arXiv subjects

Elene Anton

Publications and source records attributed to Elene Anton.

4 recordsLinked to original sources

arXiv2025

Stability of skill-based queues with deterministic waiting time thresholds

We consider skill-based queues where service is First--Come--First--Served, but some compatibility lines are only available once a customer's waiting time exceeds a threshold. For this model, we establish necessary and sufficient stability conditions. We find that the thresholds do not affect stability; an intuitive result that has not been proved in the literature up to this point. While necessity follows from a coupling argument, the sufficiency proof is more challenging. It follows by formulating the First--in--Line waiting time process as a Piecewise Deterministic Markov Process (PDMP) and constructing a Lyapunov function that accounts for the threshold structure. We show that this Lyapunov function satisfies the boundary condition of the PDMP framework, and that its generator has negative drift when waiting times are large. Finally, we show that bounded waiting-time sets are petite, so that the Foster--Lyapunov criterion applies.

math.PR↗

arXiv2022

Efficient scheduling in redundancy systems with general service times

We characterize the impact of scheduling policies on the mean response time in nested systems with cancel-on-complete redundancy. We consider not only redundancy-oblivious policies, such as FCFS and ROS, but also redundancy-aware policies of the form $\Pi$ 1 -- $\Pi$ 2 , where $\Pi$ 1 discriminates among job classes (e.g., least-redundant-first (LRF), most-redundantfirst (MRF)) and $\Pi$ 2 discriminates among jobs of the same class. Assuming that jobs have independent and identically distributed (i.i.d.) copies, we prove the following: (i) When jobs have exponential service times, LRF policies outperform any other policy. (ii) When service times are New-Worse-than-Used, MRF-FCFS outperforms LRF-FCFS as the variability of the service time grows infinitely large. (iii) When service times are New-Better-than-Used, LRF-ROS (resp. MRF-ROS) outperforms LRF-FCFS (resp. MRF-FCFS) in a two-server system. Statement (iii) also holds when job sizes follow a general distribution and have identical copies (all the copies of a job have the same size). Moreover, we show via simulation that, for a large class of redundancy systems, redundancy-aware policies can considerably improve the mean response time compared to redundancy-oblivious policies. We also explore the effect of redundancy on the stability region.

cs.PF↗

arXiv2021

A Survey of Stability Results for Redundancy Systems

Redundancy mechanisms consist in sending several copies of a same job to a subset of servers. It constitutes one of the most promising ways to exploit diversity in multiservers applications. However, its pros and cons are still not sufficiently understood in the context of realistic models with generic statistical properties of service-times distributions and correlation structures of copies. We aim at giving a survey of recent results concerning the stability-arguably the first benchmark of performance-of systems with cancel-oncompletion redundancy. We also point out open questions and conjectures.

cs.PF↗

arXiv2020

Improving the performance of heterogeneous data centers through redundancy

We analyze the performance of redundancy in a multi-type job and multi-type server system. We assume the job dispatcher is unaware of the servers' capacities, and we set out to study under which circumstances redundancy improves the performance. With redundancy an arriving job dispatches redundant copies to all its compatible servers, and departs as soon as one of its copies completes service. As a benchmark comparison, we take the non-redundant system in which a job arrival is routed to only one randomly selected compatible server. Service times are generally distributed and all copies of a job are identical, i.e., have the same service requirement. In our first main result, we characterize the sufficient and necessary stability conditions of the redundancy system. This condition coincides with that of a system where each job type only dispatches copies into its least-loaded servers, and those copies need to be fully served. In our second result, we compare the stability regions of the system under redundancy to that of no redundancy. We show that if the server's capacities are sufficiently heterogeneous, the stability region under redundancy can be much larger than that without redundancy. We apply the general solution to particular classes of systems, including redundancy-d and nested models, to derive simple conditions on the degree of heterogeneity required for redundancy to improve the stability. As such, our result is the first in showing that redundancy can improve the stability and hence performance of a system when copies are non-i.i.d..

cs.NI↗