# Introduction

The "changeability" of a system is determined as the acceptable number of changeable paths that can be accommodated by a system which means whether the system is rigid in its capabilities. The number of acceptable change paths is determined by both the "possible number of end states" and "the number of possible effects and possible mechanisms". To describe the changeability of a system, two common features, namely adaptability and flexibility are used in network analysis. Adaptability describes the ability to cope with unexpected turbulence in the environment. An adaptable system is therefore an open system that is able to retrofit itself according to changes in the environment or in parts of the system itself. Any system, not only in the transportation field, requires a consideration of how to provide value to stakeholders over time, in order to maintain itself in a dynamic and contemporary environment. As measurements of “changeability,” flexibility and adaptability reflect the external and internal location of the change agent—system boundary, respectively; while, the change agent refers to the force initiator behind changes to the system. If the change agent is an external force to the system, then the change under this circumstances is a flexible-type change. On the other hand, if the change agent is an internal modification to the system, the change is an adaptable-type change. However, in some cases, a system change can be both adaptable and flexible; therefore, the system boundary must be explicitly defined to avoid confusion.. The rest of the article is dedicated to discuss the network adaptability and flexibility.

# Adaptability
## Introduction to network adaptability

The adaptability and flexibility features are usually correlated; in other word, an adaptable network is flexible and the elements of the system are capable of learning from past experiences. The determination of whether to pursue an adaptable change depends on the maximum willingness to pay for that change. In general consensus, most of time humans are highly adaptable. Over a wide range of possibilities and changes, people decide that the costs of such changes are acceptable (i.e., the cost of self-change is reasonable, both in terms of dollars and time). To increase the acceptability of a given proposed change, a system should either decrease the actual cost for the change, or increase the cost threshold for the change.

# Flexibility
## Introduction to network flexibility

The rapidly increasing and shifting demands for transportation services frequently require underlying systems to make changes to internal characteristics, such as infrastructure, and external characteristics, such as energy supplies and policies, from time to time. Therefore, a higher degree of system flexibility becomes increasingly desirable in a more nebulously demanding environment.
Flexibility is defined as the ability for a network to adapt to external changes, both in terms of infrastructure and in operations while maintaining satisfactory system performance. The overall flexibility of the entire network is determined by the "least flexible" elements. Therefore, it is necessary to consider the individual elements of the network separately. The node flexibility, link flexibility, and temporal flexibility for building and operating the network are examples of such individual network elements to be analyzed separately. The comprehensive definition of node flexibility, link flexibility, and temporal flexibility elements are represented below.

### Node Flexibility

Node flexibility is the ease with which network nodes, points of access, can be constructed; this can be measured by the time takes to plan, approve, and implement the development of a node, and the cost of such development (the cost of expanding the network by one node).
There are four dimensions that affect the node flexibility:
1. Physical size: The spatial area that the node requires. The larger the area needed, the more constrained the possible placements for the node become, and thus this possible node becomes less flexible.
2. Specific requirements: The specifications for implementing such a node imposes constraints on the area that could be used to construct such a node. The more requirements, the lower the chance of finding an appropriate location for that node.
3. Site externalities: The extent and severity of externalities emerging from the characteristics of the node itself, which constrain the environment of setting such a node. An example for this would be the difference between an airport and telephone booth.
4. Link-node interface: The connections between nodes and links sometimes require special infrastructure implementation (such as runways or parking); such interfaces can also impose certain limitations on directionality of flow in the network.

### Link Flexibility

Similar to node flexibility, link flexibility is the ease and cost of adding additional links between nodes.
There are four dimensions that affects the link flexibility.
1. Link requirements: The technical requirements for links. For links such as railways and highways, strict engineering standards and geometric design are required.
2. Link externalities: Refers to the externalities generated by the infrastructure to establish those links, as such infrastructure may require space, thus affecting the surrounding ecosystem and environment.
3. Traffic externalities: Refers to the externalities generated by the traffic upon the links; they impose restrictions on location or operation of the link. For instance, a certain type of traffic may only use certain links or certain link alignments.
4. Complementary infrastructure: In real-life circumstances, networks are not independent, and in many cases access to one network is dependent on others, like airport transit. The limitations of a complementary network, especially the flexibility of the connecting links, affect the total network flexibility.

### Temporal Flexibility

The temporal flexibility refers to the ability to sequence infrastructure investments, and the degree to which use of the infrastructure requires coordination of other users. Two main factors, namely divisibility and flexibility in use affect the temporal flexibility.
1. Divisibility: Networks with higher divisibility can better accommodate shifts in spatial structure and are less susceptible to failure. Therefore, with greater divisibility of investments comes greater flexibility of the network.
2. Flexibility in use: The flexibility of network operation is a function of the degree of coordination between users, with the assumption that there exists some independence between users. For example, the use of one network by one user does not significantly affect the choices available to others. For a decentralized network with no need for hierarchies of control, such as the Internet, the network is deemed to be flexible. If, in contrast, all vehicles need to be strictly coordinated, such as in a railway system, the operation is deemed to be inflexible.

## The measurement of network flexibility

The following table summarizes some of the characteristics which pertain to flexibility and adaptability, for several network types. Aviation networks face the most limitations, not only because they require large nodal areas, but due to safety considerations and extensive externalities imposed upon surrounding spaces. Hence, the surveying and construction of new airports are undertaken very cautiously. In contrast, motorized networks, including roads and rail networks require significant physical infrastructure compared to airway links (where the vehicle itself essentially is the link, and only requires a designated safe path through airspace), and are thus relatively inflexible. Still, due to the inflexibility of the nodal requirements, the overall aviation network is highly inflexible.
Telecommunication systems also have a different behavior. In accordance with certain technical constraints, these networks require a relatively high degree of complementary externalities compared to other networks. The high divisibility and flexibly-sized nodes make telecommunication networks more flexible than the other networks described in Table 1. This brief discussion suggests that the least flexible network type is the international air transport network, as it requires the largest nodal areas and significant capital investments. As per Table 1, telecommunication networks are the most flexible, as they are the least constrained by dimensions. The inflexibility of motorized networks and rail networks primarily comes from infrastructure implementation, particularly for high-speed rails. These networks assume a need for absolute central control over movement, which makes them inflexible. While roads are much more flexible than rail, there is an important difference between roads and highways. Highways have significantly higher siting difficulties, physical requirements, and constraints, which make them less flexible than roads. However, as road and highway systems can complement each other, they provide, overall, a very flexible network.

## Capacity flexibility

Capacity flexibility of a system is the ability of a transport system to accommodate variations or changes in traffic demand. Its significance has been presented in two different ways. First, the continuing increase of US transport volume demands in combination with the relatively constant levels of system-kilometers available leads to increased travel per lane-kilometer. The second consideration is the changes in trade patterns, types of cargo being transported on the infrastructure, as well as the nature of transport services used. Capacity flexibility can be described as the characteristic of the interface between the network capacity and the demand changes - in other words, the acceptable turbulence with respect to changes in demand.

### Measuring Flexibility

Capacity flexibility measures the changes in overall traffic quantities with respect to traffic demand fluctuations, the spatial patterns of flows (shift from one OD pair or specific path to another), and the mix of commodities carried. The traditional approach for measurement of flexibility in engineering and economic literature is the idea of sensitivity analysis, and in particular the concepts used in break-even analysis. Figure 1 shows the illustration of measuring flexibility.
The represented flexibility measure in this graph is the range of profitable demand (sales).

#### The Fixed traffic pattern approach to measuring flexibility (MAXCAP)

The MAXCAP model estimates the "base traffic capacity" of a system by evaluating the maximum traffic that can be accommodated by the system, subject to the underlying traffic patterns. Therefore, flexibility is presented by the maximum traffic that can be carried in each traffic lane as well as the percent increase in demand that the system can accommodate. Using this application, it is possible to analyze the double-stack rail freight transportation (DDS). The objective of the model is to maximize the quantity of cargo transported from origins to destinations, across the entire network. Constraints need to be evaluated, including traffic patterns, the mix of cargo by lane (O-D pair, commodity), the limitations of link capacity, terminal capacity, the available fleet, conservation of flow, and alternative routing options. The double-stack network service examined was the subject of a major study of market potential covering the entire United States and most major railroads..
The network to be analyzed is shown in Fig. 2
The overall results for this network using the MAXCAP model are presented in Table 2. The first row represents the base capacity for the system when all users choose the shortest path between each O-D pair. The original base traffic of 1987 has traffic volume of 1.15×10$^5$. The estimated maximum capacity for the shortest path option is 1.48×10$^5$ containers/month. Compared to the original data, the model estimates that the system can accommodate a 28.6% increase in traffic. In other words, the network is sufficiently flexible to accommodate 28.6% more traffic on any combination of traffic lanes.
Besides the shortest path option, two other alternative routing options were also considered: 1. the shortest + one disjoint path (alternative second shortest path that does not share links with other nodes) 2. the level of service paths routing option (LOS), as the set of all paths between O and D that meet the given required level of service
The two alternative routing options introduce additional flexibility. Referring to the table 3, the shortest + one disjoint path yields 178.8% capacity reserve compared to the base pattern. Consider the 28.6% flexibility provided by the shortest path case; the effect of adding one additional path between each O-D pair brings a significantly greater increase in flexibility. The level-of-service path routing permits even more capacity, which is 192.1% greater compared to the base pattern reserves. However, the fact that the two alternative routing options didn't exhibit significant variation in flexibility increase suggests that providing routing options does not affect flexibility in the way we assumed.

#### Adjusted traffic pattern approach to measuring flexibility (ADDVOL)

The ADDVOL model estimates the upper bound of the system capacity flexibility; consider a flooded system - how much more traffic volume could added to each lane based on the MAXCAP estimate is given by the ADDVOL model. When deviations from the base traffic pattern are permitted, the fraction of total traffic that moves between each OD pair is now a variable. Different from the MAXCAP estimates, the objective of ADDVOL model seeks maximization of overall cargo volume. The rest of constraints follow the format of the fixed pattern model.

#### Implication in planning, operating, and policy-making

The models used in estimating the capacity of the transportation system can be applied to measure system flexibility, when flexible routing options are introduced. The fixed pattern approach provides a conservative estimator that predicts the lower bound estimate of the system flexibility. This particular study only applied the model on a limited portion of a freight transportation system. It is debatable that variations in the traffic patterns and routing options may yield different results in more extensive, realistic networks.
Measures of flexibility can be useful in many different ways. For example, the measurements can help determine which systems can function more appropriately when facing a major disaster. It is also possible to determine the extent of the network's ability to accommodate substantially increased traffic. The third use is to evaluate the investment decision with respect to a specific assumption (i.e. a sudden change) in traffic volume or patterns.

# Further readings

Gifford, Jonathan L. "Adaptability and flexibility in urban transportation policy and planning" Technological Forecasting & Social Change, 1994, Vol.45(2), pp.111-117
Yao, Ly ; Sun, Ls ; Wang, Wh ; Xiong, H, "Adaptability Analysis of Service Facilities in Transfer Subway Stations" Mathematical Problems In Engineering, 2012
Haitao Pu, Haitao Pu ; Jinjiao Lin, Jinjiao Lin, "Research on adaptability of intelligent urban transportation system Intelligent Computing and Intelligent Systems", Oct. 2010, Vol.3, pp.802-805

# Reference

* 1 2 Adam M. Ross, Donna H. Rhodes, and Daniel E. Hastings, “Defining Changeability: Reconciling Flexibility, Adaptability, Scalability, Modifiability, and Robustness for Maintaining System Lifecycle Value” Systems Engineering, 2008, Vol.11(3), pp.246-262
* ↑ Adam M. Ross, Donna H. Rhodes, and Daniel E. Hastings, “Defining Changeability: Reconciling Flexibility, Adaptability, Scalability, Modifiability, and Robustness for Maintaining System Lifecycle Value” Systems Engineering, 2008, Vol.11(3), pp.246-262
* ↑ Eran Feitelson , Ilan Salomon, “ The implications of differential network flexibility for spatial structures” Transportation Research Part A: Policy and Practice Volume 34, Issue 6, August 2000, Pages 459–479
* ↑ ] Eran Feitelson , Ilan Salomon, “ The implications of differential network flexibility for spatial structures” Transportation Research Part A: Policy and Practice Volume 34, Issue 6, August 2000, Pages 459–479
* 1 2 3 Edward K. Morlok, David J. Chang, “Measuring Capacity flexibility of a transportation system” Transportation Research Part A 38 (2004) pp 405-420
* ↑ Anthony Chen, Panatda Kasikitwiwat “ Modeling capacity flexibility of transportation networks” Transportation Research Part A 45 (2011) 105-117
* 1 2 Morlok, Edward ; Riddle, Stephanie, "Estimating the Capacity of Freight Transportation Systems: A Model and Its Application in Transport Planning and Logistics" Transportation Research Record, 1999, Vol.1653(1), pp.1-8
* ↑ Smith, D. S., et al., Manalytics, Inc. Double Stack Container Systems: Implications for U.S. Railroads and Ports. Report DTFR53-88-C- 00020. FRA and MARAD, U.S. Department of Transportation, 1990