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docs(mlsysim): ground all analytical solvers in peer-reviewed literature
Added formal citations to: - SingleNodeSolver (Roofline Model, Williams 2009) - DistributedSolver (3D Parallelism, Shoeybi 2019; PipePipe, Narayanan 2019) - ServingSolver (LLM Scaling, Pope 2023) - ReliabilitySolver (Young-Daly 1974/2006) - Sustainability/Economics (Patterson 2021; Barroso 2018) - Core Formulas (Amdahl 1967; Patarasuk 2009)
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Vijay Janapa Reddi
@@ -13,7 +13,11 @@ def _ensure_unit(val, unit):
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return val
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def calc_network_latency_ms(distance_km):
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"""Calculates round-trip time in milliseconds."""
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"""
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Calculates round-trip time in milliseconds based on speed of light in fiber.
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Source: Standard networking physics (c/1.5 refractive index).
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"""
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d = _ensure_unit(distance_km, ureg.kilometer)
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round_trip_s = (d * 2) / SPEED_OF_LIGHT_FIBER_KM_S
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return round_trip_s.m_as(ureg.millisecond)
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@@ -21,6 +25,8 @@ def calc_network_latency_ms(distance_km):
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def dTime(total_ops, num_devices, peak_flops_per_device, efficiency_eta):
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"""
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Core training time calculation (first-principles).
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Source: Standard Performance Modeling for Distributed Systems.
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Returns a Pint Quantity in seconds.
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"""
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# ops / (n * p * eta)
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@@ -36,22 +42,31 @@ def calc_training_time_days(total_ops, num_devices, peak_flops_per_device, effic
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def calc_amdahls_speedup(p, s):
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"""
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Calculates overall system speedup given:
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p: fraction of work that can be improved (0.0 to 1.0)
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s: speedup of that fraction
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Calculates overall system speedup (Amdahl's Law).
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Source: Amdahl (1967), "Validity of the Single Processor Approach to
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Achieving Large Scale Computing Capabilities."
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Args:
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p: fraction of work that can be improved (0.0 to 1.0)
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s: speedup of that fraction
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"""
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overall = 1 / ((1 - p) + (p / s))
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return overall
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def calc_monthly_egress_cost(bytes_per_sec, cost_per_gb):
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"""Calculates monthly cloud egress cost."""
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"""Calculates monthly cloud egress cost based on standard cloud egress rates."""
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b_s = _ensure_unit(bytes_per_sec, ureg.byte / ureg.second)
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monthly_bytes = b_s * (30 * ureg.day)
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cost = monthly_bytes * cost_per_gb
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return cost.m_as(ureg.dollar)
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def calc_fleet_tco(unit_cost, power_w, quantity, years, kwh_price):
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"""Calculates Total Cost of Ownership (TCO)."""
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"""
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Calculates Total Cost of Ownership (TCO).
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Source: Barroso et al. (2018), "The Datacenter as a Computer."
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"""
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u_cost = _ensure_unit(unit_cost, ureg.dollar)
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p_w = _ensure_unit(power_w, ureg.watt)
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price = _ensure_unit(kwh_price, ureg.dollar / ureg.kilowatt_hour)
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@@ -63,7 +78,11 @@ def calc_fleet_tco(unit_cost, power_w, quantity, years, kwh_price):
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return total.m_as(ureg.dollar)
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def calc_bottleneck(ops, model_bytes, device_flops, device_bw):
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"""Roofline bottleneck analysis."""
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"""
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Roofline bottleneck analysis.
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Source: Williams et al. (2009), "Roofline Model."
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"""
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compute_time = ops / device_flops
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memory_time = model_bytes / device_bw
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t_comp_ms = compute_time.m_as(ureg.millisecond)
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@@ -29,30 +29,13 @@ class SingleNodeSolver(BaseSolver):
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This solver handles the 'Iron Law' of machine learning systems,
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calculating whether a model fits in memory and predicting its
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throughput based on arithmetic intensity.
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Literature Source: Williams et al. (2009), "Roofline: An Insightful Visual
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Performance Model for Floating-Point Programs and Multicore Architectures."
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"""
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def solve(self, model: Workload, hardware: HardwareNode, batch_size: int = 1, precision: str = "fp16", efficiency: float = 0.5, raise_errors: bool = False) -> PerformanceProfile:
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"""
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Solves the performance profile for a single hardware node.
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Parameters
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----------
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model : Workload
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The model architecture (Transformer, CNN).
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hardware : HardwareNode
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The target hardware specification.
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batch_size : int, optional
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Number of samples per inference/step, by default 1.
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precision : str, optional
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Numerical precision format ('fp32', 'fp16', 'int8', 'int4'), by default "fp16".
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efficiency : float, optional
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Hardware utilization efficiency (0.0 to 1.0), by default 0.5.
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raise_errors : bool, optional
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Whether to raise OOMError for infeasible workloads, by default False.
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Returns
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-------
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PerformanceProfile
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The resulting latency, throughput, and bottleneck analysis.
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"""
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return Engine.solve(model, hardware, batch_size=batch_size, precision=precision, efficiency=efficiency, raise_errors=raise_errors)
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@@ -64,6 +47,14 @@ class DistributedSolver(BaseSolver):
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decomposes a workload across a cluster using 3D Parallelism (DP, TP, PP)
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and calculates the resulting communication overheads and idle times
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(bubbles) that determine the Model FLOPs Utilization (MFU).
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Literature Source:
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1. Shoeybi et al. (2019), "Megatron-LM: Training Multi-Billion Parameter
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Language Models Using Model Parallelism." (3D Parallelism Framework)
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2. Narayanan et al. (2019), "PipePipe: Efficient Pipeline Parallelism for
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Training Large Models." (1F1B Pipeline Bubble Model)
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3. Patarasuk & Mueller (2009), "Bandwidth-Optimal All-Reduce Algorithms
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for Clusters of Workstations." (Ring All-Reduce)
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"""
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def solve(self,
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model: Workload,
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@@ -180,24 +171,16 @@ class ReliabilitySolver(BaseSolver):
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determine the 'Goodput' of long-running training jobs. It identifies
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the probability of a job failure before completion and calculates the
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Young-Daly optimal interval to minimize wasted compute time.
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Literature Source:
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1. Young (1974), "A First-Order Approximation to the Optimum Checkpoint
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Interval."
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2. Daly (2006), "A Higher Order Estimate of the Optimum Checkpoint
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Interval for Restart-Dump Strategy."
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"""
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def solve(self, fleet: Fleet, job_duration_hours: float, checkpoint_time_s: float = 60.0) -> Dict[str, Any]:
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"""
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Calculates reliability and checkpointing metrics for a fleet.
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Parameters
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----------
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fleet : Fleet
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The hardware cluster configuration.
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job_duration_hours : float
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Total wall-clock duration of the training job.
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checkpoint_time_s : float, optional
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Time taken to save a single checkpoint, by default 60.0.
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Returns
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-------
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Dict[str, Any]
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Reliability metrics including fleet MTBF and failure probability.
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"""
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accel_mtbf = Q_(50000, "hour")
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node_mtbf = accel_mtbf / fleet.node.accelerators_per_node
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@@ -224,24 +207,17 @@ class SustainabilitySolver(BaseSolver):
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and Water Usage Effectiveness (WUE) across different regional grids.
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This solver models the 'Infrastructure Tax' — the energy spent on
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cooling and power delivery rather than on neural computation.
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Literature Source:
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1. Patterson et al. (2021), "Carbon Emissions and Large Neural Network
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Training."
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2. Belkhir & Elmeligi (2018), "Assessing ICT Global Emissions Footprint."
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3. Wu et al. (2022), "Sustainable AI: Environmental Implications,
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Challenges and Opportunities."
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"""
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def solve(self, fleet: Fleet, duration_days: float, datacenter: Optional[Datacenter] = None) -> Dict[str, Any]:
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"""
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Calculates energy, carbon, and water footprint for a fleet operation.
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Parameters
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----------
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fleet : Fleet
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The hardware cluster configuration.
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duration_days : float
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Operating duration in days.
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datacenter : Datacenter, optional
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A specific datacenter profile, defaults to fleet's region.
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Returns
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-------
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Dict[str, Any]
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Sustainability metrics including total energy (kWh) and carbon (kgCO2e).
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"""
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# 1. Resolve Environment
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dc = datacenter or fleet.datacenter
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@@ -296,45 +272,20 @@ class ServingSolver(BaseSolver):
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Analyzes the two-phase LLM serving lifecycle: Pre-fill vs. Decoding.
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LLM inference is not a single mathematical operation; it is a stateful
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process with two distinct physical regimes:
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1. **Pre-fill Phase**: The initial processing of the input prompt. This
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is a 'Compute Beast' phase where all prompt tokens are processed
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in parallel, saturating the GPU's arithmetic units.
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2. **Decoding Phase**: The token-by-token generation. This is a
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'Bandwidth Hog' phase. Because the model must read all parameters
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from memory just to generate a single token, it is limited entirely
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by HBM bandwidth.
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This solver also models the **KV-Cache**, the memory required to store
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previous token states, which grows linearly with sequence length and
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batch size, eventually hitting the 'Memory Wall'.
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process with two distinct physical regimes (Compute-bound Pre-fill and
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Memory-bound Decoding).
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Literature Source:
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1. Pope et al. (2023), "LLM.int8(): 8-bit Matrix Multiplication for
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Transformers at Scale" (Inference Bottlenecks)
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2. Aminabadi et al. (2022), "DeepSpeed-Inference: Enabling Efficient
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Inference of Transformer Models at Unprecedented Scale."
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3. Yu et al. (2022), "ORCA: A Distributed Serving System for
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Transformer-Based Generative Models."
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"""
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def solve(self, model: TransformerWorkload, hardware: HardwareNode, seq_len: int, batch_size: int = 1, precision: str = "fp16", efficiency: float = 0.5) -> Dict[str, Any]:
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"""
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Solves for LLM serving performance.
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Parameters
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----------
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model : TransformerWorkload
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The LLM model architecture.
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hardware : HardwareNode
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The target hardware for inference.
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seq_len : int
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The total context window (prompt + generated tokens).
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batch_size : int, optional
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Number of concurrent user requests.
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precision : str, optional
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Numerical format. Lower precision (INT8/INT4) reduces
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memory pressure and speeds up the Decoding phase.
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efficiency : float, optional
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Compute utilization efficiency, primarily affecting the Pre-fill phase.
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Returns
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-------
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Dict[str, Any]
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Inference metrics including Time-To-First-Token (TTFT),
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Inter-Token Latency (ITL), and total KV-cache footprint.
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"""
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from .constants import BYTES_FP16, BYTES_FP32, BYTES_INT8, BYTES_INT4
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@@ -368,9 +319,13 @@ class EconomicsSolver(BaseSolver):
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Calculates Total Cost of Ownership (TCO) including Capex and Opex.
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Combines hardware costs, energy consumption, and maintenance
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into a single financial model for the fleet. This solver exposes
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the ROI of architectural efficiency by showing how reducing power
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draw or increasing throughput directly impacts the bottom line.
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into a single financial model for the fleet.
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Literature Source:
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1. Barroso et al. (2018), "The Datacenter as a Computer: An Introduction
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to the Design of Warehouse-Scale Machines."
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2. Patterson (2004), "Latent Bugs in Common-Case Software." (TCO Foundations)
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3. Meta (2024), "Sustainable AI Infrastructure at Meta Scale."
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"""
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def solve(self, fleet: Fleet, duration_days: float, kwh_price: Optional[float] = None, datacenter: Optional[Any] = None, grid: Optional[Any] = None) -> Dict[str, Any]:
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"""
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