## 1 Introduction  
Nowadays, delay- and disruption-tolerant (DTN) networks are useful for providing communication in environments where frequent transmission discontinuities are present [1, 2, 3, 4]. The need for DTN networks appeared initially in the field of space communication networks [1, 2, 3], but later, new applications of them appeared, such as underwater communications systems with high attenuation of radio waves, rural networks, environmental monitoring networks, vehicle networks [4, 5], battlefield networks [6], intelligent transport systems, smart cities [7], etc. In DTN networks, devices update their communication routes based on the topological changes of the network. In this way, the mobility of the devices is one of the important aspects of a kind of network, detailed in [8, 9, 10]. The transmission mechanism for messages in this type of network is based on the store-carry-forward paradigm [11, 12]. Routing [13, 14, 15] is the decision taken in the process of finding the best path to follow the messages through the network to reach the destination. The problem of routing in DTN networks is thus reduced to an optimization problem, constrained by the availability or unavailability of the edges in time and the storage capacity of each node in time. Several criteria classify the routing strategies used by the DTN networks, such as type of connection between nodes, the moment to establish the path for messages, the amount of information that the nodes have about the network, and the number of copies of a message that a node sends further. The type of connection between nodes is opportunistic connection based on a schedule, considering that in space everything is in motion and the nodes that can be connected move on a well-defined route, which implies the possibility of establishing its position at a certain time, as well as the possibility of establishing a connection based on this information. This connection is used for space networks and public transport networks. If we consider the moment of path establishing, the source node can calculate and set the path and then encode it inside the message, or each intermediate node calculates only the next message hop based on the information it has from the network [15]. A series of algorithms that contain different amounts of network information are proposed for investigation [15]. Among them, a variant of the Dijkstra algorithm is considered. The main change from the classic Dijkstra algorithm is that in order to determine the cost per arc, the time when the message reaches the node and the transfer time are taken into account. These values are used to calculate the cost of sending the message to the following link. It has been shown that the performance of these algorithms is gradually increasing, depending on the amount of information about the network they use. Considering the number of copies of a message, there are single copy algorithms (forward-based) and multi-copy algorithms (flood-based) [16; 17]. Direct Delivery is a simple forward-based protocol, which involves delivering the message only to the destination node. This type of algorithm is suitable for small and high mobility networks, where the probability of meeting between nodes is high. Examples of classical flood-based protocols are Epidemic [18], Spray and Wait [19], PRoPHET [20], and MaxProp [21]. In [16] there are some comparisons between the first four of them. In the literature there are several variations of these algorithms. In buffer-limited delay-tolerant networks, maximum flow with a static approach can be considered [22]. The classic dynamic network can be adapted to the time-expanded network [23]. [PERSON] [24] investigated the performance of five routing protocols using an Opportunistic Network Environment (ONE) environment and simulated a data collection application using a DTN composed of pedestrians and cyclists equipped with smart devices. One of her conclusions was that MaxProp performs better than other protocols in terms of delivery probability, average latency, and buffer time.