# Algorithmic Techniques for GPU Scheduling: A Comprehensive Survey
## 3 Scheduling Algorithms and Their Performance
### PDE-Driven HPC Workloads  
Many scientific applications--such as compressible-flow hydrodynamics, finite-difference time-domain (FDTD) electrodynamics, magnetohydrodynamic plasma, and seismic wave propagation--solve systems of coupled partial differential equations (PDEs) [175; 176; 177]. Their execution characteristics differ markedly from the bursty, heterogeneous DL workloads discussed earlier [180]. Execution Pattern: PDE solvers are typically long-lived, tightly coupled MPI applications, where each simulation timestep alternates between compute-intensive stencil updates and communication phases--such as halo exchanges or collective reductions--resulting in a highly regular compute/communication cadence. Wall-clock durations can range from a few minutes for explicit computational fluid dynamics loops to several days for global climate ensemble runs. Job sizes scale from a single multi-GPU server to full multi-rack deployments [181]. \begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**System** & **Workload/Testbed** & **Representative Absolute Metrics** \\ \hline Tiresias-G, & 64-GPU ImageNet-style & Average queueing delay: 1005 s (G), 963 s (L); median 39 s/13 s. \\ Tiresias-L & training trace & Small-job ICT: 330 s (G), 300 s (L). Workload makespan: 27, 510\(\sim\)27, 400 s vs. 33, 270 s (YARN-CS baseline). \\ \hline \multirow{2}{*}{Llumnix}{Lumnix} & 16\(\times\) LLaMA-7B inference & Live-migration downtime: 20\(\sim\)30 ms vs. 3.5 s recompute. P99 first-token latency: up to 15\(\times\) lower than INFaaS. Up to 36\% fewer instances at equal P99 latency. \\ \hline \multirow{2}{*}{Pollux (\(p=-1\))} & 64-GPU synthetic training workload & Average JCT: 0.76 h; P99 JCT: 11 h; makespan: 16 h. \\ \hline \multirow{2}{*}{DL2} & 64-GPU parameter-server testbed & Scheduler latency: 0.7 s. GPU utilization: 78\% (\(\uparrow\) 16\% vs. DRF). Scaling overhead: 0.4\% of total training time. \\ \hline \multirow{2}{*}{Lyra} & 15-day simulation (3544 GPU training + 4160 GPU inference) & Average queueing time: 2010 s vs. 3072 s (FIFO). Average JCT: 11, 236 s vs. 16, 610 s. Cluster utilization: 86\% vs. 72\%. \\ \hline \multirow{2}{*}{Chronus} & 120-GPU Kubernetes prototype & Deadline-miss rate: 5\% (\(\approx\)14.7\(\times\downarrow\) vs. prior). Pending time cut from 2105 s to 960 s. Best-effort JCT: up to 19.9\(\times\) faster. \\ \hline \multirow{2}{*}{Helios} & 1 GPU + 12 SSD GNN training & Throughput: up to 6.4\(\times\) GIDS, 182\(\times\) Ginex. Saturates PCIe version 4.0 \(\times\) 16 with 6 SSDs; 91\(\sim\)99\% of in-memory throughput on PA dataset. \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Absolute performance summary of representative GPU scheduling systems. Metrics are reported exactly as published; queueing delay and job completion time (JCT) are in seconds unless otherwise noted (\(\uparrow\) means higher/better, \(\downarrow\) means lower/better). Resource footprint: The core kernels are predominantly memory-bandwidth bound, often saturating the node-local interconnect during collective operations [182]. After the initial field data is staged, host-device transfers largely subside, making PCIe throughput a negligible factor during steady-state execution [183]. Scheduling implications: Because runtime variance is low once mesh resolution and timestep are fixed, these workloads are well suited to static bin-packing or partitioned MILP schedules that can be computed close to the utilization optimum [184]. Communication locality is equally critical: each halo exchange traverses the interconnect fabric, so job placement must minimize hop count across NVLink, NVSwitch, or InfiniBand domains--an objective effectively addressed by communication-aware MILP formulations or topology-sensitive heuristics [185; 186]. Their pronounced memory-bound phases also make PDE solvers ideal candidates for energy-aware scheduling; techniques such as DVFS or slack reclamation during bandwidth-limited intervals can reduce power draw with minimal impact on time-to-solution [187].