Multi-Bin Batching Framework Overview

• Multi-bin batching framework is a methodology that partitions tasks into multiple bins based on predicted execution properties to optimize performance.
• It integrates queueing-theoretic models, integer programming, and analytical regressions to handle heterogeneous workloads and resource constraints.
• The approach is applied in LLM serving, serverless DNN inference, and combinatorial optimization, achieving significant throughput gains and cost savings.

A multi-bin batching framework is a class of methodologies and algorithms for partitioning tasks, requests, or items into multiple groups (“bins”) in order to optimize throughput, resource utilization, cost, or solution quality under diverse system or application constraints. In modern practice, “multi-bin batching” finds rigorous grounding in DNN and LLM serving systems, accelerator-centric batch execution for control-intensive algorithms, and classic combinatorial optimization models. The unifying objective is to avoid the inefficiencies of single-batch or single-bin policies by intelligently grouping entities sharing similar constraints or predicted execution properties.

1. Formal Definitions and Modelling Approaches

Multi-bin batching frameworks in contemporary systems fall into several mathematically formalized paradigms, the most prominent of which are queueing-theoretic models for parallel serving systems, integer programming for multicontainer optimization, and performance-plus-cost models for heterogeneous resource platforms.

1.1. Queueing-Theoretic Model (LLM Inference)

Requests arrive according to a Poisson process ($\lambda$) and are assigned to one of $k$ bins, where each bin corresponds to a predicted execution time interval $\mathcal{B}_i = [\ell_{i-1}, \ell_i)$. Batches of fixed size $B$ are formed within each bin. The batch service time is $T_{\mathrm{batch}} = \max_{j=1}^{B} L_j$, and the overall throughput is $c = B/\mathbb{E}[T_{\mathrm{batch}}]$. Throughput is maximized when bins partition the request time distribution into equal-probability mass, i.e., $$\ell_i = \ell_{\min} + \frac{i}{k}(\ell_{\max} - \ell_{\min})$$ (Guldogan et al., 2024).

1.2. Multicontainer Integer Programming (Packing/Covering)

Given a set of items with weights (and possibly profits/costs), assign each item to at most one of $m$ bins, each with capacity $C_b$ (packing) or quota $Q_b$ (covering). Decision variables ($x_{bj} \in \{0,1\}$) indicate assignment, and constraints/ objectives enforce capacity, exclusivity, and packing/covering/optimality (Fukunaga et al., 2011).

1.3. Analytical Models for Heterogeneous Serverless Inference

For serverless DNN/LLM inference across CPUs and GPUs, batch latency is estimated via empirical or semi-empirical regressions:

• CPU: $$L_{avg}^c(c,b) = \alpha_b^{avg} \exp(-c/\beta_b^{avg}) + \gamma_b^{avg}$$ (and analogous for $L_{max}$)
• GPU: time-sliced by memory ($m$): $L_{avg}^g(m,b) = \frac{M_{max}}{m} L_0^g(b)$ (Chen et al., 2024).

2. Key Algorithmic Strategies

The current state-of-the-art implements multi-bin batching using either heuristic clustering, structural search (branch-and-bound), or explicit bin-assignment with resource-aware provisioning.

2.1. Binning by Predicted Execution Time

In LLM serving, each incoming request’s predicted workload ($L$) is used to assign it to a bin $\mathcal{B}_i$. Each bin maintains a separate FIFO, and batches are formed strictly within bins, minimizing intra-batch service time variance (Guldogan et al., 2024). Bin boundaries are determined to equalize mass under the empirical or estimated $L$ distribution.

2.2. Optimization-Based Grouping (Resource-Constrained Multi-SLO Inference)

In DNN serverless platforms, applications may differ widely in SLO and arrival rate. HarmonyBatch employs a two-stage greedy merging:

• Stage I: Sequentially groups applications (sorted by SLO) until joint arrival rate triggers cost benefits from GPU use; merges are committed if total cost is reduced.
• Stage II: Fine-tunes GPU-grouped bins, merging adjacent bins if beneficial. Resource provisioning per group selects batch size $b^X$, function type (CPU/GPU), and configuration (vCPU, memory) to minimize long-run per-request cost while respecting all group SLOs (Chen et al., 2024).

2.3. Bin Completion—Branch-and-Bound for Multicontainer Problems

In combinatorial settings, bin-completion search explicitly enumerates maximal feasible (packing) or minimal (covering) bin assignments, recursing on subproblems, and aggressively pruning using dominance and nogood-based criteria. This enables exact solution of MKP, bin covering, and various extensions (Fukunaga et al., 2011).

3. Theoretical Guarantees and Performance Analysis

Performance improvements in multi-bin batching stem from exploiting variability and structure missed by single-bin approaches.

Framework/Domain	Proven Guarantees	Empirical Outcomes
LLM Inference (Guldogan et al., 2024)	Throughput $c_k$ strictly increases with $k$, approaches ideal as $k\to \infty$; O(1) per-request overhead; robustness to binning error	Up to 70% throughput gain; minor latency impact with practical $k$
Serverless DNN (HarmonyBatch) (Chen et al., 2024)	Zero SLO violation under model; up to 82.9% cost savings over single-app batching; merging reduces cost monotonically	SLO violation rate 0%; cost savings up to 83% (vs BATCH), 16–60% (vs MBS⁺)
Multicontainer Packing (Fukunaga et al., 2011)	Correctness; strong dominance–nogood pruning; worst-case O*(2^n), but substantial empirical speedups	Order-of-magnitude inference time reductions; best known for MKP & covering instances

A plausible implication is that the power of multi-bin batching lies in exposing and controlling heterogeneity: execution time variance (LLM), SLO/rate heterogeneity (DNN/serverless), or item attributes (packing/covering).

4. Implementation Details and Systems Integration

4.1. Queue Management and Batching

For LLM inference, each predicted bin instantiates a separate FIFO queue. Upon batch completion (i.e., $B$ queued requests), a batch is dispatched with processing time governed by the maximal predicted length. Implementation sets a max-wait timeout to prevent long-tail latency in under-populated bins; complexity is $O(1)$ per request (Guldogan et al., 2024).

4.2. Resource Provisioning and Group Formation

In HarmonyBatch, initial profiling fits latency models for each model and hardware type. The grouping algorithm computes cost-optimal parameters for each candidate bin via binary search (CPU: convex in vCPU count; GPU: monotonic in batch size and memory). Batch formation is restricted by the SLO of the most latency-sensitive application in the bin (Chen et al., 2024).

4.3. Classic Bin Completion Algorithm

For general multicontainer assignment, bin completion generates all undominated bin assignments for each bin at recursion, leveraging strong value-, variable-, and bound-based heuristics to prune. Nogood-based pruning minimizes redundant search; empirical evidence shows marked runtime improvements (Fukunaga et al., 2011).

5. Experimental Evidence and Quantitative Results

Significant empirical evidence supports the effectiveness of multi-bin batching across application domains.

• LLM Serving: For batch size $B=8$, infinite arrival rate, and varying bin count $k$, throughput increases from 1000 (k=1) to 1600 req/s (k=8). Oracle binning achieves up to 70% throughput gain; BERT-based length prediction model yields an 8% throughput gain with $k=4$ (for >40% with perfect binning). Throughput improves for moderate $k$; latency increases remain controlled (Guldogan et al., 2024).
• Serverless DNN Inference: HarmonyBatch reduces cost by up to 82.9% vs. single-app batching, and by 16–60% compared to SLO-agnostic multi-app batching. SLO violation rates remain zero, while baseline approaches exhibit up to 30% violations. Grouping overhead is negligible (<50 ms for 12 apps); profiling overhead is several minutes per model (Chen et al., 2024).
• Multicontainer Packing: Bin completion algorithms with dominance and nogood pruning reduce solution times by up to three orders of magnitude on benchmark MKP/min-cost covering/covering instances. For instance, average time for $n=20, m=7$ MKP is 0.0043s versus 1.57s for MTM (Fukunaga et al., 2011).

6. Limitations, Extensions, and Future Directions

• LLM inference frameworks must address starvation in low-traffic bins; max-wait timeouts provide mitigation, but dynamic bin adaptation is an open area. Multiple-server scaling requires load-balancing extensions (Guldogan et al., 2024).
• In the multi-SLO serverless context, current models assume infinite buffer per bin, and extension to memory-capped or on-the-fly drop-capable systems is noted as future work. Expansion to sharded or pipeline-parallel large-model scenarios is ongoing (Chen et al., 2024).
• Bin completion is limited by the combinatorial cost of generating all undominated bin assignments; enhancements include hybrid incremental branching and depth-limited pruning. For the classic bin packing problem, decomposition-based (cutting-stock) methods outperform bin-completion for very large instances (Fukunaga et al., 2011).

The unified multi-bin batching framework thus encompasses distinct algorithmic traditions—queue partitioning by predicted workload, SLO/rate-aware merging and batch sizing, and combinatorial multicontainer optimization—each yielding significant provable and empirical gains in resource utilization, throughput, and/or cost. Leading implementations now span from LLM serving infrastructure to serverless DNN deployment and large-scale optimization, with theoretical, algorithmic, and system-level extensions continuing to advance the state of the art.