This paper addresses the challenges of achieving ultra-reliable and low-latency communications (xURLLC) in the context of next-generation wireless networks. The authors propose a novel NOMA-assisted uplink xURLLC network architecture that leverages stochastic network calculus (SNC) to analyze and optimize key performance indicators (KPIs) such as delay, age-of-information (AoI), and reliability. The SNC-SQP theoretical framework is developed to provide reliable insights into the tail distributions of these KPIs, which are crucial for xURLLC. The framework defines statistical delay violation probability (SDVP) and statistical AoI violation probability (SAVP) to characterize the tail distributions of delay and AoI, respectively. Based on SNC-SQP, an SQP-driven power optimization problem is formulated to minimize uplink transmit power while ensuring the statistical QoS requirements. Extensive simulations validate the effectiveness of the proposed framework, demonstrating significant improvements in power efficiency and SQP performance compared to conventional OMA schemes. The paper also discusses future research directions, including flexible interference management, security, and the integration of machine learning for predictive analytics in xURLLC.This paper addresses the challenges of achieving ultra-reliable and low-latency communications (xURLLC) in the context of next-generation wireless networks. The authors propose a novel NOMA-assisted uplink xURLLC network architecture that leverages stochastic network calculus (SNC) to analyze and optimize key performance indicators (KPIs) such as delay, age-of-information (AoI), and reliability. The SNC-SQP theoretical framework is developed to provide reliable insights into the tail distributions of these KPIs, which are crucial for xURLLC. The framework defines statistical delay violation probability (SDVP) and statistical AoI violation probability (SAVP) to characterize the tail distributions of delay and AoI, respectively. Based on SNC-SQP, an SQP-driven power optimization problem is formulated to minimize uplink transmit power while ensuring the statistical QoS requirements. Extensive simulations validate the effectiveness of the proposed framework, demonstrating significant improvements in power efficiency and SQP performance compared to conventional OMA schemes. The paper also discusses future research directions, including flexible interference management, security, and the integration of machine learning for predictive analytics in xURLLC.