National Rural Infrastructure Development Agency

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Research Areas

LINK EFFICIENCY IN RURAL (VILLAGE) ROAD NETWORK PLANNING

A.K. Mahendru
P.K. Sikdar
Department of Civil Engineering, University of Roorkee (U.P.)
S.K. Khanna (Dr.), Secretary,
University Grants Commission, New Delhi

ABSTRACT

Conventional transport planning process revolves round the concept of origin and destination of trip matrices in respect of settlements for determining both the need for and the priority in the provision of road links in rural areas. Since such a process is too elaborate and time consuming, particularly in the context of low density of population, low vehicle ownership and vast spread of rural region, an alternative criterion is put forward in this paper. The suggested criterion is based on optimal link efficiency. Incorporated into this is the intensity of settlement interaction which is quantified in terms of maximum/relative force of interaction.

The concept of link effeciency is used to generate and evaluate alternative rural road network plans to meet the basic identified needs. A case study of Bahat growth center in U.P. has been given in this paper to deminstrate the application of the suggested method.

Introduction

Construction, maintenance and operation of rural road system, consumes enormous financial resource. Resources being limited, rural road planner has to make choices among alternative planning and investment opportunities, so that scarcely available resources may be optimally used to generate a more purposeful, function - based and economical rural road network. While planning rural road network at micro level, decision has to be taken about connectivity of every settlement. Conventional transportation planning process comprising subdividing the study area into smaller zones and subzones and studying the interzonal trip frequencies through O - D (Origin Destination ) matrix to decide linkage needs between various origins and destinations may not be of much use. Because, if every settlement is treated as an individual zone and an effort is made to prepare O-D matrix for all the settlements in the area, it will require a very large data base in the form of trip frequencies between all pairs of settlement nodes.

While planning even at district level, there will be 3000 to 5000 settlements and it will be a huge task to collect trip frequency data for all the settlements to form

the O-D matrix. On the other hand, if the O-D pattern is made available at the cost of a huge amount of resource, the observed trip frequencies would hardly be able to justify the road links. The data so collected may be useful only to decide the relative priorities of the linkages. Thus, rural road network planning would require a different approach which may be simple, scientific and not wasteful.

The settlements interact with each other due to their mutual dependence, and this interaction when quantified can be used in place of normally used travel data. Interaction based linkage requirements can be estimated from the inter - settlement forces of interaction. link efficiency concept can be exploited to generate alternative linkage patterns to meet the basic need identified. The networks thus generated will then be examined for optimality through chosen hypotheses and search would isolate the most efficient network. The application of the methodology has been demonstrated through a case study for the region of Behat growth centre. Behat is one of the several growth centres identified within the district of Sharanpur in Uttar Pradesh.

Linkage Development Strategy

In the process of integrated area planning, there exist developmental hierarchies for the settlements within the region. A lower order settlement is supposed to fulfill socio - economic needs and missing activity functions through its dependence on proximate higher order settlement. Due to this dependence settlements interact with each movement of men and materials. It is therefore, established that the functionally useful network for the rural area will be the one which facilitates the primary requirement of settlement interactions.

Intensity of settlement interaction can be quantified in terms of force of interaction, which can be used to evolve need oriented linkage pattern, by identifying for every settlement a corresponding settlement, with which, the settlement under consideration has got maximum force of interaction. Through this mechanism all the settlements will be linked and a need based pattern of link requirements will be obtained. But it is likely that due to the provision of direct links, there will be considerable link and route duplication. Although this will give minimum travel time and operational cost for every settlement to interact with a settlement with which it has maximum force of interaction, but it will involve huge initial capital investment in the form of construction cost due to high road kilometerage.

In rural road network planning, savings in travel time and operational cost, may not be of much significance as that of savings in construction cost, due to very low trip frequencies on most of the links. Therefore one of the goals for rural road network planning may be to maximise settlement interactions and to minimise total link length involved in the network to provide accessibility to all the settlement nodes. Optimal linkage pattern, thus evolved by using concept of maximum link efficiency, may involve somewhat longer and indirect routes for travel between some of the settlement pairs. At a later stage when the level of interaction between the two settlements rises to an extent, to justify a direct link, it can properly analysed and recommended. Link efficiency of an option for linkage can be used to generate alternative linkage patterns, and the option giving highest link efficiency may be selected for the network.

Functional Dependence and Settlement Hierarchy

Any one settlement in a region may not have all types of utility and amenity for fulfilling the social functions. Thus the settlements will have different levels of functional importance depending on the concentration of available facilities. In an integrated area planning concept such hierarchical levels of the population centres are

planned for the balanced growth of the region. The functional importance or weightage of a chosen function (infrastructural facility) is obviously related to the frequency of its occurrence. It is quite simple to understand that importance of an University is much more than a secondary school which may occur in more numbers in a particular settlement. Thus the weights of various functions may be computed using this natural law as stated in equation (1).

Wf = K1/Nf ..(1)

Where Wf is the weight of the function f; Nf is the total number of units of function in the region under consideration, and K is conveniently chosen multiplier.

To establish the hierarchy of the settlements in the region, the centrality scores have been determined. Centrality Score (CS) is an objective measure of functional importance and computed from the level of concentration of the central functions. Centrality of a settlement can be measured by the equation (2).

CSi = (?f nf Wf)i ..(2)

Where nf is the number of units of the function f existing in the settlement under consideration and Wf is the weightage obtained from equation (1). The summation, when done for all the existing functions, gives the centrality score of the settlement, which identified the hierarchy of the settlement in the region. In a region of several thousand settlements of different population sizes, only a reasonable number is chosen for providing accessibility and connectivity. This choice is based on settlement hierarchy, which effectively means that upto a chosen minimum of centrality score, the settlements are provided with road linkage.

4 Settlement Interaction and Need Oriented Linkage Pattern

The force of attraction or affinity between two population units has been traditionally derived from the gravitational hypothesis. The population sizes and the intervening distances are not ht only variables to be considered for level, of settlement interactions. In hierarchial development and planning approach, the level of interdependence in the form of potential difference should also be incorporated in the basic gravitational law to quantify intersettlement force of attraction. Level of socio-economic developments of various identified settlements which will be responsible to generate the interactions for social and economic reasons are expressed in the form of centrality score. Therefore, the force of interaction between settlements i and j can be obtained by gravitational law as given in equation (3)

Fi j = (pi pj [(CSi – CSj)]) / (di j)2 .. (3)

Where Fi j is the force of interaction between settlements i and j, dij is the spatial separation in the form of straight line distance between settlements i and j, and CSi and CSj are the centrality scores of the settlements i and j respectively as computed by equation(2) for individual settlement.

Force of interaction between all settlement pairs are computed using equation (3) and the highest value in each row of the matrix is identified. These identified cells of the matrix indicate for each settlement one other settlement with which it has maximum force of interaction; irrespective of the magnitude. This, in a way, gives the basic need of linkage requirement for connecting all identified settlements on the basis of force of interaction. Provision of direct links to satisfy this need will be highly uneconomical with unnecessary duplication in the network. Thus, the inherent requirement identified here will be the basis for generating the alternative networks.

Link Efficiency

The efficiency of a road link in this context is expressed as the amount of interaction served per unit length. This idea of link efficiency may be conveniently used for generation of alternative networks or linkage patterns. The link efficiency as defined above has been used in three different ways as detailed below:

Efficiency of Individual Link (LEIij)

The efficiency of individual link is nothing but the force of interaction served per unit length, and therefore, for any link between two settlements, the efficiency can be expressed as in equation (4)

LE’ij = Fij/ Lij ..(4)

where Lij is the link length joining the settlements i and j, which is equivalent to dij of the link is a direct and shortest length link. It may be mentioned here that by using the individual link effeciency an efficiency based pattern of linkage requirement may be derived similar to that derived from froce of interaction.

Efficiency of a Link Option (LEOij)

While connecting an unconnected settlement node to the connected ones there may be several options available for the new link to be added. Linking the node, additional interaction will be permitted in case of each option. Thus, link efficiency of an option is defined as the total amount of additional interaction facilitated per unit length

of the new link. This can be expressed as in equation (5).

LEOij = Fij/ Lij ..(5)

The numerator in equation (5) is the summation of the force of interaction of the newly connected node with all other nodes with which interaction is possible out of the already connected nodes. The denominator represents the additional link length required to connect the node to the existing network. It may be noted here that the Fij computed in equation (3) will not be useful for equation (5) and these Fij values will be computed separately for each option.

Link Efficiency of a Network (LEN)

The third use of the concept of link efficiency is in the comparison of alternative linkage patterns for their overall utility in serving the settlement interaction catered to by the network per unit of total link length involved in the network. This is expressed in equation (6).

Where LEN = Link Efficiency of a network
LL= Total link length involved in the network

Other notations are same as explained earlier.

Network Generation

The desired interaction pattern being known as the interaction pattern that is to be provided with connectivity being identified, alternative networks are to be generated to fulfil the requirements. In addition to the interaction desire, the various goals and objectives of the network generation are to be set so that hypotheses may be formulated accordingly for comparing the networks. The goals set are:

  • The network should cater for maximum force of interaction with minimum link length involved in the network.
  • Each identified settlement should be connected with at least one other settlement.
  • Network should provide accessibility between origin and destination node pairs as identified

If is aimed to maximize link efficiency of a network, a number of hypotheses can be developed to generate alternative networks and a search can be made for the hypothesis and the network giving highest link efficiency of the network. Two of such hypotheses are discussed as under:

basis of centrality score and are shown in Fig. 2. Hinter-land for every growth centre was demarcated by using criteria of equal zone of influence for all the growth centres. Behat is one of the identified growth centres selected for further study and analysis.

Various settlements to be provided with road accessibility in the zone of Behat growth centre were identified on the basis of centrality score. Table 1 shows the identified settlements along with their population and centrality score. Spatial distribution of settlements is

shown in Fig. 3. Spatial distances between pairs of settlements, measured as straight line distances, are shown in matrix form in Table 2. Existing roads are shown in Fig. 3 and network presentation is shown in Fig. 4 and Fig. 5 shows fully developed network. A matrix for force of interaction, using gravity hypothesis is shown in Table 3 and Table 4 shows matrix for individual link efficiency. Need oriented network and a network based on individual link efficiency are shown in Fig. 6 and Fig. 7.

Suggestions and Recommendations

Table 1

Settlements identified for road accessibility in Behat growth centre

Settlement Code Population Centrality
Behat 1 7179 5420
Sadholi 2 1880 2480
Mirzapur 3 4566 2313
Kalsia 11 1264 1802
Raipur 4 2012 1175
Bawel Buzurg 12 1859 1006
Randol 13 2013 566
Gandewra 5 749 435
Mayapur 6 709 429
Namoli 7 1313 347
Faizabad 8 2181 285
Alipura 9 1335 188
Akbarpur 10 702 170
Dabkora 14 1356 140

Network Generation Based on Hypothesis No. 1

Links arranged in descending order of link efficiencies are shown in table 5. Link 5-1 being first in sequence was provided as it is. Next needed link in sequence was 11-1. Both the options 11-1 and 11-5 were analysed for their link efficiencies. Option 11-1 giving highest link efficiency was selected. The process was repeated till all the needed linkages were provided. At linkage 10-3, both options10-3 and 10-4 required same link length of 5 and both gave almost same link efficiency, so two networks were generated as shown in Fig. 8A and Fig 8 B. Results of analysis for generation of network are shown in Table 6.

 

Network Generation Based on Hypothesis No 2

Nodes arranged in descending order of (Fij / dij) and properly sequenced are shown in Table 7. Node 1 being first in sequence was pocked up and was linked with node 5, with which it has got maximum link efficiency. Next in sequence was node 2, which was pocked up, and both the options 2-1 and 2-5 were analysed for their link efficiencies and link 2-5 giving higher efficiency was selected. The process was repeated till all the nodes got linked. Results of analysis are shown in table 8, and network generated is shown in Fig 9.

 

Network Evaluation

All the networks generated were evaluated for link length, route length, force of interaction and link efficiencies to illustrate the computations, detailed analysis for one network are shown in Tables 9 and 10. Similar computations were done for other networks. Computations pertaining to all networks can be made, to facilitate final selection. A comparison between existing links and predicted links is shown in Table 12.

 

9 Conclusions

It can be observed from Table 11 that fully developed network caters to maximum force of interaction, because of direct links between every settlement pair, but it requires maximum link length and gives lowest link efficiency of network. It was expected that perhaps need oriented network or network based on individual link efficiency will give highest force of interaction and link efficiency because of direct links between settlement pairs of maximum interaction or maximum link efficiency, but it is not so. In Table 11 at S No. 4 and 5 , it is observed that it is not essential for networks having same link length to have same force of interaction and link efficiency, but it gets affected by the pattern of linkages.

Table 2

Matrix for spatial distances

 

1

2

3

4

5

6

7

8

9

10

11

12

13

14

1

0

4

7.5

5

2

12

6.3

12.4

4.5

9.9

3

4.4

6.2

6

2

4

0

7.3

3.8

2.5

10.6

2.4

11.2

7

7.2

6.2

7.6

7.5

5

3

7.5

7.3

0

3.7

6

4.7

9

5.5

5

5

10

11.8

13.5

12

4

5

3.8

3.7

0

3

8.3

5.2

7.5

5.5

5

7.9

9.3

10.5

8.5

5

2

2.5

6

3

0

10.6

4.8

10.4

4.6

8

5

6.5

7.5

6

6

12

10.6

4.7

8.3

10.6

0

12.8

3.2

9

7

14.6

16.0

18

16.6

7

6.3

2.4

9

5.2

4.8

12.8

0

12

10

7

9.2

10.7

8.5

6.5

8

12.4

11.2

6.5

7.5

10.4

3.2

12

0

10.2

5

15.4

16.8

18.5

16.1

9

4.5

7

5

5.5

4.6

9

10

10.2

0

9.3

6.5

8

10.4

10.2

10

9.9

7.2

5

5

8

7

7

5

9.3

0

12.3

13.8

15

12.5

11

3

6.2

10

7.9

5

14.6

9.2

15.4

6.5

12.3

0

1.5

4

5.4

12

4.4

7.6

11.8

9.3

6.5

16.0

10.7

16.8

8

13.8

1.5

0

3.5

6

13

6.2

7.5

13.5

10.5

7.5

18

8.5

18.3

10.4

15

4

3.5

0

3.5

14

6

5

12

8.5

6

16.6

6.5

16.1

10.2

12.5

5.4

6

3.5

0

S

82.2

82.3

101.0

83.2

76.9

143.4

104.4

144.0

100.2

117.0

101.0

115.9

126.4

114.3

SS 1493.2

Table 3

Matrix for force of interaction

1 2 3 4 5 6 7 8 9 10 11 12 13 14  
1 0 2522.0 1810.0 2434.0 6472.0 176.0 1204.0 522.0 2475.0 269.6 3646.0 3041.0 1824.0 1427.0
2 2522.0 0 18.5 328.0 427.0 23.6 891.6 70.0 114.7 57.5 38.6 86.2 125.1 233.4
3 1810.0 18.5 0 763.1 168.9 275.5 145.4 667.0 517.6 274.3 29.4 79.6 88.1 93.4
4 2434.0 328.0 763.1 0 106.6 15.4 80.8 63.3 87.4 56.6 25.5 7.3 22.3 38.9
5 6472.0 427.0 168.9 106.6 0 0.5 8.0 3.7 16.4 3.0 47.9 15.5 0.8 11.1
6 176.0 23.6 275.5 15.4 0.5 0 0.5 21.6 2.8 2.6 5.8 3.0 0.6 1.0
7 1204.0 891.6 145.5 80.8 8.0 0.5 0 1.2 2.8 3.3 28.5 15.2 8.0 8.7
8 522.0 70.0 667.0 63.3 3.7 21.6 1.2 0 2.7 7.0 17.6 10.3 3.8 1.7
9 2475.0 115.7 517.6 87.4 16.4 2.8 2.8 2.7 0 0.2 64.3 31.7 9.4 0.8
10 269.6 57.5 274.3 56.6 3.0 2.6 3.3 7.0 0.2 0 9.6 5.7 2.5 0.2
11 3646.0 38.6 29.4 25.5 47.9 5.8 28.5 17.6 64.3 9.6 0 831.0 196.2 97.4
12 3041.0 86.2 79.6 7.3 15.5 3.0 15.2 10.3 31.7 5.7 831.3 0 134.3 60.6
13 1824.0 125.1 88.1 22.3 0.8 0.6 8.0 3.7 9.4 2.5 196.2 134.3 0 95.0
14 1427.0 233.4 93.4 38.9 11.1 1.0 8.7 1.7 0.8 0.2 97.4 60.6 95.0 0
S 27822.6 4935.6 4930.8 4029.2 7281.4 528.9 2398.0 1391.8 3325.8 692.1 5038.1 4321.4 2510.0 2069.2
SS 71274.9

F = 65637.45

F?= P¹ x P? ( I CS¹-CS? I) x 10¯6

Table 4

Matrix for individual link efficiency

  1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 .0 630.5 241.33 486.8 323.6 14.66 191.11 42.09 550 27.22 1215.3 691.1 294.2 237.8
2 630.5 0 2.5 86.3 170.8 2.2 371.5 6.25 16.38 7.98 6.22 11.34 16.68 46.67
3 241.33 2.5 0 206.24 28.15 58.61 16.15 121.27 103.53 64.86 2.94 6.74 6.52 7.78
4 486.8 86.3 206.24 0 35.53 1.85 15.53 8.44 15.89 11.32 3.22 .78 2.12 4.57
5 323.6 170.8 28.15 35.53 0 04 1.67 .35 3.56 .45 9.58 2.38 .11 1.85
6 14.66 2.22 58.6 1.85 .04 0 .036 6.75 .31 .37 .39 .18 .033 .06
7 191.11 371.5 16.15 15.53 1.67 .036 0 .102 .278 .47 3.1 1.42 .94 1.34
8 42.04 6.25 121.27 8.44 .35 6.75 .102 0 .26 1.41 1.14 .61 .20 .10
9 550 16.38 103.53 15.89 3.56 .31 .278 .26 0 .02 9.89 3.96 .9 .081
10 27.22 7.98 54.86 11.32 .37 .37 .47 1.41 .02 0 .78 .41 .165 .014
11 1215.3 6.22 2.94 3.22 9.58 .39 3.1 1.14 9.89 .78 0 554.2 49.05 18.03
12 691.1 11.34 6.74 .78 2.38 .18 1.42 .61 3.16 .41 554.2 0 38.37 10.1
13 294.16 16.68 6.52 2.21 .11 .033 .94 .02 .9 .165 49.05 38.37 0 27.12
14 237.83 46.67 7.78 4.57 1.85 .06 1.34 .102 .081 .014 18.03 10.1 27.12 0

Table 5

Needed links arranged in descending order of link

Link Link Efficiency Order in Sequence
5-1 3236 1
11-1 1215-3 2
12-1 691.1 3
2-1 630.5 4
9-1 550 5
4-1 436.8 6
7-2 371.5 7
13-1 294.16 8
3-1 241.33 9
14-1 237.83 10
8-3 121.27 11
6-3 58.6 12
10-3 54.86 13

Table 6

Network generation (hypothesis No.1

Needed Linkage Link Options Link Length F? LE? Final Selection
5-1 5-1 2 6472 3236 1-5
11-1 11-1 3 3693 1231.3 11-1
  11-5 5 71757 143.51  
12-1 12-1 4.4 3181.44 723.05 12-11
  12-11 1.5 3754.14 2502.7 12-11
  12-5 6.5 63.79 9.81  
2-1 2-1 4 2695.31 673.8 2-5
  2-5 2.5 2518.89 1007.56  
  2-11 6.2 642.01 103.55  
  2-12 7.6 393.13 51.72  
9-1 9-1 4.5 2625.89 583.53 9-1
  9-5 4.6 1326.33 288.33  
  9-11 6-.5 682.6 105.01  
  9-12 8 403.51 50.43  
4-1 4-2 3.8 1307.57 384.57 4-5
  4-5 3. 1545.5 515.16  
  4-9 5.5 737.48 134.08  
7-2 7-2 2.4 Direct Link   7-2
13-1 13-12 3.5 438.4 125.26 13-11
  13-11 4 1762.91 440.7  
  13-1 6.2 2108.02 340.0  
  13-2 7.5 656.61 87.54  
  13-7 8.5 388.19 45.67  
3-1 3-1 7.5 2167.4 288.99 3-4
  3-4 3.7 2555.97 751.15  
  3-5 6 2250.84 375.14  
  3-9 5 1924.48 384.89  
14-1 14-1 6 1636.32 272.72 14-1
  14-2 5 942.56 188.51  
  14-5 6 1058.7 176.45  
  14-7 6.5 445.55 68.5  
  14-13 3.5 716.56 204.73  
  14-11 5.4 994.28 184.12  
8-3 8-3 5.5 1177.34 214.6 8-3
  8-4 7.5 616.02 82.13  
6-3 6-3 4.7 457 97.23 6-3
  6-8 3.2 207.29 64.77  
10-3 10-3 5 463.31 92.6 10-3
  10-4 5 459.93 91.98 or
  10-8 5 162.82 32.5 10-4

Table 7

Settlements arranged in descending order

F? Σd? ΣF? / Σd? Settlement No.
27822.6 83.2 334.4 1
7281.4 76.9 94.68 5
4935.6 82.3 59.97 2
5038.1 101.0 49.88 11
4930.8 101.0 48.82 3
4029.2 83.2 48.42 4
4321.4 116.9 37.28 12
3325.8 100.2 33.19 9
2398.0 104.4 22.96 7
2510.8 126.4 19.85 13
2096.2 114.3 18.10 14
1391.8 144.0 9.66 8
692.1 117.0 6.91 10
528.9 143.4 3.68 6

Table 8

Network generation (Hypothesis No. 2)

Node Link Options Link Length ΣF? E? Final Selection
1 1-5       5-1
5 got connected with 1        
2 2-5 2-5 2419-69 976-8 2-5
  2-1 4 2596.13 649.03  
11 11-1 3 3720.27 1240.1 11-1
  11-2 6.2 341.04 55.0  
  11-5 5 737.17 147.43  
3 3-1 7.5 1910.87 254.78  
  3-5 6 1800.02 300.0 3-5
  3-2 7.3 682.67 93.51  
  3-11 10 662.06 66.02  
4 4-2 3.8 1938.42 510.1 4-5
  4-5 3. 2851. 950.33  
  4-3 3.7 1256.97 339.72  
12 12-11 No option     12-11
9 9-1 4.5 2738.3 608.45  
  9-6 4.6 1442.54 313.5 9-1
  9-11 6.5 995.55 156.16  
  9-12 8 443.08 55.38  
  9-3 5 878.57 175.75  
7 7-2 No Option     7-2
13 13-11 4 1781.07 445.26 13-11
  13-12 3.5 1487.23 424.92  
  13-5 7.5 995.89 132.78  
  13-2 7.5 720.53 96.07  
  13-7 8.5 730.89 50.69  
  13-1 6.2 2049.03 330.48  
14 14-1 6 1642.71 273.78 14-1
  14-2 5 953.72 190.74  
  14-5 6 1068.78 178.13  
  14-7 6.5 448.91 69.06  
  14-11 6.4 814.85 150.89  
  14-13 3.5 719.38 205.53  
8 8-3 5.5 1201 218.36 8-3
  8-4 7.5 740.35 98.71  
10 10-8 5 165.35 33.07 10.3
  10-3 5 467.75 93.55  
  10-4 5 402.95 80.59  
  10-7 7 212.82 30.40  
6 6.3 4.7 462.14 98.32 6-3
  6-8 3.2 212.57 66.13  
  6-9 9 172.99 19.22  
  6-1 12 216.11 18.01  

Table 9

Matrix for route length (Hypothesis No.1, Fig. 7B)

1 2 3 4 5 6 7 8 9 10 11 12 13 14  
1 0 4.5 8.7 5 2 13.4 6.9 14.2 4.5 10 3 4.5 7 6
2 4.5 0.0 9.2 5.5 2.5 13.9 2.4 14.7 9 10.5 7.5 9 11.5 10.5
3 8.7 9.2 0 3.7 6.7 4.7 11.6 5.5 13.2 8.7 11.7 13.2 15.7 14.7
4 5 5.5 3.7 0 3 8.4 7.9 9.2 9.5 5 8 9.5 12 11
5 2 2.5 6.7 3 0 11.4 4.9 12.2 6.5 8 5 6.5 9 8
6 13.4 13.9 4.7 8.4 11.4 0 16.3 10.2 17.9 13.4 16.4 17.9 20.1 19.4
7 6.9 2.4 11.6 7.9 4.9 16.3 0 17.01 11.4 12.9 9.9 11.4 13.9 12.9
8 14.2 14.7 5.5 9.2 12.2 10.2 17.1 0 18.7 14.2 17.2 18.7 21.2 20.2
9 4.5 9 13.2 9.5 6.5 17.9 11.4 18.7 0 14.5 7.5 9 11.5 10.5
10 10 10.5 8.7 5 8 13.4 12.9 14.2 14.5 0 13 14.5 17 16
11 3 7.5 11.7 8 5 16.4 9.9 17.2 7.5 13 0 1.5 5.5 9
12 4.5 9 13.2 9.5 6.5 17.9 11.4 18.7 9 14.5 1.5 0 5.5 10.5
13 7 11.5 15.7 12 9 2.4 13.9 21.2 11.5 17 5.4 5.5 0 13
14 6 10.5 14.7 11 8 19.4 12.9 20.2 10.5 16 9 10.5 13 0

Table 10

Matrix for force of interaction (Hypothesis No. 1, Fig. 8B)

1 2 3 4 5 6 7 8 9 10 11 12 13 14  

1

0

1992.7

1345.1

2434.0

6472.0

141.1

1003.7

398.0

2475.0

264.2

3646

2907.3

1430.9

1427.0

2

1992.7

0

11.6

156.5

427.0

13.4

891.6

40.6

69.4

27.0

26.9

61.5

53.0

52.9

3

1345.1

11.6

0

763.1

135.5

275.5

87.5

667.0

74.3

90.6

21.5

63.6

65.1

62.1

4

2434.0

156.5

763.1

0

106.5

15.0

35.0

42.1

29.3

56.6

24.9

6.7

17.1

23.0

5

6472.0

427.0

135.5

106.6

0

0.4

7.7

2.7

8.2

3.0

47.9

15.5

0.6

6.4

6

141.1

13.4

275.5

15.0

0.4

0

0.3

2.1

0.7

0.7

0.6

2.4

0.5

0.7

7

1003.0

981.6

87.5

35.0

7.7

0.3

0

0.6

2.2

1.0

24.6

13.2

3.0

2.2

8

398.0

40.6

667.0

421.1

2.7

2.1

0.6

0

0.8

0.9

14.1

8.3

2.8

1.1

9

2475.0

69.4

74.3

29.3

8.2

0.7

2.2

0.8

0

0.9

48.3

25.0

7.6

0.8

10

264.2

27.0

90.6

56.6

3.0

0.7

1.0

0.9

0.9

0

8.6

5.2

1.9

0.1

11

3646

26.9

21.5

24.9

47.9

0.6

24.6

14.1

48.3

8.6

0

831.0

103.8

35.1

12

2907.3

61.5

63.6

6.7

15.5

2.4

13.2

8.3

25.0

5.2

831.0

0

54.4

19.8

13

1430.9

53.0

65.1

17.1

0.6

0.5

3.0

2.8

7.6

1.9

103.8

54.4

0

6.9

14

1427.0

52.9

62.2

23.2

6.2

0.7

2.2

1.1

0.8

0.1

35.1

19.8

6.9

0

Σ

25936.3

3915.1

3662.6

3710.1

7233.3

453.4

2072.6

1181.1

2742.5

460.7

4833.3

4013.9

1747.6

1638.2

ΣΣ 63599.7 F = 31799.85

Table 11

Comparision of alternative network options

Network LL F LEN
Fully developed 746.6 35637.45 47.73
Need oriented 64.1 30951.95 482.86
Based on Individual Link Efficiency 60.2 31745.91 527.34
Based on Hypothesis No. 1(A) with link 10-3 47.8 30579.35 639.7
Based on Hypothesis No 1(B) with link 10-4 47.8 31799.85 665.26
Based on Hypothesis No. 2 50.1 27890.4 556.69

Table 12 indicates that all the existing links have been predicted by hypothesis No. 2 , but network generated by this hypothesis may not be considered optimal if link efficiency of the network is the criteria. Networks developed by hypothesis No. 1 also closely matches with existing network, as all the existing links are predicted by the hypothesis, except slight deviation in linkage of settlement No. 3 with that of No. 1. Instead of following route 3-4-5-1 to achieve needed linkage 3-1 the route being followed is 3-5-1. Probable reason for

Table 12

Comparision for existing and predicted links

Existing Links Predicted Links Hvp. 1(A) Hvp 1(B) Hyp.2
5-1 5-1 5-1 5-1
5-2 5-2 5-2 5-2
5-4 5-4 5-4 5-4
1-11 1-11 1-11 11-1
11-12 11-12 11-12 11-12
5-3 - - 5-3
3-6 3-6 3-6 3-6
9-1 9-1 9-1 9-1

this deviation may be that route 6-3-5-1, is a part of inter-district route. Inter-district force of interaction 3-5 appears to be predominating than local force of interaction along 3-4, due to which shorter route via 3-5-1 is being followed instead of longer and deviated route 3-4-5-1. Network generated based on hypothesis No. 1 gives highest link efficiency out of all the six different networks generated. It also predicts closely existing links, and indicates that the hypothesis No. 1 works well. All other missing links, in the network,

generated by hypothesis No. 1 may be recommended for future development id link efficiency is set as the main goal of network planning.

Summary of Conclusions

It should be noted that hypotheses No. 1 may not be the final, one giving highest link efficiency. A number of similar hypothesis may be developed and a search can be made for the hypothesis and network giving highest link efficiency.

References

Mahendru A.K., Sikdar P.K., and Khanna, S.K. "Nodal Points in Rural Road Network Planning", Indian Highways, April, 1982.

Mahendru A.K., Khanna, S. K. and Sikdar P.K., "Spatial Distribution and Functional Planning of Settlement Hierarchies in Rural Road Network", Publication in spatial number of Indian Highway, July, 1983.

Mahendru, A.K., Arora, M.G. and Khanna, S.K., "Road Network Planning on Regional Basis", paper presented at Seminar on Techniques for Development of Road Network and Methodology for Preparation of Master Plan, held at Lucknow, August, 1980.

Mahendru, A.K., Mehta, R.K., Khanna, S.K., :Graph Theoretic Approach Applied to Road Network Planning and Analysis", Indian Highways, June, 1983.

Mahendru, A.K., Sikdar, P.K., Khanna, S.K., "Linkage Pattern in Rural Road Network Planning", Indian Road Congress Vol. 44-3, Dec., 1983.

Appendix-I-Notations

CS = Centrality Score of a Settlement

F? = Force of interaction between Settlements i and j

F = Total Force of Interaction Catered by a Network.

K = A Suitable Multiplier Factor to Get Full Number of Weightage for a Function.

LL = Total Link Length Involved in a Network

Nf = Total number of Units of Function f in Entire Area.

LEI? = Link Efficiency of Link i j

LEOij = Link Efficiency of an Option i j

LEN = Link Efficiency of Network

Pi and Pj = Populations of Settlements i and j

d? = Spatial Distance Between Settlements i and j

L? = Link Length Between Settlement i and j

nf = Number of Frequency of Function f in a settlement

wf = Weight of function f

f = A Function

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