LLM Serving at Scale: Prefill, Decode & Continuous Batching

A systems mental model for LLM inference: prefill vs decode, TTFT vs TPOT, batching/scheduling, and why KV cache memory dominates.

published · difficulty 4/5 · 22 min read

Reading map and next steps

Intuition

Build the mental picture first so the rest of the page has something to attach to.

PredictName the object in plain language, then predict what should change.Leave with one reusable mental picture before notation appears.

Serving an LLM is not "run the model once." It's running the model for many users at once, while trying to keep latency low and the GPU busy.

Two phases dominate everything:

Prefill: process the prompt in parallel (big matrix multiplies, lots of compute).
Decode: generate one token at a time (small matmuls, but heavy KV cache reads).

This is why a system can feel fast on short prompts but collapse on long context: decode becomes memory-bandwidth bound, and the KV cache becomes the main resource you schedule around.

The practical goal is not raw throughput. It's goodput: how many requests you can serve while meeting latency SLOs.

Section prompt

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Math

Translate the story into symbols, assumptions, and a derivation you can inspect.

InspectTrack the same object through the notation and check each symbol.Leave with the invariant the equations preserve.

Equation 1Inspect equation objectLatency \approx \underbrace{TTFT}_{time to first token} + (T_{out}-1)\cdot\underbrace{TPOT}_{...Equation 2Inspect equation objectMem_{KV} \approx B\cdot L\cdot T\cdot H_{kv}\cdot d_{head}\cdot 2 \cdot bytes.Equation 3Inspect equation objectGoodput = Throughput \times \Pr (TTFT <= S_{TTFT} \wedge TPOT <= S_{TPOT}).

Latency decomposition (a serving mental model)

Let $T_{out}$ be the number of generated tokens. A simple but useful decomposition is:

\text{Latency} \approx \underbrace{\text{TTFT}}_{\text{time to first token}} + (T_{out}-1)\cdot\underbrace{\text{TPOT}}_{\text{time per output token}}.

In this serving mental model, TTFT often tracks prefill.
TPOT often tracks decode (and KV cache reads).

KV cache memory scaling (why long prompts hurt)

Across a batch of $B$ sequences and $L$ layers, storing keys and values for $T$ tokens costs roughly:

\mathrm{Mem}_{KV} \approx B\cdot L\cdot T\cdot H_{kv}\cdot d_{head}\cdot 2 \cdot \mathrm{bytes}.

The factor of 2 is for storing both $K$ and $V$ .

Goodput (a serving SLO mental model)

If you have SLO thresholds $S_{TTFT}, S_{TPOT}$ , a common objective is:

\text{Goodput} = \text{Throughput} \times \Pr\!\left(\text{TTFT} \le S_{TTFT} \wedge \text{TPOT} \le S_{TPOT}\right).

This captures the reality that "fast on average" is not good enough if tail latency violates SLOs.

Paging / fragmentation waste

If KV memory is allocated in blocks/pages of size $P$ (tokens per block), then for a sequence length $T$ :

\text{allocated}(T) = \left\lceil \frac{T}{P} \right\rceil P,\qquad \text{waste}(T) = \text{allocated}(T) - T.

Block-based allocators (PagedAttention-style) make growth predictable and reduce fragmentation under continuous batching.

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Code

Keep the implementation aligned with the notation so the algorithm is legible.

TraceMatch variables to symbols before reading the implementation.Leave with a runnable witness for the math.

Code witness 1import numpy as np def kv_gb(T, layers, h_kv, d_head, batch=1, bytes_per_elem=2): elems = bat...python

import numpy as np

def kv_gb(T, layers, h_kv, d_head, batch=1, bytes_per_elem=2):
    elems = batch * layers * T * h_kv * d_head * 2  # K and V
    return elems * bytes_per_elem / 1e9

def waste_tokens(T, P):
    return int(np.ceil(T / P) * P - T)

L, Hkv, dh, B = 80, 8, 128, 16  # example: 80 layers, GQA with 8 KV heads, fp16
for T in [2048, 8192, 32768, 131072]:
    print("T=", T, "KV~", round(kv_gb(T, L, Hkv, dh, batch=B), 2), "GB")

P = 256  # tokens per page/block
for T in [2000, 8192, 20000]:
    print("T=", T, "waste_tokens=", waste_tokens(T, P))

Section prompt

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Interactive Demo

Use direct manipulation to connect the explanation to a moving system.

ManipulateChange one control and predict the visible response before reveal.Leave with the observed invariant or a repaired model.

Live Concept Demo

Explore LLM Serving at Scale: Prefill, Decode & Continuous Batching

The stage is code-native and interactive. Use it to test the explanation against the mechanism.

difficulty 4/5undergraduatecode-aligned

Demo inquiry checkpoint

Manipulate one control and predict the visible change.

01Choose lensTrace a quantity

02ObserveDemo state pending

03GroundName the equation, invariant, or control that explains it.

04CarryNext: Speculative Decoding: Lossless Multi-Token Generation

Choose what to inspect in LLM Serving at Scale: Prefill, Decode & Continuous Batching. This shared fallback is an observation guide, not evidence of learning.

Loading interactive demo...

Use the demo to explore TTFT vs TPOT tradeoffs, how batching affects goodput, and how repeated KV cache reads shape decode latency in this toy lab.

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Object

4/4 sections ready

Concept: LLM Serving at Scale: Prefill, Decode & Continuous Batching

What is the smallest example that makes LLM Serving at Scale: Prefill, Decode & Continuous Batching click without losing the math?

BeforeScaled Dot-Product Attention & Transformer LayersNow4/4 sections readyTryManipulate one control and predict the visible change.NextSpeculative Decoding: Lossless Multi-Token Generation

Object contextLLM Systems

StateLLM Systems

2 sources attachedChecking local snapshot

concept:llm-systems/llm-serving

Math3 equation objectsLatency \approx \underbrace{TTFT}_{time to first token} + (T_{out}-1)\cdot\underbrace{TPOT}_{...CodeLLM Serving at Scale: Prefill, Decode & Continuous Batching code witn...elems = batch * layers * T * h_kv * d_head * 2 # K and V DemoLLM Serving at Scale: Prefill, Decode & Continuous Batching predictionManipulate one control and predict the visible change.

ConceptLearner lens

LLM Serving at Scale: Prefill, Decode & Continuous Batching

What is the smallest example that makes LLM Serving at Scale: Prefill, Decode & Continuous Batching click without losing the math?

Mode questionCan I say the mechanism back in one sentence before I reveal anything?

Start with the prediction checkpoint, then compare the reveal to the mental model.

Take this move

Study modes

Keep the object fixed; change the lens.

01PredictCommit before reveal.02ExplainName the invariant.03Ground2 source links nearby.04ExperimentChange one knob.05CarrySave the next question.

Route back through the notebook

Carry the same object through intuition, math, code, and demo.

4/4 sections ready

Carry inScaled Dot-Product Attention & Transformer Layers

Bring the mental model from Scaled Dot-Product Attention & Transformer Layers; this page will reuse it instead of restarting from zero.

Work hereLLM Serving at Scale: Prefill, Decode & Continuous Batching

A systems mental model for LLM inference: prefill vs decode, TTFT vs TPOT, batching/scheduling, and why KV cache memory dominates.

Carry outSpeculative Decoding: Lossless Multi-Token Generation

The next edge should feel earned: use the demo prediction here before following Speculative Decoding: Lossless Multi-Token Generation.

After The First Pass

Turn the concept into an inspected object.

The lower panels are one second act: keep the object fixed, inspect it visually, check source boundaries, practice transfer, then attach the research question.

ConceptLLM Serving at Scale: Prefill, Decode & Continuous BatchingLLM Systems

01MechanismInspect motionSee how the idea changes form before adding more explanation.02VisualChoose a cueBind one visible mark to one mathematical role.03SourcesCheck boundary2 source links attached to the object.04ClaimAudit evidenceTreat the page claim as something to verify.05PracticeAttempt transferWrite before feedback so the model has something to repair.06RoomAsk groundedAttach the question to the same exact object.

Mechanism Storyboard

See the idea move before the page explains it

A systems mental model for LLM inference: prefill vs decode, TTFT vs TPOT, batching/scheduling, and why KV cache memory dominates.

Demo notes open01 / Intuition

Editorial systems illustration of prefill, KV cache shelves, continuous batching lanes, and decode token streams.

Prediction lens

Start with the picture, metaphor, or geometric mechanism.

Commit first

Before reading further, choose the kind of change LLM Serving at Scale: Prefill, Decode & Continuous Batching should make visible.

Visual Inquiry

Make the image answer a mathematical question

A systems mental model for LLM inference: prefill vs decode, TTFT vs TPOT, batching/scheduling, and why KV cache memory dominates.

4/4 stages readyDemo notes connected

Visual cueWhich visible object should carry the first intuition?

Inspection depth2/4

Prediction

Which visible object should carry the first intuition?

Commit first

Pick the cue that should make LLM Serving at Scale: Prefill, Decode & Continuous Batching easier to reason about before the page gives the answer.

Source Grounding

Canonical references for the mechanism on this page.

Object - ConceptLLM Serving at Scale: Prefill, Decode & Continuous BatchingQuestion

What is the smallest example that makes LLM Serving at Scale: Prefill, Decode & Continuous Batching click without losing the math?

concept:llm-systems/llm-serving

Boundary

sources: yu-2022-orca, kwon-2023-pagedattention

Check

Open the closest source note before trusting the local explanation.

Evidence

2 selected-object sources shown first; 2 references total.

Next move

Audit the claim boundary, then ask from the same selected object.

selected object source · paper · 2022Orca: A Distributed Serving System for Transformer-Based Generative ModelsYu et al.

Located CF editorial boundary

Primary serving-scheduler source. Orca frames generative transformer inference as multi-iteration autoregressive serving, where each iteration generates one output token, and proposes iteration-level scheduling plus selective batching.

Used here as

Orca supports the scheduling part: generative Transformer serving is multi-iteration autoregressive inference with one output token per iteration, and fixed request-level batches motivate...

Caveat

Checks the serving mechanism only. TTFT/TPOT, goodput, KV formula, code, and demo are toy witnesses, not source-derived formulas or production benchmarks. Does not certify vendor latency,...

Open source

selected object source · paper · 2023Efficient Memory Management for Large Language Model Serving with PagedAttentionKwon et al.

Located CF editorial boundary

Primary KV-cache serving source. PagedAttention frames high-throughput LLM serving as constrained by huge dynamically growing KV caches, fragmentation, batch-size limits, and paged block allocation.

Used here as

Orca supports the scheduling part: generative Transformer serving is multi-iteration autoregressive inference with one output token per iteration, and fixed request-level batches motivate...

Caveat

Checks the serving mechanism only. TTFT/TPOT, goodput, KV formula, code, and demo are toy witnesses, not source-derived formulas or production benchmarks. Does not certify vendor latency,...

Open source

Claim Review

A systems mental model for LLM inference: prefill vs decode, TTFT vs TPOT, batching/scheduling, and why KV cache memory dominates.

Object - ConceptLLM Serving at Scale: Prefill, Decode & Continuous BatchingQuestion

What is the smallest example that makes LLM Serving at Scale: Prefill, Decode & Continuous Batching click without losing the math?

concept:llm-systems/llm-serving

Boundary

sources: yu-2022-orca, kwon-2023-pagedattention

Check

Treat every claim as provisional until source support and a local witness agree.

Evidence

1 structured claim check on this concept.

Next move

Run the prediction or practice transfer before asking for a grounded review.

1 CF editorial source-scope review recorded

Publisher-side editorial review is not independent replication. Claims without it still need exact source-support review. 2 references and 3 local witnesses are available for inspection.

LLM serving is a multi-iteration scheduling and memory-management problem: autoregressive decode advances one token at a time, batching must adapt between iterations, and KV cache memory can limit throughput.

Registered CF editorial boundary

Orca: A Distributed Serving System for Transformer-Based Generative ModelsPrimary serving-scheduler source. Orca frames generative transformer inference as multi-iteration autoregressive serving, where each iteration gene...Efficient Memory Management for Large Language Model Serving with PagedAttentionPrimary KV-cache serving source. PagedAttention frames high-throughput LLM serving as constrained by huge dynamically growing KV caches, fragmentat...

Used here as

Orca supports the scheduling part: generative Transformer serving is multi-iteration autoregressive inference with one output token per iteration, and fixed request-level batches motivate iteration-level sch...

Local witness

source-span-yu-2022-orca source-span-kwon-2023-pagedattention math-object-1 math-object-2 code-witness-1 interactive-demo

Equation 1

\text{Latency} \approx \underbrace{\text{TTFT}}_{\text{time to first token}} + (T_{out}-1)\cdot\underbrace{\text{TPOT}}_{\text{time per output token}}.

Equation 2

\mathrm{Mem}_{KV} \approx B\cdot L\cdot T\cdot H_{kv}\cdot d_{head}\cdot 2 \cdot \mathrm{bytes}.

Caveat

Checks the serving mechanism only. TTFT/TPOT, goodput, KV formula, code, and demo are toy witnesses, not source-derived formulas or production benchmarks. Does not certify vendor latency, scheduler optimalit...

Review stateCF editorial source-scope reviewClaim metadata: source checkedPublisher-side editorial review only; not independent replication. Check caveats and exact source scope.

Checked Orca and PagedAttention: Orca supports autoregressive generative Transformer serving as multi-iteration inference where each iteration emits one token, motivating iteration-level scheduling and selective batching because fixed request-level batches waste capacity. PagedAttention supports KV cache memory as large, dynamic, fragmentation-prone state that can limit batch size and throughput. Local latency/KV math, code, and demo are toy serving witnesses only.

Reviewer: codex+oracle; reviewed 2026-05-07

Practice · LLM Serving at Scale: Prefill, Decode & Continuous Batching

Try the idea in your own words

A systems mental model for LLM inference: prefill vs decode, TTFT vs TPOT, batching/scheduling, and why KV cache memory dominates.

Concept · Current object

LLM Serving at Scale: Prefill, Decode & Continuous Batching

Source boundary: sources: yu-2022-orca, kwon-2023-pagedattention

Object context and links

LLM Systems

concept:llm-systems/llm-serving

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Explain the mechanism

For LLM Serving at Scale: Prefill, Decode & Continuous Batching: What is the smallest example that makes LLM Serving at Scale: Prefill, Decode & Continuous Batching click without losing the math? Explain your answer, including what changes, why, and which assumption matters.

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Grounded object roomClose

Selected object routeAsk from this object; carry one invariant back.sources: yu-2022-orca, kwon-2023-pagedattention

ObjectConceptLLM Serving at Scale: Prefill, Decode & Continuous Batching
PredictBefore revealLLM Serving at Scale: Prefill, Decode & Continuous Batching prediction
WitnessCompare codeLLM Serving at Scale: Prefill, Decode & Continuous Batching code witn...
RoomAsk groundedChecking local snapshot

ConceptLLM Serving at Scale: Prefill, Decode & Continuous BatchingLLM Systems

Code witness comparisonLLM Serving at Scale: Prefill, Decode & Continuous Batching code witness 1elems = batch * layers * T * h_kv * d_head * 2 # K and V Prediction before revealLLM Serving at Scale: Prefill, Decode & Continuous Batching predictionManipulate one control and predict the visible change.

Grounded room questionWhat is the smallest example that makes LLM Serving at Scale: Prefill, Decode & Continuous Batching click without losing the math?Checking local snapshot

Research Room

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conceptLLM Systems

LLM Serving at Scale: Prefill, Decode & Continuous Batching

Anchored question

What is the smallest example that makes LLM Serving at Scale: Prefill, Decode & Continuous Batching click without losing the math?

Source boundaryInspect source ids: yu-2022-orca, kwon-2023-pagedattentionStable content-object key attached

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Learner evidence requestAsk what would make "LLM Serving at Scale: Prefill, Decode & Continuous Batching" feel predictable rather than familiar.

Assumption

Source ids yu-2022-orca, kwon-2023-pagedattention must support the exact object, not just the surrounding topic.

Source-checking summary

Treat this as a mechanism object: connect the definition to one equation, code witness, or demo before broadening the discussion.

Proposed experiment

Ask the learner to perturb one representation, then check whether the same invariant survives in math, code, and demo.

Next action

The learner can state the mechanism in their own words

Evidence4 checks

PredictionChecking carried observation

ActionReady for one action

AILearner handoff ready

Open source object

01PredictionChecking browser-local route memory

02EvidenceChecking for a carried observation

03BoundaryInspect source ids: yu-2022-orca, kwon-2023-pagedattention

04Next moveSave one next action

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Evidence to inspect

Source ids to inspect: yu-2022-orca, kwon-2023-pagedattention
Definition, prerequisite, and contrast concept links
The equation or code witness that makes the concept operational
One demo state that shows the invariant instead of a slogan

What would resolve this

The learner can state the mechanism in their own words
The learner can name the prerequisite that would repair confusion
The learner can predict how the mechanism changes under one perturbation

Object-attached AI handoff

I am working in Continuous Function's research reading room. Object: concept - LLM Serving at Scale: Prefill, Decode & Continuous Batching Object key: concept:llm-systems/llm-serving Context: LLM Systems Anchor id: concept/concept-notebook/llm-systems/llm-serving Open question: What is the smallest example that makes LLM Serving at Scale: Prefill, Decode & Continuous Batching click without losing the math? Evidence to inspect: - Source ids to inspect: yu-2022-orca, kwon-2023-pagedattention - Definition, prerequisite, and contrast concept links - The equation or code witness that makes the concept operational - One demo state that shows the invariant instead of a slogan Deterministic role lenses for this object: - Boundary: fixed perspectives, not people, community contributions, or independent review - Source-checking summary: Treat this as a mechanism object: connect the definition to one equation, code witness, or demo before broadening the discussion. - Proposed experiment: Ask the learner to perturb one representation, then check whether the same invariant survives in math, code, and demo. - Teach/transfer move: Turn the mechanism into one sentence that predicts a neighboring concept. - Assumptions: - Source ids yu-2022-orca, kwon-2023-pagedattention must support the exact object, not just the surrounding topic. - The stable content-object key lets local drafts, prompts, and route memory attach without changing the source page. - The concept explanation is local atlas prose until checked against its math, code, and source support. - Prerequisite gaps should become a repair route, not a reason to leave the object vague. - Role-lens requests: - Learner: ask for "Ask what would make "LLM Serving at Scale: Prefill, Decode & Continuous Batching" feel predictable rather than familiar." | assumption: Source ids yu-2022-orca, kwon-2023-pagedattention must support the exact object, not just the surrounding topic. | next action: The learner can state the mechanism in their own words - Researcher: ask for "Source ids to inspect: yu-2022-orca, kwon-2023-pagedattention" | assumption: The stable content-object key lets local drafts, prompts, and route memory attach without changing the source page. | next action: The learner can name the prerequisite that would repair confusion - Experimenter: ask for "Choose one variable or condition to perturb before asking for an explanation." | assumption: The concept explanation is local atlas prose until checked against its math, code, and source support. | next action: The learner can predict how the mechanism changes under one perturbation - Professor: ask for "Find the smallest transferable rule a learner could reuse without the AI." | assumption: Prerequisite gaps should become a repair route, not a reason to leave the object vague. | next action: Teach or transfer: Turn the mechanism into one sentence that predicts a neighboring concept. What would resolve this: - The learner can state the mechanism in their own words - The learner can name the prerequisite that would repair confusion - The learner can predict how the mechanism changes under one perturbation Answer as a careful research tutor: stay source-grounded, separate verified evidence from assumptions, name the relevant math objects, and end with one next action. Current deterministic role lens for this object: - Role lens: Learner - Evidence request: Ask what would make "LLM Serving at Scale: Prefill, Decode & Continuous Batching" feel predictable rather than familiar. - Assumption to keep visible: Source ids yu-2022-orca, kwon-2023-pagedattention must support the exact object, not just the surrounding topic. - Proposed experiment: Ask the learner to perturb one representation, then check whether the same invariant survives in math, code, and demo. - Next action: The learner can state the mechanism in their own words

concept/concept-notebook/llm-systems/llm-serving
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Reading map

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Speculative Decoding: Lossless Multi-Token Generation

Connections and sources

Domain

LLM Systems

llm-systems
serving
batching
kv-cache
latency

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A systems mental model for LLM inference: prefill vs decode, TTFT vs TPOT, batching/scheduling, and why KV cache memory dominates.

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Context prompt

You are my AI learning companion for Continuous Function. Current context: LLM Systems concept. Learning surface: LLM Serving at Scale: Prefill, Decode & Continuous Batching. What this page says: A systems mental model for LLM inference: prefill vs decode, TTFT vs TPOT, batching/scheduling, and why KV cache memory dominates. Current section: Intuition, math, code, and interactive demo. Suggested next step: Manipulate one control and predict the visible change.. Learner goal: Understand the idea. Learner comfort level: New to this. Preferred explanation style: Visual first. Task: Explain the central idea in plain language, then restate it with the exact math objects from the page. Answer in a way that helps me learn: ask one clarifying question only if needed, use intuition before notation, and end with one thing I should try on the page.

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