Backlog-Driven ACI: Frame-Based Scheduling

• Backlog-driven ACI is a dynamic, frame-based scheduling framework that uses queue backlogs to guide resource allocation amid stochastic pair-dependent switchover delays.
• It leverages Lyapunov drift analysis and an urgency metric to achieve throughput optimality while effectively amortizing switching overhead.
• Evaluations, such as in multi-UAV FSO scenarios, demonstrate significant improvements in latency and throughput compared to classical Max-Weight policies.

Backlog-driven ACI is a non-myopic, frame-based scheduling framework designed for dynamic resource allocation in network systems featuring a single server and multiple parallel queues, where switchover delays are both stochastic and pair-dependent, and link rates vary in time. Unlike classical slot-by-slot approaches, backlog-driven ACI leverages control frames to amortize switchover delay costs, employs a queue-backlog-driven urgency metric, and provably achieves throughput optimality with respect to a constant-factor-scaled capacity region under rigorous Lyapunov drift analysis. It addresses key limitations of myopic policies such as Max-Weight, particularly in environments with inhomogeneous switching delays and high link variability (Mohammadalizadeh et al., 22 Jan 2026).

1. System Model and Fundamental Notation

The system comprises $N$ parallel queues indexed by $i \in \{1, ..., N\}$, served by a single server in discrete time. At slot $t$:

• $Q_i(t) \geq 0$ is the backlog at queue $i$.
• $A_i(t) \geq 0$ are new arrivals, modeled as Poisson random variables with mean $\lambda_i \Delta t$.
• $R_i(t)$ is the instantaneous physical link rate for queue $i$.
• The effective service rate is $\mu_i(t) = \min\{\bar{\mu}, R_i(t)\}$, with $i \in \{1, ..., N\}$0 a cap.
• The scheduling decision $i \in \{1, ..., N\}$1 indicates which queue is served; at most one per slot with $i \in \{1, ..., N\}$2.
• Switchover unavailability is denoted $i \in \{1, ..., N\}$3, set to $i \in \{1, ..., N\}$4 for the duration of a switch.
• Pairwise stochastic switchover delay from $i \in \{1, ..., N\}$5 to $i \in \{1, ..., N\}$6 is $i \in \{1, ..., N\}$7.

Queue dynamics obey

$i \in \{1, ..., N\}$8

encapsulating the coupling between selection, instantaneous rate, and switching overhead.

2. Frame-Based ACI Algorithm Structure

Backlog-driven ACI aggregates slots into control frames for scheduling. Let frame $i \in \{1, ..., N\}$9 begin at $t$0 and span $t$1 slots (randomized length). At frame boundary $t$2, the scheduler observes current backlogs $t$3, link rates $t$4, and switchover delays $t$5 for all $t$6 pairs (with $t$7). ACI resolves:

• The serving queue $t$8.
• The dwell time $t$9 (planned service slots before switch).

Urgency Metric: For candidate queue $Q_i(t) \geq 0$0, urgency is

$Q_i(t) \geq 0$1

emphasizing quadratic Lyapunov stability.

Amortized Goodput and Switch Modulation:

If switching from queue $Q_i(t) \geq 0$2 to $Q_i(t) \geq 0$3 at $Q_i(t) \geq 0$4, remaining for $Q_i(t) \geq 0$5 slots, the expected bits delivered is

$Q_i(t) \geq 0$6

with $Q_i(t) \geq 0$7 per-slot processing overhead. The total investment is $Q_i(t) \geq 0$8. Amortized goodput:

$Q_i(t) \geq 0$9

Switch Modulator:

$i$0

where $i$1 quantifies transition affinity and $i$2 are tunable.

Frame-Level Scheduling Optimization:

At each frame start, the maximization is

$i$3

The server switches, serves $i$4 for up to $i$5 slots, halting early if the queue empties, link fails, or another queue’s score overtakes.

3. Theoretical Foundations: Lyapunov Drift and Throughput Optimality

The Lyapunov analysis centers on the quadratic function

$i$6

The one-slot drift is bounded:

$i$7

with $i$8 encapsulating second moments.

Over a frame $i$9:

$A_i(t) \geq 0$0

where $A_i(t) \geq 0$1 is the total service in frame $A_i(t) \geq 0$2.

Dividing by $A_i(t) \geq 0$3 gives per-unit-time drift:

$A_i(t) \geq 0$4

with

$A_i(t) \geq 0$5

The Constant-Factor Approximation Lemma asserts $A_i(t) \geq 0$6, $A_i(t) \geq 0$7.

Backlog-driven ACI stabilizes all arrival vectors $A_i(t) \geq 0$8 within

$A_i(t) \geq 0$9

where $\lambda_i \Delta t$0 is the long-run average under ideal scheduling, conferring throughput optimality up to constant factor $\lambda_i \Delta t$1 (Mohammadalizadeh et al., 22 Jan 2026).

4. Performance Analysis and Trade-Offs

Empirical validation involves a six-UAV FSO backhaul scenario with slot $\lambda_i \Delta t$2 ms, aggregate $\lambda_i \Delta t$3 Mbps. Backlog-driven ACI delivers $\lambda_i \Delta t$490% useful service time under correlated switchover delays, and 75–80% under full FSO-modeled delays (including acquisition retries, FOV misses). In contrast, Max-Weight retargets frequently, incurring excessive overhead and collapsing service to $\lambda_i \Delta t$51%.

Delay CDFs show backlog-driven ACI achieves substantial reductions in median and tail latency versus Max-Weight. Age-aware variants (ACI-A: urgency $\lambda_i \Delta t$6, and pure-age ACI-PA) further compress the upper tail, sacrificing strict throughput optimality.

Tuning $\lambda_i \Delta t$7 and $\lambda_i \Delta t$8 in $\lambda_i \Delta t$9, or adjusting $R_i(t)$0, directly modulates the throughput-latency operating point. Higher $R_i(t)$1 suppresses costly switches, attenuating jitter and tail delay at moderate loads but shrinking the stabilizable region if excessive. Increasing $R_i(t)$2 accentuates affinity, expediting service in topological clusters but potentially reducing flexibility under sparse or edge conditions.

5. Guidelines for Deployment and Extension

Frame-Length Selection: Set $R_i(t)$3 comparable to typical switching delay divided by slot duration ($R_i(t)$4), ensuring sufficient amortization of switch cost.

Urgency Scaling: Begin with $R_i(t)$5; increment $R_i(t)$6 just enough to manage tail latency, avoiding excessive values ($R_i(t)$7) to preserve throughput. For topologies with clusters, let $R_i(t)$8 for intra-cluster switches (0 otherwise), then raise $R_i(t)$9 for prioritizing local transitions.

Handling Heterogeneous Delays: Model switchover delays $i$0 with AR(1) or geometric retry processes when applicable (e.g., FSO acquisition). The frame-based method is robust to temporal correlation, though heavy-tailed delays yield broader latency distribution.

Extensions: The theoretical foundation generalizes to multi-server systems by treating each server as a frame-maker interlinked through aggregate switching loads. Age-based urgency overlays can support latency-sensitive flows, with an explicit trade-off against strict throughput guarantees.

6. Connections and Practical Significance

Backlog-driven ACI offers a principled scheduling architecture accounting for both time-varying links and stochastic switchover delays. By structuring service into frames, amortizing transition costs, and using queue-length-based urgency, the approach supports provable throughput guarantees within a scaled capacity region. Simulations indicate practical advantages in throughput and latency, with graceful trade-offs managed via policy parameters. The framework is directly validated in multi-UAV FSO environments and shown to outperform classical Max-Weight under realistic switching constraints (Mohammadalizadeh et al., 22 Jan 2026).