queueing theory

This paper investigates stability and heavy-traffic delay optimality for parallel single-server load balancing systems with heterogeneous service rates, under periodic queue-length observations every $T$ time units; the central dispatcher bases decisions solely on the most recent scaled queue-length ordering and server rates. We propose a general class of scheduling policies that jointly leverage scaled ordering and rate awareness. For the first time, we derive necessary and sufficient conditions for system stability under such policies. Furthermore, we establish sufficient conditions for heavy-traffic delay optimality and prove that, in the heavy-traffic limit, the scaled queue-length vector converges weakly to a deterministic vector multiplied by an exponential random scaling factor. Our analysis integrates stochastic process theory, modeling of periodic information updates, and heavy-traffic scaling limit techniques. This work provides the first rigorous stability criterion and delay optimality guarantee for load balancing in heterogeneous systems operating under limited, periodically updated state information.

This work addresses the high bias and variance commonly observed in A/B tests of datacenter scheduling policies, which arise due to Markovian interference. To tackle this challenge, the paper introduces a novel hybrid causal inference method that uniquely integrates Little’s Law with a Differences-in-Q estimator. This approach explicitly models key complexities inherent in real-world queueing systems, including non-stationary arrival rates, heterogeneous service rates, and communication delays. Theoretical analysis and extensive simulations demonstrate that the proposed method substantially reduces both estimation bias and variance, achieving superior robustness and higher accuracy across a variety of practical scenarios compared to existing approaches.

This paper investigates the joint optimization of server count, scheduling policy, and system architecture under a fixed computational budget to minimize average job response time. Using high-resolution traces from Google Cloud production workloads, we develop a multi-stage server cluster model and systematically compare classical policies—including Join-Idle-Queue (JIQ) and Round-Robin (RR)—against state-of-the-art size-aware schedulers. Our findings reveal: (1) an optimal critical server scale that minimizes response time; (2) in high-parallelism or multi-tier architectures, RR and JIQ significantly outperform conventional size-aware policies; and (3) parallelism degree and architectural design exert greater influence on performance than scheduling algorithm sophistication. Collectively, these results establish a new optimization paradigm wherein “architecture–parallelism” dominates over “algorithmic refinement.”

This study addresses a critical limitation in classical queueing analysis—its frequent neglect of preemption overhead—which hinders accurate assessment of stability and response time in preemptive scheduling systems. Focusing on the M/G/1 queue with preemption overhead, this work investigates class-based preemptive priority scheduling and presents the first exact analysis of response time distributions for such systems. By introducing a novel theoretical construct termed “task joint transform,” which integrates Laplace transforms with stochastic process techniques, the authors derive recursive formulas for the Laplace transforms of response times for tasks of arbitrary classes. This framework enables closed-form computation of all response time moments, clearly elucidates the performance impact of preemption overhead, and establishes a general analytical foundation extendable to broader scheduling overhead models.

This paper addresses the optimal admission control problem for an M/M/k/k+N queueing system with unknown service rates, where only arrival epochs and system states (but not service times or departure epochs) are observable, aiming to maximize the long-run average reward. To overcome the exploration-exploitation deadlock inherent in classical certainty-equivalence approaches, we propose a parameterized learning-based self-correcting adaptive control framework that integrates structured policy design, a cautious exploration mechanism, and the certainty-equivalence principle. We establish the first asymptotically optimal learning of extremal heterogeneous optimal policies—namely, “always admit” and “always reject”—and prove that the learned policy converges to the true optimal policy for any underlying service rate. Furthermore, we derive tight finite-time regret upper bounds of both constant and logarithmic order, substantially improving upon existing reinforcement learning methods.

Existing scheduling theory struggles to handle multi-resource job scenarios with continuously distributed resource demands, as it relies on the assumption of finitely many job types—a simplification inconsistent with the high heterogeneity observed in real-world workloads. This work proposes the first family of throughput-optimal scheduling policies for continuous multi-resource job models, encompassing both preemptive and non-preemptive variants. The approach employs an adaptive discretization mechanism that dynamically adjusts granularity based on system load and demand distribution. By integrating throughput-optimal control, distribution-aware scheduling, and queueing optimization, the method achieves theoretical optimality while substantially improving computational efficiency. Experiments demonstrate superior performance over state-of-the-art index-based policies under both parametric distributions and real-world Google Borg traces, attaining industry-leading results.

This study addresses the opacity of Starlink’s queue management mechanism, which has hindered a thorough understanding of its network performance and congestion control behavior. By employing high-precision, controlled burst traffic generation combined with one-way delay measurements, packet loss analysis, and queue simulations, this work provides the first evidence that Starlink employs a drop-front buffering strategy rather than conventional per-flow fair queuing or drop-tail mechanisms. While this approach effectively reduces queuing delay, it may adversely impact loss-based congestion control algorithms, potentially leading to reduced throughput. These findings offer critical insights for optimizing transport protocols in satellite internet environments.

This work proposes a parameter estimation method based on the Expectation–Maximization (EM) algorithm for Markovian Arrival Process (MAP)-driven Quasi-Birth–Death (QBD) queueing systems, tailored to realistic scenarios where only coarse-grained data such as system utilization are available. Within a maximum likelihood framework, the approach infers sufficient statistics—including sojourn times, phase transitions, and service dynamics—underlying the hidden states directly from utilization time series. To the best of our knowledge, this is the first method capable of fully estimating MAP-QBD model parameters using solely utilization data. The study further introduces an innovative use of the Akaike Information Criterion (AIC) to automatically select the number of MAP phases, thereby mitigating overfitting. Experimental results demonstrate that the method accurately recovers both arrival and service parameters, offering a practical performance modeling tool for real-world systems lacking fine-grained event logs.

This study addresses the complex interplay of dynamically evolving customer classes, abandonment behavior, and dynamic prioritization in finite-capacity, multi-server queueing systems. To tackle this challenge, the authors propose a scalable continuous-time Markov chain (CTMC) modeling framework that integrates quasi-birth–death processes, matrix-analytic methods, and Krylov subspace approximations to efficiently compute both conditional and steady-state waiting time distributions for two customer classes. Notably, this work is the first to incorporate dynamic customer-type evolution and reneging into waiting time analysis for such systems. The model’s validity is demonstrated using real-world data from a tertiary referral hospital in Australia, where it successfully quantifies the disparity in waiting times between complex and routine patients, thereby offering actionable, quantitative insights for healthcare operational decision-making.