Serverless computing are invented to free developers of analytic services from the management of cloud resources. Developers only need to submit their code to a serverless edge cloud (SEC) and the cloud platform matches the submitted code to itsserverless functions, enabled by the paradigm of Function as a Service (FaaS). However, serverless functions usually are short-lived with limited resources. In this paper, we aim to address the challenge of how to fully utilize the short-lived serverless functions to enable continuous analysis of the most freshly-generated big data. We first formulate an optimization problem of age-aware big data query evaluation in an SEC network so that theage of datais minimized, where the age of data is the duration between the generation time of the data and the current time. We then propose approximation algorithms for the age-aware big data query evaluation problem of a single query, by proposing a parameterized virtualization technique that smartly handles the large resource demands of big data queries in short-lived and resource-constraint serverless functions. We further consider the scenario where big data queries arrive into the system one-by-one and their resource demands are uncertain. To this end, we devise an online learning algorithm with bounded regret by leveraging a memory repacking mechanism to improve resource utilization, for the problem of online age-aware big data query evaluation. We evaluate the performance of the proposed algorithms through extensive simulations to testify their performances in large scales. We also validate the effectiveness of the proposed mechanism in a real test-bed built on Kubernetes and OpenWhisk with TPC-DS benchmarks. Experimental results show that the proposed algorithms outperform the state-of-the-arts, by reducing the age of data by$8.82\%$on average.

Metaverse, as the cyberspace against the real world, offers various immersive services enabling users to entertain, learn and work. The digital twin (DT) technology acts as a fundamental enabler of Metaverse services by mapping user devices to DTs and timely analyzing the status of user devices. Mobile edge computing (MEC) significantly improves the QoS of DT-empowered Metaverse services because it can deploy DTs in cloudlets closer to user devices. However, each user device often has a complex structure with multiple interdependent subsystems that frequently communicate. Further, the resources in MEC network are highly distributed and limited. Thus, provisioning DT-empowered Metaverse services in MEC networks faces the challenge of efficiently mapping intertwining subsystems in user devices to DTs, maximizing admitted service requests and resource utilization. In this paper, we first formulate throughput maximization problems for DT-empowered Metaverse services in an MEC network, with the aim to maximize the total data rate of service requests of Metaverse services while meeting resource capacity constraints of the MEC network. We then propose an approximation algorithm with a provable approximation ratio for the problem with a given set of service requests if both monitoring and analytical DTs are consolidated into a single edge server. Otherwise, we devise an efficient heuristic for the problem with monitoring and analytical DTs possibly being placed into different edge servers. We also consider a dynamic throughput maximization problem of Metaverse service provisioning for a given monitoring period, in which service requests arrive into the system dynamically without the knowledge of future arrivals, service resource demands, and service delay requirements, for which we devise an online learning algorithm. We finally evaluate the performance of the proposed algorithms by extensive simulations. Simulation results show that the throughputs of the proposed algorithms outperform their comparison counterparts by at least 50 %.