## 1 Introduction  
The multistate flow network (MFN) is a popular and generic construction of an intelligent wireless sensing system. The MFN is a network composed of a plurality of nodes and edges, and the network satisfies the following assumptions: the nodes must satisfy the flow conservation law, and the flow of the edge must satisfy the following conditions, i.e.,  
1. The flow values are multiple independents;
2. The flow values are discrete, have an upper limit, and are random values. Then, we call this network an MFN, which has been the subject of many related studies, including reliability evaluation [1], the development of an improved algorithm [2], and a merge search method [3] for an MFN. The reliability of an MFN, which is the probability that the specified flow will be delivered from the source of the network to the sink, has been widely studied and applied in various fields of practice under numerous conditions, such as two-terminal networks [4], the proposed quickest path approach [5], constant delivery characteristics [6], a used recursive algorithm [7], binary element states [8], a novel direct approach [9], a proposed adjacent-first-based branch-and-bound approach [10], a used artificial neural network [11], a considered time constraint [12], a studied vehicle routing problem [13], a production network [14], priority components based on considered cost [15], a power system [16], an adopted cut vectors approach [17], the quickest method studied considering deterioration [18] and a studied angle network [19]. Several scholars continue to contribute to the study of new algorithms to assess MFN reliability. In addition to the traditional flow capacity constraints, several scholars added other conditions, such as a delivery lead time limit [12]. Several scholars applied MFN reliability to practical environments, such as logistics distribution systems [12], factory production systems [14], and power distribution systems [16]. The construction of intelligent logistics with intelligent wireless sensing is a global trend. Though several scholars have contributed to the relevant research on MFN reliability over the years, fewer works on the type of roads, that is, the type of the edges of the network, have been produced. Intelligent logistics require an investment in sensor devices. In order to effectively increase the effective value of this investment, and therefore of intelligent logistics, it is necessary to have a good driving plan for the choice of road types in advance to effectively improve the reliability of delivery and ensure and enhance the value of this investment in intelligent logistics. In each country's domestic transportation, most of the goods are carried by trucks, and trucks can choose different road types to complete the delivery of goods. Therefore, this study proposes two different types of roads, namely highways and slow roads. Here, the speed limit of the road is used as the basis for distinguishing the road types. The study of the types of roads in this study not only can contribute to the effective planning of intelligent logistics and enhance the investment value of sensors but also can be applied to general logistics. This study further explores the limitations of the proposed different road types. Trucks travel at different speeds on two types of roads; the speed of the highway is higher than that of the slow road, so the truck is limited by the turning angle due to the fast speed on the highway. If the speed is fast, and the turning angle is too large, it is easy to cause the risk of a truck rollover. In addition, the weight of trucks carrying goods includes a lower capacity on highways than that of slow roads, so it is necessary to include constraints. Moreover, today's logistics delivery is time-sensitive to enhance the competitiveness of the company, so the completion of delivery time should also be included in the constraints.