Federated Regression-Based Remaining Queue Time Estimation in Cloud-Edge Multiprocessor Systems with Fault Tolerance and Cost Optimization

Distributed multiprocessor systems operating across cloud-edge infrastructures face unpredictable node failures, network partitions, and communication overheads that complicate accurate estimation of the remaining ready-queue processing time. Classical regression-type estimators have shown strong efficiency gains over simple mean-based estimation in multiprocessor ready queue time estimation, but they assume a centralized, fully observable queue and a single point of computation, which makes them unsuitable for distributed, failure-prone cloud-edge environments. This paper proposes a Federated Regression-based Remaining Queue Time Estimation (FR-RQTE) framework that reformulates the classical auxiliary-variable regression estimator in a federated setting: each cloud-edge node computes a local regression-type estimate of its own remaining queue processing time using locally observed auxiliary information such as queue length, service rate and processor load, and shares only regression coefficients and summary statistics — never raw job-level data — with a federated aggregation server. To prevent from corrupted updated, stragglers and crashed nodes to not distort the global estimates, the fault tolerance layer is appended with the help of partial state replication checkpoints, redundant node grouping and the byzantine resilient trimmed weighted aggregation rule. A cost-optimization layer jointly minimizes communication cost, computation cost and expected recovery cost subject to a bounded estimation-error constraint, giving system administrators a tuneable trade-off between accuracy and operating expense. The proposed framework is expected to outperform both the classical centralized regression estimator and existing non-regression federated queue-estimation approaches in terms of estimation efficiency, fault resilience, and cost efficiency, particularly under node failure rates and network degradation typical of edge-cloud multiprocessor deployments.