# On Maximizing the Probability of Achieving Deadlines in Communication Networks
## 2 Related Work  
In wireless networks with stochastic link characteristics, where link quality is subject to random variations, achieving deadlines becomes a complex task. A growing number of works have proposed paradigms and techniques to address these challenges and achieve deadlines in such conditions [7]. In the sequel, we highlight contributions relevant to this study. We will examine diverse techniques and protocols designed to enhance real-time capabilities in wireless networks, with a particular focus on the metrics essential for meeting deadlines. In scenarios where the topology of the network and the links between nodes are subject to high dynamics or the routing layer has limited information about the network, approaches such as geographic routing (GR) can be particularly useful. Those conditions can be found in mobile ad hoc networks and wireless sensor networks (WSNs). GR leverages the geographic locations of nodes to make routing decisions, eliminating the requirement for explicit knowledge of the network topology. For deadline-aware traffic under this paradigm, velocities, understood as the speed or rate of movement of packets, are commonly utilized as a variable to support timely delivery. An early key contribution in this respect is the SPEED protocol [8], which proposes a GR approach with soft real-time guarantees and congestion avoidance for WSNs. Several extensions of SPEED have been proposed, including energy awareness [9; 10] and packet prioritization combined with probabilistic multi-path forwarding [11]. Also, a combination of transmission power control and GR for improved energy efficiency was considered in [12]. In [13], the real-time routing problem is transformed into a 0/1 integer linear programming problem to effectively balance energy efficiency and reliability for real-time applications. Predictive models can be employed to anticipate and adapt to future link variations. Reinforcement learning (RL) is a prevailing machine learning technique in the literature for routing. Unlike other machine learning techniques, it does not require large data sets [14]. RL provides a high level of adaptability, which allows the protocols to work in dynamically changing networks. Furthermore, RL approaches have been used to optimize for multiple criteria. For instance, [PERSON] et al. [15] proposed an energy-aware quality of service (QoS) routing protocol. In another study by [PERSON] et al. [16], a joint optimization approach for routing and transmission power in dynamic environments was proposed, specifically targeting delay-sensitive applications. Furthermore, various other techniques have been employed to enhance the performance of time-critical networking. For example, in [17], the authors proposed a routing mechanism for real-time communication in WSNs based on composite potential fields. The method, inspired by physics, models nodes as charged particles, and communication paths are determined by attractive and repulsive forces. The metric employed for decision making is the hop count, reflecting the number of intermediate nodes. Also, various cluster-based routing schemes have been proposed [18]. Cluster-based routing can be beneficial for time-critical applications as it optimizes communication by organizing nodes into clusters, reducing latency, enhancing reliability, and facilitating efficient coordination for timely data transmission. A cluster-based protocol for real-time traffic in industrial wireless sensor networks was presented in [19]. The protocol focuses on energy efficiency and reduced end-to-end delay. Real-time updates of routing information, focusing on geographical position, hop counts, and residual energy metrics, enhance overall system performance and scalability. Another cluster-based protocol, detailed in [20], caters to delay-sensitive, bandwidth-intensive, time-critical, and QoS-aware applications.