$) should use $V \approx 32$k; datacenter serving ($B \geq 64$, $λ\geq 10$) should use $V \approx 131$-262k.

LLM-Guided Transportation Hub Capacity Planning with Textual Business Inputs

While traditional hub capacity planning models optimize effectively for quantitative inputs, they often fail to digest qualitative business context. We propose a novel framework where a large language model (LLM) agent iteratively proposes hub capacity decisions guided by natural-language business context descriptions. The key mechanism is a chain-of-thought reasoning protocol: the LLM constructs a structured decision table that maps each contextual item to specific capacity adjustments based on the implied direction and magnitude of changes. The new capacity decision is then validated through a feedback loop with an optimization model, which provides routing-based performance metrics to guide the agent's selection. On a real-world 13-hub freight network in the southeastern US, our framework achieves a 2.8% optimality gap relative to the hidden ground-truth, a significant improvement over the 11.0% gap produced by the traditional optimization model without textual business inputs. This demonstrates that LLMs can serve as a contextual bridge, integrating qualitative business insights into Operations Research workflows.

Load Testing for Machine Learning Model Serving Systems at Scale

Machine learning (ML) model serving has become a dominant consumer of GPU infrastructure, yet capacity planning in these systems remains largely ad hoc. Under-provisioning leads to service-level objective (SLO) violations and production incidents, while over-provisioning results in substantial resource waste. This paper presents \sys, an industrial load testing framework for ML serving systems that systematically estimates serving capacity through an adaptive, feedback-driven search strategy. The approach leverages real-time performance signals, incorporating dampening, spike tolerance, and convergence detection to efficiently identify maximum sustainable throughput under SLO constraints. We evaluate \sys through a longitudinal analysis of 14 industrial case studies spanning four ML architecture classes: recommendation, ranking, vision, and NLP. This study demonstrates that systematic load testing leads to substantial improvements in GPU resource efficiency and operational reliability. Prior to adopting \sys, a significant fraction of model launches were under-provisioned, resulting in recurring incidents; these issues were substantially reduced after deployment. Our results show that ML-specific design decisions are critical to accurate capacity estimation: workload calibration using recorded traffic reduces estimation error from approximately 30\% to 2--6\%, while proper warmup handling yields a 22.2\% improvement in accuracy. Further analysis reveals key factors influencing prediction error, including model size and co-location effects. This paper distills six lessons and derive architectural guidelines for ML load testing, offering actionable insights for building reliable and efficient ML serving systems.

Optimal Scheduling in a Question-Answering Forum of Knowledge Workers

As individuals turn to the Internet to find answers to questions they may have, several Question Answering (QA) forums have evolved, where users knowledgeable in certain topics can contribute their expertise to answering these requests for information. While these are currently volunteer based, we consider a future version employing knowledge workers who are experts in certain topics. In such a system, the request-answer processes forming the queuing system may utilize schedulers that assign requests in different topics to the experts in the forum, who may be able to answer them according to their expertise levels in different topics. With this model, we calculate the capacity of the system for handling the requests while keeping the system stable, and design schedulers that achieve capacity. We also investigate how collaboration between experts in answering requests can potentially increase capacity.

Qualified Educational Capacity Planning under Heterogeneous Student Support Needs: A Synthetic Benchmark and Decision-Support Framework

Educational support services often face a qualified-capacity problem: staff time is scarce, qualifications decay, new support needs can appear before anyone is prepared for them, and training consumes the same hours needed by current students. We introduce a synthetic benchmark and decision-support framework for qualified educational capacity planning. The model is a stylized single-institution service system with heterogeneous support-demand categories, backlog-only dynamics, continuous preparation states with hard threshold qualification and decay, and capacity-consuming training. The benchmark includes seed-controlled scenarios for announced and surprise new support categories, staff absences, and demand surges; exact feasibility discipline; declared per-policy information sets; requalification and greenfield-qualification counters; access-dispersion metrics; replay checksums; and paired statistics. We compare service-only, reactive, static-insurance, water-filling, and rolling-horizon mixed-integer controllers, with an attribution chain separating service planning, qualification maintenance, and acquisition, plus a perfect-foresight reference. The central result is a regime map governed by whether a newly required qualification can be acquired within the controller's reaction reach. When it can, the closed-loop controller wins across the core and adversarial suites, with value concentrated in just-in-time qualification acquisition. When the training lag exceeds the horizon, lean static insurance wins structurally, and a reactive trainer that starts after onset can be worse than no training. Backlog perishability shifts this boundary without erasing either regime. EduCapacity Studio reproduces exported scenarios bit-for-bit. All evidence is stylized and synthetic; the framework makes no claims about real student outcomes, compliance, or individual placements.