# Improving the Functional Reliability of an Urban Public Transport Line
## 1 Introduction
### Literature Review  
The literature offers a wide range of references that deal with the issue of the quality of public transport services and the reliability of services as an important part of this quality. In the following, we present some articles that are representative of a category of works on the topic of reliability that are closer to the approach of the present work. By investigating approximately one hundred works, the authors of the review article [24] identify the most important aspects that measure the reliability of transport services. Most often these are related to time: travel time, waiting time, boarding/disembarking time, etc., or the availability of seats in the vehicle, missing connections, or compliance with the schedule. By considering the total generalized cost of the urban public transport trip, the authors of the paper [25] try to take into account the users' perception in estimating the reliability of the service; this being the most important merit of the paper. The model considers users separated into three categories depending on their generalized cost and their level of acceptability to make the trip under the conditions of a capacity reduction of the transport network links. The characteristics of the category that does not accept the trip when the transport capacity is reduced by a certain value represent the measure of reliability. The reliability of the infrastructure network, just one of the components of the transport service, is addressed in the paper [26], which proposes an evaluation model by decomposing the network into several series and parallel configurations of the component elements using graph theory. This category of papers is widely spread, with graph theory addressing both the reliability and the vulnerability but also the resilience of transport networks, for example, paper [27], which, however, does not deal with the problem of service dysfunction in the network. The problem of introducing the reliability of the service as an element in its design is brought into discussion by the paper [28]. The author surveys the international level and another at the level of the network of Dutch operators and highlights the inconsistency in defining the reliability of the public transport service. Inspirational works [29; 30] that rigorously describe the utility and the mode of operation of bi-directional trans. Assessments are made of the advantages (including those of land saving) of introducing this type of flexible-use tram. However, their advantage in increasing the reliability of the service is not addressed. An important class of papers deals with the solution of using the short turning pattern. In the paper [31], the authors demonstrated that the short-turning solution leads to a more efficient management of resources in the case of some over congested metro lines on certain sections. The degree of loading of metro services is the main tool in determining the congested section. The authors of the paper [32] study different short-turning solutions for transit services (differentiated by length, frequency, and position concerning the full service) to reduce the waiting time and identify an acceptable level of vehicle occupancy. An interesting model for predicting the length of dysfunctionality [33] for the conventional railway (with optimistic and pessimistic assumptions) is proposed together with a short-turning solution for train rescheduling. The present paper novelty consists in defining the functional reliability concept by considering all the three main components of a transport system, i.e., infrastructure, vehicle, and operational management. The framework for the evaluation of functional reliability is set considering the user's point of view. We analyze the impact of specific technical interventions (crossing connections between the two lines of a generic tram line with a dedicated way, using bi-directional trans and appropriate operational management) on the functional reliability of tram services in two cases of disruptions.