Network Performance Assessment Research Articles

Enhancing reflection and self-determination in a real-life community mesh network

This article discusses the Network Characterization Daemon (NCD), a piece of software that provides users of Community Mesh Networks (CMNs) with an interactive tool to monitor, evaluate and fine-tune their network nodes.First, CMNs are introduced as a particular case of Community Networks (CNs), and their participation challenges are analysed. The NCD is then discussed as a novel solution that provides CMN end users with mechanisms to assess network performance and improve their quality of experience by modifying their devices’ network configuration. The relation of the NCD with Quick Mesh Project (qMp) and the BatMan-eXperimental version 6 (BMX6) routing protocol is detailed as part of the social and technological context.The NCD also provides an experimentation framework to evaluate network performance in real-life CMNs. The latter part of this article covers the experiments performed using the NCD to assess network performance (in terms of path selection, Round-Trip Time (RTT), etc.) when different BMX6 routing policies are applied. The results show how, under different traffic conditions (e.g. distinct packet sizes), using specific routing policies leads to an improvement in network performance.Finally, the integration of the NCD in qMp is discussed, in order to ensure its long-term sustainability.

Scalable Synchrophasors Communication Network Design and Implementation for Real-Time Distributed Generation Grid

There has been a growing interest in the deployment of phasor measurement units (PMUs) not only in high-voltage transmission, but in lower-voltage distribution systems. For a distributed generation (DG) grid, this would require deployment of PMUs at critical locations, which implies accurate phase measurement with the support of a low delay, highly reliable network infrastructure. In the absence of such a network, the most cost-effective solution would be to consider a wireless network to support centralized control for situational awareness in the transmission, as well as the DG grid environment. Therefore, the main objective in this paper is to design and implement a scalable synchrophasor network using wireless LAN technology to assess network performance and requirements under real-world conditions. To achieve this, we have designed an emulation platform that can support physical and medium access control layers. The data communication at the application is based on the IEEE C37.118-2011-2 Standard. By considering a hierarchical network architecture for our testbed implementation, we propose an efficient method to reduce bandwidth, as well as provide capabilities for control and management at each hierarchical level. In addition, an efficient tree-based multihop routing protocol has been designed to match a specific distribution feeder structure. The testbed is then used to access different network configurations under various test conditions.

Flattening: An efficient approach to improving the performance of conventional MINs

Numerous conventional interconnection networks have been designed in a way in which they use indirect or multistage topologies. The reason behind this idea is the fact that such topologies can minimize the network hop count. However, the constraints of technology and packaging have given impetus for fundamental changes in the approach to designing topologies. Increasing the radix of the network׳s routers lowers the total cost of the network, which is related to the number of routers׳ pins and connectors. This increase also results in lowering the power consumption, which plays a crucial role in the performance. Kim, Dally and Abts have provided a cost-efficient topology for high-radix networks, named the flattened Butterfly. They have shown that this approach is comparable to the conventional Butterfly networks with regard to cost. It is much the same as a Folded-Clos topology in terms of the performance per cost ratio under adversarial traffic, whilst under benign traffic, the flattened Butterfly has approximately twice this ratio. In this paper, we have generalized the idea of flattening to all Delta networks, in addition to some non-Delta ones such as Beneš and Clos. Moreover, the conditions on which multistage networks can be converted to the flattened ones have been generally provided. All the mentioned networks have also been compared with another cost-efficient topology, named the HyperX, in order to gain deep insight into the key facets of the microarchitecture of high-radix networks. On the other hand, advances in designing digital circuits and reduction in their size rely upon knowledge in nano-electronics for refinements of the standard copper interconnect technology. This copper interconnects have become a major performance bottleneck in Multistage Interconnection Network (MIN) platforms. Consequently, a minor contribution of this paper is the performance assessment of the aforementioned networks using the Carbon NanoTube (CNT) technology under trace-driven and synthetic traffic patterns; inasmuch as this technology has been introduced as one of the six most important architectures in future digital systems. CNT is considered to be a promising technology in the design and fabrication of the next-generation chips since it is capable of handling extremely high current densities for a long time without considerable performance degradation. Although the comparative study of different networks with various parameters is the main goal, it should be taken into consideration that in some situations, these parameters provide similar conditions in different networks. As such, they can be combined with an efficient method to present a simple model. Finally, we have used data mining in order to reach a unified and meaningful performance parameter.

Optimization model for regional evacuation transportation system using macroscopic productivity function

The simulation of mass evacuation traffic processes, while enormously valuable in emergency planning and management, presents a number of challenges to transportation modelers and analysts. One area where evacuation modeling and analysis has lacked is in the ability to determine the specific evacuation travel demand and capacity and conditions under which a road network can most effectively carry the maximum outflow rate for an area under threat of catastrophic disasters. This is a difficult question to answer because evacuations are so complex and can include millions of people, traveling on tens of thousands of miles of roads, lasting several hours or even days in duration. Knowledge of how to reduce the likelihood of over-saturation would be useful, for example, to develop temporally and spatially phased evacuation plans that meter demand into the system for maximum overall benefit. In this paper an optimization model is proposed to maximize evacuation throughput traffic for regional networks. This model aims at optimizing network outflow and trip complete percentage at a macroscopic level by changing the distribution of evacuation traffic in the time horizon. The productivity function, pioneered by Geroliminis and Daganzo (2007, 2008) is used to assess network performance from a macroscopic point of view. Then, an optimization model with the objective of maximizing both total network productivity and outflow rate is proposed. Further, a simulation based study of the New Orleans metropolitan area is used to validate the effectiveness of the optimization model.

Network performance assessment for collaborative disaster response

Purpose– The purpose of this paper is to propose a modified network performance assessment method to address issues of coordination among organizations in the context of disaster response.Design/methodology/approach– The study introduces affiliation networks to map disaster response system integrated with task/function and unit identifications. The study also assesses performance in two successive procedures including ineffective networks identification and assessment on organizational effectiveness.Findings– The study emphasizes problems in the current emergency management system in China with a focus on Sichuan earthquake experience. Specifically, some problems with the traditional central planning and control mechanisms in coordination across boundaries are highlighted, including participants’ inexact perception of information or resource accessibility, confusion of functional designation of organizations.Originality/value– The study builds network performance assessment method to other contexts where different emergency management systems exist and modifies them to facilitate quick complex networks evaluation. The theoretical insights from affiliation networks and cognitive accuracy provide additional contributions to the literature.

An intersection-movement-based stochastic dynamic user optimal route choice model for assessing network performance

Different from traditional methods, this paper formulates the logit-based stochastic dynamic user optimal (SDUO) route choice problem as a fixed point (FP) problem in terms of intersection movement choice probabilities, which contain travelers’ route information so that the realistic effects of physical queues can be captured in the formulation when a physical-queue traffic flow model is adopted, and that route enumeration and column generation heuristics can be avoided in the solution procedure when efficient path sets are used. The choice probability can be either destination specific or origin–destination specific, resulting into two formulations. To capture the effect of physical queues in these FP formulations, the link transmission model is modified for the network loading and travel time determination. The self-regulated averaging method (SRAM) was adopted to solve the FP formulations. Numerical examples were developed to illustrate the properties of the problem and the effectiveness of the solution method. The proposed models were further used to evaluate the effect of information quality and road network improvement on the network performance in terms of total system travel time (TSTT) and the cost of total vehicle emissions (CTVE). Numerical results show that providing better information quality, enhancing link outflow capacity, or constructing a new road can lead to poor network performance.

Performance assessment of smart distribution networks with strategic operation of battery electric vehicles

Energy security, greenhouse gas emission, and debate on climate change gained an increased interest for penetrating renewable power generation into distribution networks. Among the renewable power technologies, the wind power takes a considerable share to supply the electricity demand in many networks. The wind is intermittent and its power output needs an auxiliary support to serve the energy customers and to limit impacts. The emerging battery electric vehicles (BEVs) are a potential source that can be used to mitigate intermittent effects of wind power outputs in modern distribution networks. BEVs are inherited with the mobility advantage and they can be used as a battery-based energy storage solution to smooth intermittent power outputs. Taking into account the mobility advantage of BEVs, the paper investigates the strategic ability of them to enhance the reliability performance of an unbalanced power distribution network by incorporating the provision of smart coordination of vehicles. Operation of BEVs is characterized by using charging and discharging rates, depth of discharge, and their states of charge at times of operation. A set of case studies were performed by integrating generic distribution network models to a power transmission network model. The results suggest that strategic operation of BEVs can potentially provide a considerable opportunity to build capacity required for wind power in smart power distribution systems. Results also depict that the necessary BEV capacity to mitigate wind impacts on reliability does not necessarily correlate with installed capacities of wind plants. A quantitative assessment provides detailed information of impact thresholds.

Feasibility of Secondary Networks: Analysis Methodology and Quantitative Study of Cellular and Wi-Fi-Like TVWS Deployments

Recent rulings by US and UK regulators allowing access to unused portions of TV spectrum have elicited high hopes for the practical value of these TV whitespaces (TVWS) for secondary exploitation. However, this optimism has been largely fueled by rather simple early studies, which do not consider all the system aspects in sufficient detail; the few early experimental works reported are proprietary and consider only a small number of nodes, whereas the existing more sophisticated theoretical studies focus on singular aspects of secondary spectrum access in isolation from the overall system interactions. In this paper we study quantitatively the deployment of secondary networks in TVWS by considering two archetypal candidate systems: LTE-like cellular and Wi-Fi-like networks. We develop a systematic framework for the performance evaluation of secondary networks, which we then use to obtain realistic estimates of the performance of our example systems. The secondary network performance assessment methodology demonstrated in this paper can be directly applied for other regions and systems. Our work explicitly takes into account limitations arising from aggregate interference, user density, and specific secondary transceiver characteristics. We argue that a systematic analysis, jointly considering all of these aspects, is key for obtaining realistic and robust results on the estimated value of whitespace spectrum. Our detailed system-level approach reveals a much more conservative picture of the realistic benefit of TVWS deployments than what has been commonly assumed thus far. We find that cellular TVWS networks have limited capabilities, but that a macro-cellular-only network may be a viable option for traffic offloading. Our results also show that Wi-Fi-like secondary deployments in TVWS, although increasing coverage range, lead to increased congestion, which limits the system capacity.

Transportation Network Post-Disaster Planning and Management: A Review Part II: Decision-Making and Planning of Post-Disaster Operations

This is the second part of a two-part survey investigating transportation network postdisaster planning and management. The first part focused on efforts and models for the estimation and assessment of post-disaster network performance (PDNP). This paper addresses the problem of decision-making and planning of post-disaster network operations (Post-Disaster Network Operations Planning – PDNOP). The paper reviews existing work in the field of post-disaster network planning, as realized by the deployment of different operational actions for improving service provision by a surviving network. Three distinct types of operations are considered: evacuation, network design and emergency traffic management. The survey highlights important aspects of PDNOP, offers a detailed discussion on the strategies and parameters found in the literature and indicates potential future research directions.

Estimation of mean and covariance of peak hour origin–destination demands from day-to-day traffic counts

This paper proposes a generalized model to estimate the peak hour origin–destination (OD) traffic demand variation from day-to-day hourly traffic counts throughout the whole year. Different from the conventional OD estimation methods, the proposed modeling approach aims to estimate not only the mean but also the variation (in terms of covariance matrix) of the OD demands during the same peak hour periods due to day-to-day fluctuation over the whole year. For this purpose, this paper fully considers the first- and second-order statistical properties of the day-to-day hourly traffic count data so as to capture the stochastic characteristics of the OD demands. The proposed model is formulated as a bi-level optimization problem. In the upper-level problem, a weighted least squares method is used to estimate the mean and covariance matrix of the OD demands. In the lower-level problem, a reliability-based traffic assignment model is adopted to take account of travelers’ risk-taking path choice behaviors under OD demand variation. A heuristic iterative estimation-assignment algorithm is proposed for solving the bi-level optimization problem. Numerical examples are presented to illustrate the applications of the proposed model for assessment of network performance over the whole year.

New models for conventional and heat exchangers enhanced with tube inserts for heat exchanger network retrofit

The retrofit of heat exchanger networks requires detailed models of the heat exchangers for the detailed assessment of network performance. Network retrofit options include heat transfer enhancement. There is thus a requirement for detailed models of heat exchanger performance, including heat transfer enhancement, suitable for inclusion in network retrofit optimization algorithms. Such models must be robust, computationally efficient and accurate enough to reflect the heat transfer and pressure drop performance of actual equipment. This paper presents a simple but reliable method to model the performance of shell-and-tube heat exchangers, including heat transfer enhancement with tube inserts. Two commonly used tube inserts, twisted tapes and coiled wires, are investigated for tube-side heat transfer augmentation. A new set of consistent performance correlations covering all flow regions for twisted-tape and wired-coil inserts is introduced. The models can be conveniently used for existing exchanger simulation, rating and assessment of heat transfer enhancement. They can also be used for sizing new exchangers to be introduced in a network. A case study illustrates the application of these performance models.

Modeling Network Interference in the Angular Domain: Interference Azimuth Spectrum

The performance of wireless networks is fundamentally limited by interference [or, equivalently, the signal-to-interference ratio (SIR)]. In an attempt to characterize the interference as a direction-selective quantity and motivated by the useful analogy between classical propagation channels and wireless networks, we propose a novel network description framework, namely the interference azimuth spectrum (IAS). The IAS represents the distribution of interference in the angular domain and is parallel to the conventional power azimuth spectrum (PAS) used in propagation channels. We also extend this concept to the directional characterization of average achievable rate, assuming that interference is treated as noise. Provided with this analytical framework, we present the notion of local area outage, defined as the probability that a receiver is in the state of outage within a local area where both interference and desired signal are assumed to be wide-sense stationary (WSS). We further propose the geometry-based stochastic models (GBSMs) as a part of the IAS framework, where the interfering terminals are randomly distributed according to a specific probability density function (pdf) of their positions. The GBSMs are applicable to a wide variety of wireless network environments without and with interferer clustering. The proposed methodology would provide useful insight on the design and performance assessment of future networks, featured by opportunistic, randomized, and dense placement of nodes.

A multi-objective assessment of an air quality monitoring network using environmental, economic, and social indicators and GIS-based models

In the United States, air pollution is primarily measured by Air Quality Monitoring Networks (AQMN). These AQMNs have multiple objectives, including characterizing pollution patterns, protecting the public health, and determining compliance with air quality standards. In 2006, the U.S. Environmental Protection Agency issued a directive that air pollution agencies assess the performance of their AQMNs. Although various methods to design and assess AQMNs exist, here we demonstrate a geographic information system (GIS)-based approach that combines environmental, economic, and social indicators through the assessment of the ozone (O3) and particulate matter (PM10) networks in Maricopa County, Arizona. The assessment was conducted in three phases: (1) to evaluate the performance of the existing networks, (2) to identify areas that would benefit from the addition of new monitoring stations, and (3) to recommend changes to the AQMN. A comprehensive set of indicators was created for evaluating differing aspects of the AQMNs’ objectives, and weights were applied to emphasize important indicators. Indicators were also classified according to their sustainable development goal. Our results showed that O3 was well represented in the county with some redundancy in terms of the urban monitors. The addition of weights to the indicators only had a minimal effect on the results. For O3, urban monitors had greater social scores, while rural monitors had greater environmental scores. The results did not suggest a need for adding more O3 monitoring sites. For PM10, clustered urban monitors were redundant, and weights also had a minimal effect on the results. The clustered urban monitors had overall low scores; sites near point sources had high environmental scores. Several areas were identified as needing additional PM10 monitors. This study demonstrates the usefulness of a multi-indicator approach to assess AQMNs. Network managers and planners may use this method to assess the performance of air quality monitoring networks in urban regions.Implications:The U.S. Environmental Protection Agency issued a directive in 2006 that air pollution agencies assess the performance of their AQMNs; as a result, we developed a GIS-based, multi-objective assessment approach that integrates environmental, economic, and social indicators, and demonstrates its use through assessing the O3 and PM10 monitoring networks in the Phoenix metropolitan area. We exhibit a method of assessing network performance and identifying areas that would benefit from new monitoring stations; also, we demonstrate the effect of adding weights to the indicators. Our study shows that using a multi-indicator approach gave detailed assessment results for the Phoenix AQMN.

E-Posters

Lifelong surveillance is not cost-effective after endovascular aneurysm repair (EVAR), but is required to detect aortic complications which are fatal if untreated (type 1/3 endoleak, sac expansion, device migration). Aneurysm morphology determines the probability of aortic complications and therefore the need for surveillance, but existing analyses have proven incapable of identifying patients at sufficiently low risk to justify abandoning surveillance. This study aimed to improve the prediction of aortic complications, through the application of machine-learning techniques. Patients undergoing EVAR at 2 centres were studied from 2004–2010. Aneurysm morphology had previously been studied to derive the SGVI Score for predicting aortic complications. Bayesian Neural Networks were designed using the same data, to dichotomise patients into groups at low- or high-risk of aortic complications. Network training was performed only on patients treated at centre 1. External validation was performed by assessing network performance independently of network training, on patients treated at centre 2. Discrimination was assessed by Kaplan-Meier analysis to compare aortic complications in predicted low-risk versus predicted high-risk patients. 761 patients aged 75 +/− 7 years underwent EVAR in 2 centres. Mean follow-up was 36+/− 20 months. Neural networks were created incorporating neck angu- lation/length/diameter/volume; AAA diameter/area/volume/length/tortuosity; and common iliac tortuosity/diameter. A 19-feature network predicted aor- tic complications with excellent discrimination and external validation (5-year freedom from aortic complications in predicted low-risk vs predicted high-risk patients: 97.9% vs. 63%; p < 0.0001). A Bayesian Neural-Network algorithm can identify patients in whom it may be safe to abandon surveillance after EVAR. This proposal requires prospective study.

Data Envelopment Analysis (D.E.A.) for Urban Road System Performance Assessment

Improving the efficiency of transport networks by enhancing road system performance, lays the foundations for the positive change process within a city, achieving good accessibility to the area and optimizing vehicle flows, both in terms of cost, management and attenuation of environmental impacts. The performance of an urban road system can be defined according to different thematic areas such as traffic flow, accessibility, maintenance and safety, for which the scientific literature proposes different measurement indicators. However variations in performance are influenced by interventions which differ from one another, such as infrastructure, management, regulation or legislation, etc. Therefore sometimes it is not easy to understand which areas to act on and what type of action to pursue to improve road network performance. Of particular interest are the tools based on the use of synthetic macro-indicators that are representative of the individual thematic areas and are able to describe the behavior of the entire network as a function of its characteristic elements. These instruments are of major significance when they assess performance not so much in absolute terms but in relative terms, i.e. in relation to other urban areas comparable to the one being examined. Therefore the objective of the proposed paper is to compare performances of different urban networks, using a non-parametric linear programming technique such as Data Envelopment Analysis (DEA), Farrel (1957), in order to provide technical support to the policy maker in the choice of actions to be implemented to make urban road systems efficient. This work is the conclusive study of road system performance analysis using DEA.The study forms part of a research project supported by grant, PRIN-2009 prot. 2009EP3S42_003, in which the University di Cagliari is a partner with a research team comprising the authors of this paper, and which addresses performance assessment of road networks, Fancello, Uccheddu and Fadda (2013a),(2013b).

Performance assessment of stochastic node-failure computer networks according to routing scheme under packet reliability

Under the strict assumption that each component’s (branch/node) capacity of the network is deterministic, the quickest path problem is to find a path sending specific packets of data from the source to the sink such that the transmission time is minimized. However, in many real-time networks such as computer systems, each component (branch or node) has a stochastic capacity and a packet reliability. In particular, the capacity is a random variable with arbitrary probability distribution. Such a network is named a stochastic node-failure computer network (SNFCN). In an SNFCN, each component has several capacities, lead time, and packet reliability. A routing scheme is a transmission rule to indicate the first and second priority minimal path. Hence, this paper assesses the system reliability when d units of data are sent through the SNFCN under both the required packet reliability and time constraints according to two different routing schemes. Such a probability is a performance indicator that can provide managers with an understanding of the system capability and can help to identify possible improvements. The system reliability with respect to the routing scheme is subsequently calculated.

Modeling distribution tail in network performance assessment: A mean-excess total travel time risk measure and analytical estimation method

Risk measures are often used by decision makers (DMs) as a scalar risk characterization by integrating the statistical characteristics of risk as well as the DMs’ risk strategy towards uncertainty. A good risk measure typically needs to have a risk preference control mechanism, a complete uncertainty characterization, and a practical implementation strategy. Total travel time reliability (TTTR) and total travel time budget (TTTB) are two risk measures recently proposed for assessing transportation network performance under uncertainty. In this paper, we propose the mean-excess total travel time (METTT) as an alternative network-wide risk measure to more cost-effectively capture the distribution tail, and develop an analytical method to estimate risk measures without knowing the explicit distribution form of TTT uncertainty. Methodologically, the METTT measure characterizes the distribution tail of exceeding the TTTB via the conditional expectation without requiring an extraordinary reliability level. It is able to account for the tradeoff between planners’ risk-aversion attitude and the unacceptable risk, which avoids the need of setting a too conservative reliability requirement in the TTTB to reduce the unacceptable risk. The explicit distribution tail consideration in the METTT could lower the construction cost and substantially reduce the unacceptable risk of network capacity enhancement under uncertainty. To enhance the practicality of METTT, we develop an analytical estimation method to efficiently calculate the METTT by using the first four TTT moments as well as the planners’ risk attitude. The TTTR and TTTB measures can also be analytically estimated as a byproduct of the proposed method for assessing the METTT. The analytical feature of the proposed method avoids the burdensome computation of simulation method and also circumvents the need of fitting the explicit TTT distribution form. Numerical results indicate that the proposed method has a desirable and comparable estimation quality in comparison with the theoretical derivation and curve fitting methods.

The Performance of an Urban Road System: An Innovative Approach Using D.E.A. (Data Envelopment Analysis)

Improving the efficiency of transport networks by enhancing road system performance, lays the foundations for the positive change process within a city, achieving good accessibility to the area and optimizing vehicle flows, both in terms of cost management and attenuation of environmental impacts. The performance of an urban road system can be defined according to different thematic areas such as traffic flow, accessibility, maintenance and safety, for which the scientific literature proposes different measurement indicators. However variations in performance are influenced by interventions which differ from one another, such as infrastructure, management, regulation or legislation, etc. Therefore sometimes it is not easy to understand which areas to act on and what type of action to pursue to improve road network performance. Of particular interest are the tools based on the use of synthetic macro-indicators that represent the individual thematic areas and are able to describe the behavior of the entire network as a function of its characteristic elements. These instruments are of major significance when they assess performance not so much in absolute terms but in relative terms, i.e. in relation to other comparable urban areas. Therefore the objective of the proposed paper is to compare performances of different urban networks, using a non-parametric linear programming technique such as Data Envelopment Analysis (DEA), Farrel (1957) , in order to provide technical support to the policy maker in the choice of actions to be implemented to make urban road systems efficient. This work forms part of a research project supported by grant, PRIN-2009 prot. 2009EP3S42_003, in which the University di Cagliari is a partner with a research team comprising the authors of this paper, and which concerns performance assessment of road networks (2013a, 2013b).

A new set of water losses-related performance indicators focused on areas facing water scarcity conditions

As almost all Mediterranean countries are facing water scarcity problems today, water losses in drinking water supply networks have grown to an urgent problem, needing immediate confrontation, representing a too valuable to be neglected water potential. The first step towards water losses reduction is the water supply network performance assessment process. The most commonly used methodology is the one introduced by the International Water Association (IWA), including the International Standard Water Balance and a list of Performance Indicators (PIs). Five years after the second PIs handbook edition was launched increasing the PIs included to 170 from 133 of the first edition, there is a need to re-evaluate them, including also new PIs adapted/focused to regional conditions and addressing other important topics such as environmental issues. The paper presents a new set of water losses-related PIs, focused on areas facing water scarcity conditions met in the Mediterranean countries, forming a solid basis for an integrated Decision Support System (DSS) to evaluate water supply networks and prioritize alternative water losses reduction strategies. The new set includes 75 out of the 170 IWA PIs and 42 new proposed PIs. The new PIs set is formed, selecting the most appropriate existing PIs and suggesting new ones. An integrated approach using a survey among local stakeholders in each partner’s country is used. The platform and the basic components of this user-friendly DSS tool are also being presented here.

Frontier-based performance analysis models for supply chain management: State of the art and research directions

Effective supply chain management relies on information integration and implementation of best practice techniques across the chain. Supply chains are examples of complex multi-stage systems with temporal and causal interrelations, operating multi-input and multi-output production and services under utilization of fixed and variable resources. Acknowledging the lack of system’s view, the need to identify system-wide and individual effects as well as incorporating a coherent set of performance metrics, the recent literature reports on an increasing, but yet limited, number of applications of frontier analysis models (e.g. DEA) for the performance assessment of supply chains or networks. The relevant models in this respect are multi-stage models with various assumptions on the intermediate outputs and inputs, enabling the derivation of metrics for technical and cost efficiencies for the system as well as the autonomous links. This paper reviews the state of the art in network DEA modeling, in particular two-stage models, along with a critical review of the advanced applications that are reported in terms of the consistency of the underlying assumptions and the results derived. Consolidating current work in this range using the unified notations and comparison of the properties of the presented models, the paper is closed with recommendations for future research in terms of both theory and application.