---
title: Vertical Scheduling Strategies
url: https://www.emergentmind.com/topics/vertical-scheduling
type: topic
---

# Vertical Scheduling Strategies

Vertical Scheduling refers to a family of scheduling strategies and models that organize the temporal or spatial allocation of system resources in a vertically structured manner. While the term is used in diverse technical domains, leading exemplars occur in wireless communication (layered LDPC decoding), urban air mobility (takeoff and terminal operations for VTOL/eVTOL vehicles), and containerized workflow management in cloud-edge architectures. Vertical scheduling approaches address resource conflicts, throughput bounds, and quality-of-service objectives through structured decision frameworks, often contrasting with horizontal or flat scheduling baselines.

## 1. Vertical Scheduling in Urban Air Mobility and VTOL/eVTOL Operations

Vertical scheduling in Urban Air Mobility (UAM) and Vertiport/Vertiminal management is centered on optimizing the time and resource allocation for Electric or general Vertical Takeoff and Landing (eVTOL/VTOL) vehicles over a network of pads, gates, taxiways, and airspace segments.

### Vertiport Terminal Scheduling and Throughput Analysis

Saxena et al. [2408.01152] address the scheduling of VTOL vehicle operations at vertiport terminals by proposing a Mixed Integer Linear Program (MILP) for holistic optimization of all operational phases: gate holding, taxiing, pad occupation (takeoff/landing), assigned climb/approach surface direction, and turnaround. The problem is structured as follows:

- **Decision Variables**
  - $t_n^i$: Timestamp at which VTOL $i$ reaches node $n$ (gates, pads, taxiway segments)
  - $y_{ij}^n$: Binary precedence variable for VTOLs $i,j$ at node $n$
  - $z_{ij}$: Auxiliary binary for sequencing turnaround flights at gates

- **Objective**
  - Minimize a weighted sum of all VTOL delays, partitioned by phase: gate, taxiway, pad, climb, and turnaround.

- **Constraints**
  - Enforce conflict-free transitions (gate, taxiway, OFV, pad), time separation (wake-vortex, surface-direction), no overtaking, non-negativity, and logical ordering across shared links.

- **Throughput Capacity**
  - The vertiminal's max throughput $\rho_{\text{vertiminal}}$ is analytically determined as the minimum bottleneck across (i) TLOF pad system, (ii) taxiway network via max-flow/min-cut, and (iii) gate system with turnaround constraints.

- **Case Study Findings**
  - MILP yields ≈50% reduction in mean and median departure delays versus FCFS. When flight presence exceeds saturation threshold, scheduled movements reach the theoretical throughput envelope (e.g., 8 movements/min for typical LA-inspired setups).

### Throughput Maximizing Takeoff Scheduling

Tavildar et al. [2503.17313] formulate the vertical scheduling of eVTOL takeoffs and network movements via the VertiSync policy. The system is modeled as a directed graph of vertiports and pad resources. The VertiSync policy executes as:
- Collect all outstanding trip requests,
- Solve an integer program (extension of the Traffic Flow Management Problem) across slotted time and all active vehicles,
- Enforce all sector, pad, and energy constraints,
- Allocate takeoffs to maximize system throughput within conflict-free and energy-aware boundaries.

The throughput region is shown to be a convex polytope defined by time-sharing over achievable pad-limited takeoff service vectors. With sufficient fleet size and symmetric network structure, VertiSync is throughput-optimal. Empirically, VertiSync maintains bounded queueing delays under peak load, outperforming simple greedy baselines by servicing a full $100\%$ of requests at critical demand, versus $\approx80\%$ for FCFS.

## 2. Vertical Layered Scheduling in Iterative Decoding

Mohr & Bauch [2212.02144] analyze vertical layered scheduling in quasi-cyclic LDPC decoding by revisiting the per-iteration update order and hardware implications.

- **Vertical (Column-Layered) LDPC Scheduling**
  - Variable nodes partitioned into $d_c$ layers, each corresponding to a base-matrix column.
  - Each iteration consists of $d_c$ sequential partial check-node (CN) updates for each column-layer, followed by full variable-node (VN) updates on corresponding variables.
  - Contrasts with horizontal scheduling (row-layered), where CN updates proceed by base-matrix rows and VNs are updated partially.

- **Algorithmic Mechanics**
  - Partial CN updates use high-precision calculations mapped to quantized $w$-bit messages, with recursive updates enabling hardware-efficient state tracking.
  - Full VN updates operate on entire variable layers.
  - Mutual-information–maximizing compression (MIM) quantizes updates at both CN and VN boundaries via offline information bottleneck design.

- **Complexity and Performance Trade-offs**
  - MIM-vertical (MIM-V) achieves nearly identical BER to MIM-horizontal (MIM-H), both surpassing classic offset-min-sum at equal bit width.
  - MIM-V incurs a ≈14% average increase in iteration count compared to MIM-H at equivalent $E_b/N_0$; 2-bit MIM-V increases iteration count by ≈40%.
  - Most hardware cost is incurred by routing network barrel shifters, not node updates.
  - Memory cost per edge for vertical is ≈2.11 bits, exceeding the 2 bits for horizontal due to tracking partial CN state.

- **Hardware Architecture**
  - Both 2D processor graph embedding and 3D stacking are detailed: straight-line wires and local barrel shifter logic reduce crossbar congestion.
  - Routing dominates silicon area; uniform quantization cuts logic by half with negligible BER penalty.
  - Vertical places memory for state with CNs, horizontal with VNs.

## 3. Vertical Offloading in Cloud–Edge Workflow Scheduling

Vertical scheduling in cloud-edge computational workflows refers to the dynamic assignment of tasks to either edge or cloud environments, with runtime offloading contingent on local resource exhaustion [2401.01217].

- **Model Formulation**  
  - Each task $s_{i,j}$ assigned via binary selector variables $\alpha^e_{s_{i,j}}$ (edge) and $\alpha^c_{s_{i,j}}$ (cloud) with $\alpha^e_{s_{i,j}} + \alpha^c_{s_{i,j}} = 1$.
  - Delay constraint ensures that assignment plus execution and transfer time does not exceed task deadline.
  - Objectives include optimized global resource utilization bounded by CPU/RAM quotas.

- **Vertical Offloading Algorithm**
  - When a Pod is killed by OOM, the informer triggers offloading: the scheduler selects a suitable cloud node based on maximum residual resources and updates the task's mapping.
  - The process involves label and image address management, and state synchronization with Redis.

- **Performance Metrics and Observations**
  - Offloading rate scales with system load: at $N=10$ concurrent workflows, up to 19% of tasks are offloaded.
  - Each vertical offloading event incurs a lifecycle penalty of $38$–$50$ s.
  - Offloading is reactive (OOMKilled), not predictive or preventative.
  - Edge nodes are preserved for latency-sensitive workloads, while cloud nodes absorb overflow.

- **Trade-offs**
  - Increased system complexity (dual image registries, metadata management).
  - Offloading latency may impact deadline-sensitivity for some workflow types.
  - System limits are tested under high frequency of OOMKilled events; excessive load can saturate metadata handling infrastructure.

## 4. Comparative Overview of Vertical Scheduling Variants

| Domain                     | Vertical Schedule Type         | Objective                                 | Trade-off                              |
|----------------------------|-------------------------------|-------------------------------------------|----------------------------------------|
| UAM/Vertiports             | Takeoff/terminal sequencing   | Throughput, queue stability, safety       | MILP size, enforcement of constraints  |
| LDPC Decoding              | Layered update (column)       | Error rate, complexity, quantization      | More iterations, more state per edge   |
| Cloud-Edge Orchestration   | Task offloading (run-time)    | Fault-tolerance, utilization, deadlines   | Offloading latency, complexity         |

Each instantiation of vertical scheduling is domain-specific in constraints, objectives, and hardware or system impact but shares the common principle of strict temporal or spatial ordering along a vertical (hierarchical or layer-wise) axis.

## 5. Architectural and Analytical Foundations

- **Analytical Frameworks**
  - MILP modeling underpins scheduling for urban air mobility [2408.01152], enabling explicit handle on complex delay, capacity, and safety relations.
  - Integer programming with renewal-reward and Foster–Lyapunov arguments rigorously delineate throughput regions in cyclic eVTOL scheduling [2503.17313].
  - Information bottleneck and density evolution methods are foundational in mutual-information–maximizing layered LDPC schedules [2212.02144].
  - Cloud–edge scheduling leverages binary decision variables, scheduling engine logic (e.g., Algorithm 5), and resource-constraint enforcement for vertical task placement [2401.01217].

- **Key Parameters**
  - Pad occupancy, wake-vortex separation, path travel and taxi times, turnaround for UAM.
  - Bit-width, partial node update state, routing logic in LDPC decoding.
  - Compute/data transfer times, minimum resource thresholds, and failure detection for offloading in cloud-edge collaboration.

## 6. Generalizations, Scalability, and Limitations

- Vertiport/vertiminal models are topology-agnostic and extendible to stochastic arrivals via rolling or receding-horizon MILPs [2408.01152].
- VertiSync’s throughput-optimality holds under symmetry and adequate fleet, but less so when network asymmetries or tight fleet supply dominate [2503.17313].
- Cloud-edge offloading in KCES is currently reactive; proactive or predictive resource management remains a challenge [2401.01217].
- Vertical LDPC schedules yield efficient hardware, but resource-constrained scenarios may favor horizontal layering due to fewer required iterations [2212.02144].

A plausible implication is that, across domains, vertical scheduling frameworks that explicitly model both resource and sequencing constraints admit rigorous throughput analysis and practical capacity certification—enabling provable guarantees under domain-tailored architectures and operational regimes.

Source: https://www.emergentmind.com/topics/vertical-scheduling