## 1 Introduction  
Seas and oceans have been used as a channel of communication, transportation and navigation from the very beginning. With the advancement in technology, different types of paradigms have been developed to enable the applications in water, such as ocean sampling, pollution monitoring and assisted navigation. One of these architectures is Underwater Wireless Sensor Network (UWSN). In this network, nodes are deployed underwater to perform specific tasks such as sensing of physical attributes of water. After sensing, sensor nodes transmit data to sinks/on-surface stations. They can also forward their data through intermediate nodes or underwater vehicles. One of the major subclasses of UWSN is Underwater Acoustic Sensor Network (UASN) in which acoustic signal is used for the communication between sensor nodes and the sinks. Acoustic signals can travel to longer distance due to lower frequency than radio waves. Such signals work well in water environment, however, acoustic signal causes high delay in data communication due to its speed of 1500 m/s. Acoustic signal has a frequency range between 10 kHz and 1 MHz. UWSNs have huge number of applications such as seismic monitoring, submarine detection and oil spillage monitoring which require specific deployment strategies of sensor nodes. UWSNs may be of any shape, _i.e._, rectangular, cylindrical or square. In this research work, we propose routing schemes specifically for application-oriented cylindrical networks. These applications require energy-efficient and delay-sensitive routing designs. [PERSON] _et al._[1] examine important challenges in acoustic communication and routing. They also address the routing challenges, according to the network protocol stack. They explore open research challenges in both 2-dimensional and 3-dimensional UWSNs. There are mainly two types of routing protocols in UWSNs _i.e._, localization-based and localization-free routing protocols. In the first type, nodes perform data routing by using their location information. There are different ways to achieve localization information of the nodes, e.g., through GPS. In localization-free routing protocols, node does not have any localization information. [PERSON] _et al._[2] recommend an efficient way to achieve localization information of sensor nodes and environment mapping scheme utilizing robotic fish. It is mainly based on cooperative location and particle filter. Machine learning-based adaptive routing protocol for UWSNs, QELAR [3], discusses an outline for distributing residual energy equally among the nodes in order to compute reward function. In this scheme, reward function plays main role in selecting the optimal forwarder for sensor nodes. QELAR achieves enhanced network lifetime by using the reinforcement learning method. Another data-efficient scheme, Path Unaware Layered Routing Protocol for UWSNs, PULRP [4], provides a detailed algorithm to acquire low packet drop ratio along with decreased overhead of the network. In this scheme, nodes do not require localization information of their neighbor nodes. As mentioned earlier that acoustic signal experiences high delay in data communication due to its speed of 1500 m/s. Thereby, authors in [5] study queuing system with the assumption of slotted operation such that servers can serve in the beginning of the slot only. However, this assumption seems to be restrictive in many practical scenarios. Similarly, authors in [6, 7] state that the back-pressure algorithm requires maintenance of separate queue for each destination, which prevents its implementation in large-scale networks. In this paper, we propose 4-chain, 2-chain and single-chain based routing schemes for a cylindrical network as shown in Figure 1. The 4-chain routing scheme is introduced and the global optimum solution is found in terms of transmission distance. In the 2-chain routing scheme, we divide the deployed nodes in two separate regions and create 2-chain network to share the forwarding load.