In most networks, not all edges can connect to all other junctions. Also, not all edges can connect to all other edges through a specified junction. For example, a hydrant lateral in a water network can connect to a hydrant, but not to a service lateral. Similarly, a 10-inch transmission main can only con-nect to an 8-inch transmission main through a reducer.
Connectivity rules constrain the type of network features that may be con-nected to one another and the number of features of any particular type that can be connected to features of another type.
Connectivity rules let you easily maintain the integrity of the network features in a geometric network. At any time, you can selectively validate features in the database and generate reports as to which features in the network are violating one of the connectivity or other rules. The following are the connectivity rules for network features.
edge–junction rule
When building a network, you can specify which types of junctions are allowed to connect on an edge of a certain type. For example, electical meters can only connect to low-voltage lines. Or, transmission towers carry only high-voltage lines.
The edge–junction rule constrains which types of junctions can connect to a type of edge.
edge–edge rule
You can specify valid type combinations for connecting two edges at a junc-tion. For example, a 10” pipe can only be connected to a 8” pipe through a proper reducer. This connectivity rule could be applied to two subtypes of a water pipe feature class for pipe sizes and a subtype of a junction feature class.
The edge–edge rule establishes which combinations of edge types can con-nect through a given junction.
edge–junction cardinality
You can restrict the cardinality (count) of edges that connect at a junction.
For example, a valve cannot be placed at the junctions of many lines; a valve restricts flow from one edge to another. You can limit the cardinality of edges to specified junction types.
The edge–junction rule lets you precisely define the acceptable range of lines that can be connected at a junction.
default junction type
When you connect one type of edge to another, you can specify a default junction type to be inserted. When a 14.4-kV line is added to an end-junc-tion of a 28.8-kV line, a step-down transformer with the correct electrical ratings is assigned to the junction.
The default junction type rule adds new junctions of that type at the free end of new edges just added to the network.
c oNNectivity rules
iN A GeOMeTRiC NeTWORk
Yes, a service tap can be terminated with a meter.
No, a meter cannot be connected to a main line.
METER
SERVICE TRANSMISSION
METER
Yes, this reducer properly connects the two pipes.
No, there is no reducer at the
junc-tion of two pipes.
REDUCER AT
NO AT
When you connect a 14.4-kV electric distribution line to a 28.8-kV line, a properly sized transformer can be automatically inserted.
STEP
K6 K6
Yes, a valve con-nects exactly two lines.
No, a valve cannot connect one or three or more lines.
VALVES VALVE
Linear modeling with networks
The network imposes flow direction by its configuration of sources, sinks, and switches. In utility network applications, the direction of commodity flow along edges must be an intrinsic part of the network.
If the geometric network is used for operational decision making, such as whether to close a switch or open a valve, you have to know if the decision will result in incorrect flow. In analysis, it is usually a requirement to know what features are downstream (with the flow) or upstream (against the flow) of some location.
A geometric network has a method to establish flow direction. This method decides how commodities flow in the network based on the current con-figuration of sources and sinks and the enabled state of each feature. The result of this method aligns the direction that commodities flow along each edge, either with the direction of the feature or against the direction of the feature, relative to its digitized direction.
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Sources and sinks
In a utility network, sources and sinks are used in determining flow direc-tion. Any junction feature class can take on the ancillary role of a source or a sink. A source is a junction from which a commodity flows, such as a well-head pump. A sink is a junction where all commodity flow terminates, such as a wastewater treatment plant.
When you build a geometric network, you say whether or not features in a junction feature class can assume this ancillary role. If they can, the editor can specify whether an individual junction within the feature class is a source, sink, or neither.
The ancillary role field determines if a junction feature and element are a source or sink.
N etwork flow
ON GeOMeTRiC NeTWORkSAll line features have an implicit direction of digitization, which is the x,y coordinate order. In this simple network at right, flow goes opposite the digitized direction of edge e1, but with the digitized direction of e2 and e3.
Junction features can have an ancil-lary role of source, sink, or neither.
The role is stored in an attribute of the feature class, which is accessed by the establish flow direction method.
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ESRI Technical Paper Draft
0
disabed features
All features participating in a network have an enabled or disabled state.
Disabled features do not participate in network flow: nothing flows into or out of the feature. Disabled features are useful for representing lines affected by open electrical switches or closed valves.
Sources, sinks, and the enabled/disabled state all affect how flow is estab-lished in a netwok.
Indeterminate flow
It may not be possible to establish flow direction for an edge when the sources, sinks, and disabled features do not give enough information. An edge has indeterminate flow when flow direction cannot be established.
Indeterminate flow occurs when the establish flow direction method cannot determine which direction commodities flow in a network.
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Every junction and edge in a geo-metric network has an enabled or disabled state. In this example, edge e2 is disabled.
The enabled state of an element is also kept in the junction and edge
ele-ment tables in the logical network.
It may not be possible to determine the direction of flow given a configuration of sources, sinks, and enabled features.
This example is missing a source, so flow across the loop formed by e1 and e2 is indeterminate. The establish flow direction method will write
“Indeter-minate” as a flow direction when the flow direction cannot be established.
N etwork flow , coNtiNueD
ON GeOMeTRiC NeTWORkSLinear modeling with networks 1 Uninitialized Flow
Flow is said to be uninitialized when a flow is isolated because the edges are disconnected from the rest of the network (that has flow).
Weights
Edges and junctions can have any number of weights associated with them.
Weights are typically used to store the cost of traversing across an edge or through a junction. A typical weight is the length of the edge. Weights are created from field values on the edge and junction feature classes.
The logical network stores weights so that analysis programs can access them efficiently. When a weight value is modified on a feature table, it is automati-cally updated in the logical network.
Any numeric field can be a weight. The types of analyses you wish to per-form determines which fields should be weights.
Bitgates
A bitgate is a special type of weight that is most useful for categorical data and to represent hierarchies. Bitgates are useful when you want to capture categories of edges or junctions, such as the electric phase in a transmission line or the allowable vehicles on a street.
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Edge and junction features can have any number of weights associated with them. The logical network stores weights.
ESRI Technical Paper Draft
In ArcGIS, network analysis is a procedure that navigates through the connectivity of the network to yield meaningful result such as finding all elements upstream of a point or the shortest path between two points.
You can analyze networks in other ways, of course. For example, the basic selection tools found in ArcMap can select edge features and then calculate statistics about them, such as the total edge length by type of edge. This is certainly a valid analysis on a network, but it is not a “network analysis”
because the network connectivity is not involved.
Solvers
A program that performs network analysis is called a solver, because it solves a problem, such as isolating flow to an edge by turning off a set of valves.
Inputs to the flow isolation solver in this example would be the logical net-work, the edge to isolate, and the set of junctions that are valves. The output would be the set of valves to turn off. The inputs and outputs of solvers have no rules, except that input always includes a logical network.
Solvers have user interfaces for specifying inputs and reporting outputs.
Collections of solvers that perform similar tasks can usually be plugged into a common user interface framework. For example, the ArcGIS trace solvers are all accessed through a common toolbar. ArcMap is part of the user interface for a solver. Through ArcMap you graphically identify solver input, such as start points for a trace.
NetFlags
A NetFlag is a location on a network. Solvers use NetFlags to represent a multitude of real-world objects such as stops for a shortest path, start points for tracing, locations of valves, locations of services, and so on. NetFlags are not part of a logical network. They are used to describe any location in a network.
NetFlags have two types: EdgeFlags and JunctionFlags. NetFlag properties include the logical network element’s feature class, feature ID, and feature sub-ID. An EdgeFlag additionally includes the percent along the edge ele-ment. This means that an EdgeFlag can fall anywhere along the edge, from zero percent (from-junction) to 100 percent (to-junction).
Barriers
Barriers are used by solvers to represent disabled logical network elements.
Barriers do the same job as setting an element’s enabled/disabled state to disabled, except that barriers are not stored with the logical network—they are known only to the solver. Barriers are just a way to temporarily disable elements. Barriers are either on edge or junction elements.
You can use four methods to capture and represent barriers to a solver:
• Interactively add simple barriers.
• Use the features in your selection set.
• Disable feature classes.
• Apply a weight as a filter.
N etwork aNalysis
ON GeOMeTRiC NeTWORkSAn almost infinite variety of solvers exist for the many types of network analyses. ArcGIS provides a suite of solvers that address the more common types of problems. For less common types of network analyses, developers can create solvers using any
program-ming language that can access the ArcGIS components.
NetFlags are used to describe any loca-tion on a network. Examples include
places to visit on a shortest path, the origin of a trace, a warehouse or a service center or a valve, switch, or transformer. Solvers rely heavily on NetFlags to describe input parameters.
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Linear modeling with networks
Tracing
Tracing means to follow the flow in a network until some condition is met.
You are most certainly looking at using a trace solver to find the answer when you hear problems expressed as “search against the flow until you find a transformer,” or “follow the flow upstream to the first discharge point,”
or “trace upstream and find all valves.” The ArcGIS trace solvers include upstream trace, downstream trace, isolation trace, and path trace.
Weights
Choosing which edge or junction attributes should become weights in the logical network depends on your collection of solvers. Adding a weight to a network will not work if there are no solvers that can use it. For example, trace solvers typically do not use weights—but rather the connectivity information found in the logical network.
For example, suppose you have a water distribution network with a numeric attribute containing the pipe manufacture ID. Adding this attribute is unnecessary unless you have a solver that can use it. Even with a short-est path solver, it would not make sense to find the shortshort-est path based on manufacturer ID.
But suppose you had a solver that could return all junctions that share edges of certain characteristics. In this case, you may want to use this solver to find all junctions where pipes from one manufacturer connect with pipes from another. In this case, it might make sense to add manufacturer ID as a weight.
Below is a table of just a few possible weight attributes and the types of solv-ers that would use these weights.
Length of edge Diameter of pipe Impedance (electrical resistance) Time to traverse an edge Number of lanes on a street Road classification Miles per hour Hazardous material route Toll (cost to use a road)
Shortest path solvers. Many solvers have a need for length.
Solvers that calculate pressure or head in a network.
Calculating voltage drop in an electrical network.
Shortest path solvers.
Calculating traffic capacity or congestion on a street.
Describing network hierarchy in hierarchical shortest path solvers.
A shortest path solver that allows dynamic calculation of weights.
A filter to find a path only on hazardous material routes.
Shortest path solvers based on monetary cost.
Used for Weight description
ESRI Technical Paper Draft
Solver Solver description Solver application
sink Trace upstream
flow direction needed to solve
flag
Given an origin set by a flag, the trace upstream solver traces against flow, finding all upstream edges and junctions until stopped by barriers, sources, or the end of the network.
A water utility could use the trace upstream solver to determine valves to shut off water to a burst pipe. This solver can also be used to find sources of pollution from a monitoring station
flow direction needed to solve
sink
Trace downstream flag
Starting from an origin set by a flag, the trace downstream solver traces with flow until stopped by barriers, sinks, or the end of the network.
This solver can be used to identify parts of a network affected by a resource flowing downstream, such as a chemical spill. You can also use this solver to calculate distances from sinks.
Find common ancestors
source flags
flow direction needed to solve
From each flag, the find common ancestor solver traces against flow to sources or barriers then finds the features (ancestors) common to all traces.
When an outage occurs, an electric utility receives phone calls from affected customers. These locations can be entered as flags, from which this solver can narrow the list of the suspect transformers or downed lines that caused the outage.
Find loops
flow direction not required
The find loops solver finds cycles or circuits in your network. Flow direction is not a consideration.
In certain utility applications, loops are considered faults to be identified. For example, any loop in an electric system is a short circuit and cannot be allowed.
This tool enforces logical consistency of radial networks and can also be used to troubleshoot causes of indeterminate flow directions when loops are allowed, such as water utilities.
Find path
flow direction not required
The find path solver discovers a path between two netflags regardless of flow direction. If there is more than one path, only the first path found is returned.
This solver is used to inspect the logical consistency of a network and check for connectivity between two points.
N etwork trace solvers
FOR GeOMeTRiC NeTWORkSThese are the network solvers that operate on geometric networks. Network solvers operate on the geometric network and honor the network flags, bar-riers, and flow direction set on the network.
Each of these solvers can also report the total cost of tracing all elements in the trace or the cost of a segment of the trace. For example, you can accu-mulate water flow on successive reaches of a stream network and calculate the flow contribution to a single stream reach.
In the illustrations below, the yellow elements represent the features on the geometric network that are selected by applying the solver in that situation.
Linear modeling with networks
Solver Solver description Solver application
Find connected
flow direction not required
The find connected solver locates all elements that are connected to the edge on which the netflag resides. The connected elements are referred to as the connected component.
This solver can be used to identify the connected parts of the network and validate data integrity and connectivity.
sink
Find upstream accumulation
flow direction needed to solve
The find upstream accumulation solver traces on all elements upstream from origin (a netflag) and returns the total value of these elements.
This solver can generate flow statistics at a point, such as finding the number of facilities upstream from a monitoring station.
Find path upstream
source
flow direction
needed to solve flag
The find path upstream solver determines a path from a netflag against flow to the source.
This solver can be used to assure logical consistency of the network and can be used in applications such as finding the source of pollution from a monitoring station
Find disconnected
flow direction not required
The find disconnected solver is the inverse of the find connected solver; it finds all elements that cannot be reached from the netflag.
This solver can be used to identify isolated parts of the network so that they can be properly reconnected if required.
For gas and the water data, the most common network analysis is valve isolation tracing. A pipe is leaking or otherwise needs repair at a certain location, and the field operator needs to know which valves to shutoff and which customers will lose service.
In this map, four valves will need to be closed and 129 customers will lose
In this map, four valves will need to be closed and 129 customers will lose