Editing Transport network analysis (section)

==Analysis methods==
A wide range of methods, algorithms, and techniques have been developed for solving problems and tasks relating to network flow. Some of these are common to all types of transport networks, while others are specific to particular application domains.<ref>{{cite book |last1=deSmith |first1=Michael J. |last2=Goodchild |first2=Michael F. |last3=Longley |first3=Paul A. |title=Geospatial Analysis: A Comprehensive Guide to Principles, Techniques, and Software Tools |date=2021 |edition=6th revised |chapter=7.2.1 Overview - network and locational analysis | chapter-url=https://www.spatialanalysisonline.com/HTML/index.html?overview_-_network_analysis.htm}}</ref> Many of these algorithms are implemented in commercial and open-source GIS software, such as [[GRASS GIS]] and the Network Analyst extension to Esri [[ArcGIS]].

===Optimal routing===
{{main | Shortest path problem | Dijkstra's algorithm}}

One of the simplest and most common tasks in a network is to find the optimal route connecting two points along the network, with ''optimal'' defined as minimizing some form of cost, such as distance, energy expenditure, or time.<ref name="Worboys">{{cite book |last1=Worboys |first1=Michael |last2=Duckham |first2=Matt |title=GIS: A Computing Perspective |date=2004 |publisher=CRC Press |pages=211–218 |edition=2nd|chapter=5.7 Network Representation and Algorithms}}</ref> A common example is finding directions in a street network, a feature of almost any web street mapping application such as [[Google Maps]]. The most popular method of solving this task, implemented in most GIS and mapping software, is [[Dijkstra's algorithm]].<ref name="Dijkstra1959">{{cite journal | author-link = Edsger W. Dijkstra | first1 = E. W. | last1 = Dijkstra | s2cid = 123284777 | url= http://www-m3.ma.tum.de/twiki/pub/MN0506/WebHome/dijkstra.pdf | title = A note on two problems in connexion with graphs | journal = Numerische Mathematik | volume = 1 | year = 1959 | pages = 269–271 | doi = 10.1007/BF01386390}}</ref>

In addition to the basic point-to-point routing, ''composite routing problems'' are also common. The [[Traveling salesman problem]] asks for the optimal (least distance/cost) ordering and route to reach a number of destinations; it is an NP-hard problem, but somewhat easier to solve in network space than unconstrained space due to the smaller solution set.<ref>{{cite web |title=v.net.salesman command |url=https://grass.osgeo.org/grass78/manuals/v.net.salesman.html |website=GRASS GIS manual |publisher=OSGEO |access-date=17 March 2021}}</ref> The [[Vehicle routing problem]] is a generalization of this, allowing for multiple simultaneous routes to reach the destinations. The [[Route inspection]] or [[Chinese postman problem|"Chinese Postman" problem]] asks for the optimal (least distance/cost) path that traverses every edge; a common application is the routing of garbage trucks. This turns out to be a much simpler problem to solve, with [[polynomial time]] algorithms.

===Location analysis===
{{main|Facility location problem (disambiguation){{!}}Facility location problem|Location-allocation}}

This class of problems aims to find the optimal location for one or more facilities along the network, with ''optimal'' defined as minimizing the aggregate or mean travel cost to (or from) another set of points in the network. A common example is determining the location of a warehouse to minimize shipping costs to a set of retail outlets, or the location of a retail outlet to minimize the travel time from the residences of its potential customers. In unconstrained (cartesian coordinate) space, this is an NP-hard problem requiring heuristic solutions such as [[Lloyd's algorithm]], but in a network space it can be solved deterministically.<ref>{{cite book |last1=deSmith |first1=Michael J. |last2=Goodchild |first2=Michael F. |last3=Longley |first3=Paul A. |title=Geospatial Analysis: A Comprehensive Guide to Principles, Techniques, and Software Tools |date=2021 |edition=6th revised |chapter=7.4.2 Larger p-median and p-center problems | chapter-url=https://www.spatialanalysisonline.com/HTML/index.html?larger_p-median_and_p-center_p.htm}}</ref>

Particular applications often add further constraints to the problem, such as the location of pre-existing or competing facilities, facility capacities, or maximum cost.

===Service areas===
A network service area is analogous to a [[Buffer (GIS)|buffer]] in unconstrained space, a depiction of the area that can be reached from a point (typically a service facility) in less than a specified distance or other accumulated cost.<ref>{{cite book |last1=deSmith |first1=Michael J. |last2=Goodchild |first2=Michael F. |last3=Longley |first3=Paul A. |title=Geospatial Analysis: A Comprehensive Guide to Principles, Techniques, and Software Tools |date=2021 |edition=6th revised |chapter=7.4.3 Service areas | chapter-url=https://www.spatialanalysisonline.com/HTML/index.html?service_areas.htm}}</ref> For example, the preferred service area for a fire station would be the set of street segments it can reach in a small amount of time. When there are multiple facilities, each edge would be assigned to the nearest facility, producing a result analogous to a [[Voronoi diagram]].<ref>{{cite web |title=v.net.alloc command |url=https://grass.osgeo.org/grass78/manuals/v.net.alloc.html |website=GRASS GIS documentation |publisher=OSGEO |access-date=17 March 2021}}</ref>

===Fault analysis===
A common application in [[public utility]] networks is the identification of possible locations of faults or breaks in the network (which is often buried or otherwise difficult to directly observe), deduced from reports that can be easily located, such as customer complaints.

===Transport engineering===
{{main | Transport engineering|Traffic flow}}
Traffic has been studied extensively&nbsp;using statistical physics methods.<ref>{{Cite journal|last=Helbing|first=D|date=2001|title=Traffic and related self-driven many-particle systems|journal=Reviews of Modern Physics|volume=73|issue=4|pages=1067–1141|arxiv=cond-mat/0012229|bibcode=2001RvMP...73.1067H|doi=10.1103/RevModPhys.73.1067|s2cid=119330488}}</ref><ref>{{Cite book|title=The Physics of Traffic : Empirical Freeway Pattern Features, Engineering Applications, and Theory|last=S.|first=Kerner, Boris|date=2004|publisher=Springer Berlin Heidelberg|isbn=9783540409861|location=Berlin, Heidelberg|oclc=840291446}}</ref><ref>{{Cite book|last1=Wolf|first1=D E|last2=Schreckenberg|first2=M|last3=Bachem|first3=A|title=Traffic and Granular Flow|date=June 1996|pages=1–394|language=en-US|publisher=WORLD SCIENTIFIC|doi=10.1142/9789814531276|isbn=9789810226350}}</ref>

===Vertical analysis===
To ensure the railway system is as efficient as possible a complexity/vertical analysis should also be undertaken. This analysis will aid in the analysis of future and existing systems which is crucial in ensuring the sustainability of a system (Bednar, 2022, pp.&nbsp;75–76). Vertical analysis will consist of knowing the operating activities (day to day operations) of the system, problem prevention, control activities, development of activities and coordination of activities.<ref>Bednar, 2022, pp. 75–76</ref>