This article deals with the problem of observability of traffic networks, understanding as such the problem of identifying which is the subset of OD-pair and link flows that can be calculated based on a subset of observed OD-pair and link flows and related problems. Two algebraic methods for solving the observability problems are given, one global approach based on null-spaces and a step by step procedure allowing updating the information once each item of information (OD-pair or link flow) becomes available. In particular, seven different observability problems are stated and solved using the proposed methods, which are illustrated by their application to the Nguyen-Dupuis network problem. The results show that the proposed methods provide useful information on which OD-pair or link flows are informative on other OD-pair and link flows, and that the methods are applicable to large networks.

This paper deals with the problem of observability of traffic networks, understanding as such the problem of identifying which is the subset of the origin-destination (OD)-pair and link flows that can be calculated based on a subset of observed OD-pair and link flows, and related problems. A modified topological version of an existing algebraic method for solving observability problems is given. The method is based on a step-by-step procedure, allowing us to update the information once each item of information (OD-pair or link flow) becomes available. In particular, three different observability problems are stated and solved using the proposed methodology, which is illustrated by its application to the Nguyen-Dupuis network and compared with the algebraic version. The topological version is much faster, uses much less memory, and presents no rounding errors or zero test problems but identifies fewer observable flows.

Waste collection is one of the targets of smart cities. It is a daily task in urban areas and it entails the planning of waste truck routes, taking into account environmental, economic and social factors. In this work, an optimal path planning algorithm has been developed together with a practical software platform for smart and sustainable cities that enables computing the optimal waste collection routes, minimizing the impact, both environmental (CO₂ emissions and acoustic damage) and socioeconomic (number of trucks to be used and fuel consumption). The algorithm is executed in Net2Plan, an open-source planning tool, typically used for modeling and planning communication networks. Net2Plan facilitates the introduction of the city layout input information to the algorithm, automatically importing it from geographical information system (GIS) databases using the so-called Net2Plan-GIS library, which can also include positions of smart bins. The algorithm, Net2Plan tool and its extension are open-source, available in a public repository. A practical case in the city of Cartagena (Spain) is presented, where the optimal path planning for plastic waste collection is addressed. This work contributes to the urban mobility plans of smart cities and could be extended to other smart cities scenarios with requests of optimal path planning.