Performance analysis of charging strategies for shared mobility: a queuing network modelling approach

Sharing mobility systems are an established reality in many cities and their role in urban mobility is set to gain further relevance as the sharing economy gains momentum. Free-floating, one-way services are the most flexible, allowing users to pick up a vehicle and leave it anywhere within the operational area. This is a great advantage for the user, but at the same time it makes management harder. The lack of predefined parking stations and the uneven demand patterns often result in unbalances in the fleet distribution, requiring operator interventions. Relocation of vehicles in shared mobility has topical relevance because it allows to increase the number of trips, bringing additional revenues to the operator and satisfaction to the customers. Recently, thanks to an increased climate crisis awareness, many mobility service providers are including electric vehicles (EV) in their fleet. This requires additional planning of infrastructures (charging stations) and new policies to implement charging operations which can be complex to manage due to the long time required. The optimal relocation problem is then joined by an optimal charging one. This thesis work fits into the analysis of free-floating shared mobility services employing an EV fleet. A special focus is given to the performance analysis of metrics related to charging policies and relocation. The used approach is analytical and different models based on queuing theory are proposed. Unlike other approaches such as simulation, analytical modelling allows to build a generic model with the advantage of requiring low computational power and time resources, guaranteeing the convergence of the solution and its clear interpretation. However, too many details may increase the model complexity, resulting in a not derivable mathematical formulation. Starting from simple models of single city zones and charging stations, more complex ones are built using queues networks. Mobility-only networks are first studied, charging station queues are then included showing the impact of charging operations and eventually trip times are modelled through delay queues. Many case studies are presented with model parameters inferred from real data from a car2go database for the city of Turin, giving a spatial characterisation of inputs and results. The number, placement and aggregation of stations in the network are first studied. Charging policies implementing decisions on when, where to and which EV bring to charge are then explored taking also into account relocation, which considers where to reposition vehicles when the process is completed. The performance indicators have been obtained through mathematical formulas and algorithms such as the Mean Value Analysis. The reference metrics are the system throughput (total number of trips) and the percentage of unsatisfied mobility demand. Moreover, the distribution and number of vehicles, the average utilisation and throughput of the stations as well as the probability for an EV to wait in line to charge are discussed. Eventually, a brief study on how charging operations affect the power grid is proposed and the effect of varying trip times on mobility is observed. Results showed a good capacity of the model to represent typical dynamics of a shared mobility system. With the best combination of policies for charge and relocation, a decrease in the unsatisfied percentage of demand has been observed up to 20.4% for a balanced network, corresponding to an increase of around 48% of the throughput.