Reflected UAS: Corrected Deterministic Stability and Direct CTMC Drift Calculation

We study finite-horizon queue peaks in generalized switches, a standard stochastic-network model in which many queues share constrained service resources. Arrivals may be dependent, nonstationary, and responsive to the system history; the only load condition is uniform interior slack, meaning the conditional mean arrival vector stays in a fixed contraction of the capacity region. We show that this slack reshapes the finite-time peak law for drift-minimizing scheduling policies such as MaxWeight. The square-root envelope that is sharp without slack persists only up to a geometry-dependent threshold; beyond that threshold, the running maximum grows only logarithmically with the horizon, both with high probability and in expectation. The mechanism is self-normalization: in the current queue direction, the projected fluctuation scale is normalized by the stabilizing drift scale. This removes capacity geometry from the logarithmic coefficient, while geometry remains in the threshold. Matching lower bounds show that both the logarithmic term and a geometric threshold are unavoidable. When finite-time state-space collapse is available, the threshold can be sharpened using local bottleneck geometry. For generalized input-queued switches, we obtain finite-time peak bounds with tight logarithmic coefficients. Simulations illustrate the two-phase envelope, local geometric refinements, and variance-sensitive improvements predicted by the theory.

The growing deployment of delay-tolerant networks (DTNs) has made store-carry-forward (SCF) communication indispensable under sparse connectivity. However, intermittent contacts, finite buffers, and limited message time-to-live (TTL) often give rise to sparse delivery and congestion, leading to substantial end-to-end performance degradation. To address this challenge, this study explores the joint optimization of decentralized opportunistic routing and controllable unmanned aerial vehicle (UAV) flight, aiming to enlarge future contacts through discrete UAV headings while enabling per-node replication under contact-limited observations. Building upon this architecture, we study cooperative factored routing--UAV control under centralized training and decentralized execution (CTDE) and propose JUROR (Joint UAV flight and Opportunistic Routing, based on the proximal policy optimization (PPO) framework. In our design, we first cast the problem as a factored partially observable Markov decision process with sequential motion--routing coupling and a per-step team reward; subsequently, decentralized actors act on local observations while a training-time critic uses global statistics, and an optional multi-horizon hotspot predictor provides auxiliary supervision. Simulation results over four traffic modes demonstrate effective gains over PRoPHET and MaxProp, while retaining contact-limited decentralized execution.

Contextual queueing bandits provide a framework for learning to schedule heterogeneous jobs under unknown context-dependent service rates. Under stochastic contexts, existing algorithms achieve $\widetilde{\mathcal{O}}(T^{-1/4})$ queue length regret, defined as the expected difference between the learner's and oracle's queue lengths at horizon $T$. In this paper, we improve this rate to $\widetilde{\mathcal{O}}(T^{-1/2})$. The key observation is that random exploration is needed only up to a carefully chosen cutoff round, rather than throughout the entire horizon. We propose CQB-$η$-2, a three-phase algorithm: (i) pure random exploration to construct an initial estimator, (ii) $η$-random exploration combined with a UCB rule to continue learning while maintaining negative drift, and (iii) pure UCB after the exploration cutoff. Our proof decomposes the queue length regret at the cutoff round. Before the cutoff, negative drift suppresses queue length differences caused by suboptimal choices. After the cutoff, the first two phases provide sufficient random exploration samples, ensuring that UCB decisions incur small departure-rate gaps. Combining these two bounds yields queue length regret of order $\widetilde{\mathcal{O}}(T^{-1/2})$. We further prove a minimax lower bound of order $Ω(T^{-1/2})$. The proof constructs two hard instances that are statistically indistinguishable up to the final service decision, and uses a queue-specific coupling argument to convert the resulting testing error into queue length regret. Together, our upper and lower bounds characterize the minimax dependence on the horizon $T$ up to logarithmic factors.