Hyper-Scalable JSQ with Sparse Feedback

Load balancing algorithms play a vital role in enhancing performance in data centers and cloud networks. Due to the massive size of these systems, scalability challenges, and especially the communication overhead associated with load balancing mechanisms, have emerged as major concerns. Motivated by these issues, we introduce and analyze a novel class of load balancing schemes where the various servers provide occasional queue updates to guide the load assignment. We show that the proposed schemes strongly outperform JSQ($d$) strategies with comparable communication overhead per job, and can achieve a vanishing waiting time in the many-server limit with just one message per job, just like the popular JIQ scheme. The proposed schemes are particularly geared however towards the sparse feedback regime with less than one message per job, where they outperform corresponding sparsified JIQ versions. We investigate fluid limits for synchronous updates as well as asynchronous exponential update intervals. The fixed point of the fluid limit is identified in the latter case, and used to derive the queue length distribution. We also demonstrate that in the ultra-low feedback regime the mean stationary waiting time tends to a constant in the synchronous case, but grows without bound in the asynchronous case

Load Balancing in Large-Scale Systems with Multiple Dispatchers

Load balancing algorithms play a crucial role in delivering robust application performance in data centers and cloud networks. Recently, strong interest has emerged in Join-the-Idle-Queue (JIQ) algorithms, which rely on tokens issued by idle servers in dispatching tasks and outperform power-of-$d$ policies. Specifically, JIQ strategies involve minimal information exchange, and yet achieve zero blocking and wait in the many-server limit. The latter property prevails in a multiple-dispatcher scenario when the loads are strictly equal among dispatchers. For various reasons it is not uncommon however for skewed load patterns to occur. We leverage product-form representations and fluid limits to establish that the blocking and wait then no longer vanish, even for arbitrarily low overall load. Remarkably, it is the least-loaded dispatcher that throttles tokens and leaves idle servers stranded, thus acting as bottleneck. Motivated by the above issues, we introduce two enhancements of the ordinary JIQ scheme where tokens are either distributed non-uniformly or occasionally exchanged among the various dispatchers. We prove that these extensions can achieve zero blocking and wait in the many-server limit, for any subcritical overall load and arbitrarily skewed load profiles. Extensive simulation experiments demonstrate that the asymptotic results are highly accurate, even for moderately sized systems

Impact of the COVID-19 pandemic and initial period of lockdown on the mental health and well-being of adults in the UK

The impact of the COVID-19 pandemic on mental health and well-being were assessed in a convenience sample of 600 UK adults, using a cross-sectional design. Recruited over 2 weeks during the initial phase of lockdown, participants completed an online survey that included COVID-19-related questions, the Hospital Anxiety and Depression Scale, the World Health Organization (Five) Well-Being Index and the Oxford Capabilities Questionnaire for Mental Health. Self-isolating before lockdown, increased feelings of isolation since lockdown and having COVID-19-related livelihood concerns were associated with poorer mental health, well-being and quality of life. Perceiving increased kindness, community connectedness and being an essential worker were associated with better mental health and well-being outcomes

Optimal Hyper-Scalable Load Balancing with a Strict Queue Limit

Load balancing plays a critical role in efficiently dispatching jobs in parallel-server systems such as cloud networks and data centers. A fundamental challenge in the design of load balancing algorithms is to achieve an optimal trade-off between delay performance and implementation overhead (e.g. communication or memory usage). This trade-off has primarily been studied so far from the angle of the amount of overhead required to achieve asymptotically optimal performance, particularly vanishing delay in large-scale systems. In contrast, in the present paper, we focus on an arbitrarily sparse communication budget, possibly well below the minimum requirement for vanishing delay, referred to as the hyper-scalable operating region. Furthermore, jobs may only be admitted when a specific limit on the queue position of the job can be guaranteed. The centerpiece of our analysis is a universal upper bound for the achievable throughput of any dispatcher-driven algorithm for a given communication budget and queue limit. We also propose a specific hyper-scalable scheme which can operate at any given message rate and enforce any given queue limit, while allowing the server states to be captured via a closed product-form network, in which servers act as customers traversing various nodes. The product-form distribution is leveraged to prove that the bound is tight and that the proposed hyper-scalable scheme is throughput-optimal in a many-server regime given the communication and queue limit constraints. Extensive simulation experiments are conducted to illustrate the results