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 $\bar{\mu}$ a cap.
• The scheduling decision $a_i(t) \in \{0,1\}$ indicates which queue is served; at most one per slot with $\sum_i a_i(t) \leq 1$.
• Switchover unavailability is denoted $b(t) \in \{0,1\}$, set to $1$ for the duration of a switch.
• Pairwise stochastic switchover delay from $i$ to $j$ is $D_{ij}(t) \in \mathbb{N}$.

Queue dynamics obey

$$Q_i(t+1) = \max\bigl\{Q_i(t) - S_i(t), 0\bigr\} + A_i(t), \qquad S_i(t) = \mu_i(t) a_i(t) (1 - b(t)),$$

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 $k$ begin at $t_k$ and span $T_k$ slots (randomized length). At frame boundary $t_k$, the scheduler observes current backlogs $Q_i(t_k)$, link rates $R_i(t_k)$, and switchover delays $D_{ij}(t_k)$ for all $i, j$ pairs (with $i \ne j$). ACI resolves:

• The serving queue $i^*$.
• The dwell time $L$ (planned service slots before switch).

Urgency Metric: For candidate queue $i$, urgency is

$U_i(t_k) = Q_i(t_k),$

emphasizing quadratic Lyapunov stability.

Amortized Goodput and Switch Modulation:

If switching from queue $j$ to $i$ at $t_k$, remaining for $L$ slots, the expected bits delivered is

$\hat{B}_i(t_k; L) = L (\Delta t - t_p)^+ R_i(t_k),$

with $t_p$ per-slot processing overhead. The total investment is $D_{ji}(t_k) + L \Delta t$. Amortized goodput:

$$\bar{\mu}_{i|j}(t_k, L) = \frac{\hat{B}_i(t_k; L)}{D_{ji}(t_k) + L \Delta t}.$$

Switch Modulator:

$$f_{ji}(t_k) = \frac{1 + \gamma \chi_{ji}(t_k)}{1 + \beta D_{ji}(t_k)},$$

where $\chi_{ji} \in [0,1]$ quantifies transition affinity and $\gamma, \beta \geq 0$ are tunable.

Frame-Level Scheduling Optimization:

At each frame start, the maximization is

$$(i^*, L^*) = \arg\max_{i \in \mathcal{N}, 1 \leq L \leq L_{\text{max}}} U_i(t_k) \cdot \bar{\mu}_{i|j}(t_k, L) \cdot f_{ji}(t_k).$$

The server switches, serves $i^*$ for up to $L^*$ 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

$V(Q(t)) = \sum_{i=1}^N Q_i^2(t).$

The one-slot drift is bounded:

$$\Delta(t) = E[V(Q(t+1)) - V(Q(t)) \mid Q(t)] \le B + \sum_{i=1}^N Q_i(t) (\lambda_i \Delta t - E[S_i(t) \mid Q(t)]),$$

with $B < \infty$ encapsulating second moments.

Over a frame $k$:

$$E[V(Q(t_{k+1})) - V(Q(t_k)) \mid Q(t_k)] \le B E[T_k \mid Q(t_k)] + \sum_{i=1}^N Q_i(t_k)\left(\lambda_i \Delta t E[T_k|Q(t_k)] - E[\mu_i(k)|Q(t_k)]\right),$$

where $\mu_i(k)$ is the total service in frame $k$.

Dividing by $E[T_k|Q(t_k)]$ gives per-unit-time drift:

$$\frac{\Delta_k}{E[T_k|Q(t_k)]} \le B' + \sum_{i=1}^N Q_i(t_k)\lambda_i - G(i^*, L^* | Q(t_k)),$$

with

$$G(i, L | Q) = \frac{Q_i(t_k) E[\mu_i(k) | Q(t_k)]}{E[D_{ji}(t_k) + L \Delta t | Q(t_k)]}.$$

The Constant-Factor Approximation Lemma asserts $G(i^*, L^* | Q) \ge \zeta \max_{i, L}G(i, L | Q)$, $\zeta = f_{\min} / f_{\max}$.

Backlog-driven ACI stabilizes all arrival vectors $\lambda$ within

$$\Lambda' = \left\{ \lambda : \exists \varepsilon > 0,\ \lambda_i + \varepsilon \le \zeta \bar{\mu}_i,\ \forall i \right\},$$

where $\bar{\mu}_i$ is the long-run average under ideal scheduling, conferring throughput optimality up to constant factor $\zeta$ (Mohammadalizadeh et al., 22 Jan 2026).

4. Performance Analysis and Trade-Offs

Empirical validation involves a six-UAV FSO backhaul scenario with slot $\Delta t \approx 10$ ms, aggregate $\lambda \approx 350$ Mbps. Backlog-driven ACI delivers $\sim$90% 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 $\sim$1%.

Delay CDFs show backlog-driven ACI achieves substantial reductions in median and tail latency versus Max-Weight. Age-aware variants (ACI-A: urgency $U_i = HoL\ age \cdot \bar{\mu}$, and pure-age ACI-PA) further compress the upper tail, sacrificing strict throughput optimality.

Tuning $\beta$ and $\gamma$ in $f_{ji}$, or adjusting $L_{max}$, directly modulates the throughput-latency operating point. Higher $\beta$ suppresses costly switches, attenuating jitter and tail delay at moderate loads but shrinking the stabilizable region if excessive. Increasing $\gamma$ 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 $L_{max}$ comparable to typical switching delay divided by slot duration ($\Delta t$), ensuring sufficient amortization of switch cost.

Urgency Scaling: Begin with $\gamma \approx 1,\, \beta \approx 1$; increment $\beta$ just enough to manage tail latency, avoiding excessive values ($\beta \gg 1$) to preserve throughput. For topologies with clusters, let $\chi_{ji} = 1$ for intra-cluster switches (0 otherwise), then raise $\gamma$ for prioritizing local transitions.

Handling Heterogeneous Delays: Model switchover delays $D_{ij}$ 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).