Cluster Capacity:
128 GPUs
|
8192 GB RAM
Total Makespan
7,100 ms
Time to final dependency sink
GPU Utilization
89.4 %
Active GPU-time vs allocated window
Avg Waiting Time
620 ms
Mean queue dispatch latency
Completed Jobs
5 / 5
All DAG constraints satisfied
Congestion Events
1
Cross-chassis barrier syncs
Task Dependency Graph (DAG)
State: Optimal Critical Path
Cluster GPU Fabric Matrix (16 Nodes)
Allocation: 28 / 128 GPUs
Discrete-Event Schedule Timeline
Scale: 0 ms — 7,100 ms
0 ms
1,500 ms
3,000 ms
4,500 ms
6,000 ms
7,100 ms
Mathematics to Systems Bridge: Why Graph Theory Shapes AI Infrastructure
In modern multi-tenant AI training clusters, scheduling workflows represented as a Directed Acyclic Graph (DAG) \( G = (V, E) \) is NP-hard.
Algorithms like Critical-Path First (HEFT) compute the bottom-level rank \( rank(v) = w_v + \max_{u \in succ(v)} (c_{v,u} + rank(u)) \), factoring in computation duration \( w_v \) and network communication overhead \( c_{v,u} \) across InfiniBand switches.
Notice how scheduling job_01 and job_02 concurrently reduces the makespan to exactly the longest critical path through job_03 (Distributed Training) and job_04 (AllReduce).