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                           USE OF A HYBRID ALGORITHM FOR MODELLING

    COORDINATED FEEDER BUS ROUTE NETWORK AT SUBURBAN RAILWAY STATION

                             Shrivastava Prabhat, M.ASCE1 and O’Mahony Margaret2

ABSTRACT

In the metropolitan cities of developed and developing countries, longer journeys are mostly performed

by two or more modes. In the event of availability of suburban trains and public buses, commuters prefer

to travel a longer stretch of their journeys by train, so as to avoid traffic congestion on roads, and the

remaining part by buses to reach local areas if their final destination is not in close proximity to railway

stations. Normally suburban trains have fixed corridors and buses have flexibility to serve remote local

areas. Thus design of feeder routes from railway stations to various destinations and the transfer time

from trains to buses play a very important role and can be controlled by transport planners.                                 A

considerable amount of research has been done on independent design of a bus route network without

considering the effect of train services. Researchers have made attempts using heuristics, simulation,

expert systems, artificial intelligence and optimization techniques for design of routes and schedules. So

far, limited effort has been made in modelling coordinated operations. In this research, a new hybrid

algorithm which exploits the benefits of Genetic Algorithms and a well tested heuristic algorithm for the

study area is discussed. More convincing results in terms of feeder routes and coordinated schedules at

the selected railway station are obtained by the proposed hybrid algorithm as compared to earlier

approaches adopted by the authors for the same study area.

CE DATABASE SUBJECT HEADINGS: Routing and scheduling, Genetic Algorithms, Optimisation,

Hybrid Algorithm, public transportation, Intermodal coordination, Heuristic Approach, Transportation

Planning




1
  Professor (Transportation Engg), Civil Engg Dept., Sardar Patel College of Engg., Andheri (W), Mumbai, India
2
 ,Professor & Head Dept. of Civil, Struct & Env Engg, Director , Centre for transp Research, Trinity College, Dublin-2, Ireland
                                                                                                         2


INTRODUCTION

In metropolitan cities of developed and developing countries significant growth of private and

intermediate transport has taken place. Due to this growth and limited capacity of carriageways, traffic

congestion, environmental pollution, poor level of service and longer travel times are very common.

These problems can be solved only by reducing dependency on private vehicles. The dependency can be

reduced only by making public transport more efficient. The efficiency of the public transport system can

be enhanced by better integration of its various components. Most metropolitan cities have suburban

railway and public buses as major public transport facilities. Feeder bus routes and coordinated schedules

critically determine the performance of an integrated public transport system specially when longer

journeys are made by suburban trains and public buses feed the local areas. The purpose of this paper is to

develop a methodology for development of feeder routes for public buses and also to develop coordinated

schedules of public buses for the existing schedules of suburban trains at a suburban railway station.

        The heuristic approach had been very popular for bus route network design problems. In places

where practical realistic solutions are more important than optimal solutions one can opt for the heuristic

approach. Using intuition and experience the analyst may be able to guide the heuristic search process far

more efficiently than a predetermined set of rules. Good heuristics have obvious advantages over the

more standard algorithms of combinatorial optimization (Reklaitis et al, 1983). Desirable characteristics

of the heuristic process include execution in reasonable computational time, solutions which are close to

optimality on average and the simplicity of both design and computational requirements. In the case of

route design, the designer has to strike a balance between satisfaction of demand at various destinations

and shorter lengths of routes. Shrivastava and O‟Mahony (2007) have discussed in detail about the

application of an heuristic approach in development of routes or network of routes.

        The transit network design problems become more complex due to the difficulty in combining

user costs and operator costs in a single objective function. Non-linearity and non-convexities are

involved in the objective function along with the discrete nature of route design and various other

constraints relating to route coverage, route duplication, route length and directness of service. Thus
                                                                                                           3

complexities involved in network design problems necessitate intelligent searches and the use of robust

optimization techniques. Application of Genetic Algorithms for route scheduling and network design

problems has been discussed in detail in Shrivastava and O‟Mahony (2007) and Shrivastava and

O‟Mahony (2006). .

        Limited efforts have been made for the design of feeder route networks for feeder buses at

railway stations (Shrivastava and Dhingra, 2000). However, Wirasinghe (1980), Geok and Perl (1988)

attempted routing and scheduling problems for coordinated operations using analytical models. They had

considered a highway grid which is assumed to be rectangular and parallel to a single railway line which

may not always be true in practice. They had made an attempt to describe complex transit systems by

approximate analytical models. Zhao and Ubaka (2004) presented a mathematical methodology for transit

route network optimization. The objective was to minimize transfers and optimize route directness while

maximizing service coverage.

        The authors have communicated research papers on development of feeder routes for the same

study area using different approaches. This paper builds on the work of earlier research papers and

contains significant differences from previous work. In other words it inherits the best qualities of earlier

papers. In Shrivastava and Dhingra (2001) feeder routes were generated with the help of a heuristic

algorithm which was suitable for the typical case study. The heuristic algorithm does not promise an

optimal solution but it may give a near optimal or suboptimal solution. In Shrivastava and O‟Mahony

(2006) a Genetic Algorithm has been used for simultaneous development of feeder routes and schedules

but it was found that demand at all nodes is not satisfied. This is because in the typical study area under

consideration some of the nodes are connected in the form of a chain without any additional connectivity

with any other node / nodes. Thus very limited alternatives are available for such nodes and even with

higher penalties demand remains unsatisfied. In Shrivastava and O‟Mahony (2007), well scattered nodes

are selected as potential nodes and an heuristic algorithm is used as the repair algorithm. This research

work differs from earlier work of the authors in following ways:
                                                                                                        4


   The demand at nodes (destinations) is given priority for development of routes over the location of

    nodes. Thus nodes with more than average demand are identified as potential destinations.

   In the case of any network, if higher demand nodes are located on the outskirts of the study area then

    the heuristic algorithm acts as repair algorithm otherwise the genetic algorithm develops a partially

    optimized network giving due consideration to higher demand nodes.

   After development of the partially optimized network the heuristic algorithm further modifies the

    network. In the modification process using the heuristic algorithm again the demand of nodes is given

    priority for development of the route system.

   The proposed approach in this paper is oriented towards demand satisfaction of nodes but their

    locations are also given due consideration for modification of routes which is the key idea for

    development of networks especially in the context of the public transport system.

   A judicious use of both genetic algorithms and heuristic approaches can be seen in this research. If

    the higher demand nodes are close to the DART station then the heuristic algorithm plays a major role

    and if higher demand nodes are well scattered and away from DART station then the genetic

    algorithms plays the main role.

        In this paper, first potential destinations having more than average demands are identified and

with k – path algorithm and Genetic Algorithms an optimized feeder route structure is developed. This

route structure is modified with heuristic algorithms so that all other nodes having less demand are

connected. Thus in this process an optimized feeder route structure is developed by Genetic and K – path

algorithms which is desirable because nodes with higher demand should be given priority over lower

demand nodes. Lower demand nodes are connected to the developed route structure by a heuristic

algorithm. Thus a judicious use of both the algorithms is shown in this paper.

        In this research the Shrivastava - O‟Mahony Hybrid Feeder Route Generation Algorithm

(SOHFRGA) which is a combination of Genetic Algorithms and Heuristic Approach has been developed.

It has been found that the feeder routes developed by SOHFRGA are more efficient than those developed
                                                                                                           5

by authors using other approaches. Dun Laoghaire is a rapidly growing suburb in Dublin city of Ireland

and DART station is selected as the study area for coordination between Dublin buses and DART

services. Assessment of the number of commuters currently using DART services, the percentage of

commuters using Dublin buses after arriving by DART at Dun Laoghaire and the number of commuters

who would shift from other modes to bus is discussed in previous research papers i.e. Shrivastava and

O‟Mahony (2007) and Shrivastava and O‟Mahony (2006). Table 1 indicates potential demand to various

destinations which includes current demand by buses and the expected shift of commuters from other

modes. Readers are advised to refer to the above papers for further details of the study area and data

collection

PROPOSED METHODOLOGY

The overall methodology for development of feeder routes and coordinated schedules is indicated in

figure 1. As discussed in Shrivastava and O‟Mahony (2006) and Shrivastava and O‟Mahony (2007) the

potential demand is assessed, travel time matrices are developed, other parameters and values have been

decided (refer to steps 1, 2 and 3 of proposed methodology in the above papers). The remaining

methodology used in the research presented here can be explained in the following.

(1) Feeder routes are developed by Shrivastava – O‟Mahony Hybrid Feeder Route Generation Algorithm

    (SOHFRGA). Figure II indicates the various steps involved in SOHFRGA which are described

    below.

Step I:

Identification of Potential Destinations

From the traffic surveys, demand at various destinations (nodes) is identified. The destinations having

more than average demand were identified as potential destinations. This has been done in order to

develop an initial feeder route network for potential destinations. In doing so the demands at potential

destinations get satisfied by shorter routes and then other nodes of which demand is less than average are

inserted / attached to developed „K – Paths‟ using the heuristic algorithm. This is explained in later steps.
                                                                                                          6

The preference is given to small number of routes with higher percentage of demand satisfaction with

lower travel time. Large number of routes will be generated if K- Paths are developed for each

destination. Large number of routes will require more buses and also some routes will be very short and

some may be very long, which will pose problems in the scheduling process. Buses will have to be

scheduled on many routes where demand may not be substantial which will lead to uneconomical

operations. In view of this K – Paths were developed for destinations with demand more than average

with upper limits on lengths of routes.

Step II:

Development of K –Paths between Origin (DART station) and Potential Destinations

There were five potential destinations having more than average demand from the DART station. With

the help of K-path algorithms (Eppstein, 1994) five short paths between origin (DART station) and each

potential destination were developed. Thus between each pair of origin (DART station) and potential

destination five alternative paths were available for further analysis as explained in the next step.

As there were 16 destinations to which demand from DART station exists, out of these 16 destinations

five had more than average demand and thus selected as potential destinations, remaining 11 nodes

(destinations) were used for development of short paths to potential destinations. It can be seen in Table -

2 that variation in lengths between first (smallest) and fifth (largest) path for each pair is considerable

therefore, if more than five paths are developed for each destinations there will be additional paths with

higher travel times. Routes with higher travel times are not desirable as there will not be any improvement

in result. In view of this five „k‟ paths are developed for each destination. The value of „k‟ can be

selected higher if more nodes are available as there will be possibility of having more number of short

paths without considerable variation in travel time between shortest and longest path.

Step III:

Determination of optimized K-Paths and Schedules

A computer program to calculate the penalised objective function (summation of objective function and

penalties due to violation of constraints) was developed in the „C++‟ environment. The developed „K‟
                                                                                                             7

paths are used with the objective function program. The provision is made so that each alternative path

out of five „K‟ paths for each potential destination is selected with random frequencies generated by

Genetic Algorithms. The alternative paths and frequencies corresponding to minimum penalized objective

functions are selected as optimized feeder routes and frequencies.

        Thus frequencies ‘fj’ and a set of routes (with different lengths ‘lj’) are the decision variables. The

time of departure of buses is decided on the basis of frequencies and the scheduled arrival time of DARTs

from either direction at the DART station. The typical analysis in the paper has been carried out for peak

hour only. From the traffic surveys it was found that from each train during the peak hour almost the same

numbers of passengers alight and relatively similar percentages of passengers would select buses to their

destinations for further travel. Due to this uniformity in the alighting pattern, the frequencies of

connecting feeder buses are also found to be same, for example, on route number „1‟ each bus is

scheduled at 6 minute headway starting from 8.07 am to 8.55 am. This frequency will change as per

demand and with the distribution of commuters at any other time interval. In off peak hours, the headway

between trains will increase due to lower demand. This frequency will change as per demand in other

time intervals. During off-peak periods there will be less DART commuters and thereby headway

between buses will increase which will lead to a lower requirement of buses. The binary digit coding to

represent routes and schedules together has been adopted (Shrivastava et al 2002).

Details of Objective Function, Penalties and use of GAs in SOHFRGA

The objective function is adopted as the minimization of user and operator costs. The user cost is the

summation of the in-vehicle time cost and the transfer time cost between DARTs and buses. The operator

cost is associated with the running cost (vehicle operation cost) of buses. Constraints are related to load

factor, fleet size and unsatisfied demand. Readers are requested to refer Shrivastava and O‟Mahony

(2007) as mathematical representation of objective function, constraints, and penalties along with detailed

discussion is given there. In this paper, the same objective function and constraints are solved by using a

different approach which differs in the way it selects potential destinations.
                                                                                                            8

The developed objective function is used with LibGA software (Lance Chambers, 1995) for Genetic

Algorithms in the Linux environment. The objective function and constraints pose a multi-objective

problem. Some of the         constraints are in favor of users and some are in favor of the operator. For

example, lower load factor and higher load factor constraints are in favor of users and operators

respectively. If the load factor is above „1‟ some of the users may not be able to get a seat but the operator

will earn a profit. The fleet size constraint ensures that the scheduling of buses should be done within the

limited fleet size and this is in favor of the operator. The unsatisfied demand constraint ensures that all

commuters should be able to get on a bus, thus this constraint is in favor of the operator. Assigning a

very high penalty to one of the constraint results in a biased solution. Thus these penalties are decided so

as to keep the load factors between the minimum and maximum values, the fleet size within a specified

limit and the unsatisfied demand to zero. The adopted set of penalties for the feasible solutions is decided

so as to get a judiciously balanced solution.

The demand satisfaction and load factors on various routes are two dominating factors for both users and

operators. It has been found during the interviews with commuters that they prefer to have connecting

buses within five minutes of waiting after arriving at bus stops but most of them even accept ten minutes

of waiting as a reasonable time. Thus the variation of penalty coefficients for a minimum load factor is

related to the percentage satisfaction of demand within ten minutes of waiting. The coefficient for the

minimum load factor is selected because it is observed that the load factor frequently goes below 0.4

(minimum value) due to low demand which is not compatible to the adopted existing bus capacity (74).

This typical variation is observed when the penalty coefficient corresponding to the minimum load factor

(less than 0.4) is varied keeping other coefficients the same. A weighted factor is calculated by awarding

equal weights to the overall load factor and the percentage demand satisfaction within ten minutes of

waiting. The penalty coefficient corresponding to the higher weighted factor is selected for further

analysis.

Step IV:
                                                                                                          9

Check whether the entire demand is satisfied and routes are within the specified length. If the entire

demand is satisfied and routes are within the specified lengths then developed feeder routes and the

frequencies are optimum. The frequencies are used to calculate coordinated schedules for the existing

schedules of the DART.

Step V:

If the entire demand is not satisfied and routes are within specified lengths then these routes are used for

modification. Destinations leading to unsatisfied demand are inserted in routes by node selection and

insertion strategies. If the lengths of routes are not within specified limits (very small due to higher

demands close to a railway station) then these routes are discarded.

If the potential destinations are very close to a DART station then they lead to very short routes

mushrooming near to a station (Shrivastava and Dhingra, 2001 & Baaj and Mahamassani, 1995). Such

short routes are not acceptable in actual practice. Thus in the proposed case study a length of 2.5 km

equivalent to travel time of 10 minutes is adopted as the minimum length of feeder routes and the routes

less than or equal to this value are discarded. The nodes present on discarded routes and not duplicated in

other routes are also used for heuristic insertion/attachment process along with other nodes with

unsatisfied demand (destinations not included in any developed feeder route). Readers are requested to

refer to Shrivastava and Dhingra (2001) where the full description of node selection and insertion /

attachment process along with various insertion strategies are discussed in detail.

Use of Genetic Algorithms for the objective function and constraints

The proposed objective function is used with LibGA software (Lance Chambers, 1995) of Genetic

Algorithms in the Linux environment to determine optimal routes and frequencies in SOHFRGA and

thereafter for determination of final frequencies leading to coordinated schedules on developed feeder

route network. The details of Genetic Algorithms, its application and adopted values of various operators

etc is discussed in Shrivastava and O‟Mahony (2007).
                                                                                                          10


RESULTS AND DISCUSSION

In the initial stage of SOHFRGA, nodes having more than average demand were selected as potential

destinations and feeder routes with frequencies for feeder buses (leading to coordinated schedules) were

developed simultaneously using Genetic Algorithms. There were six destinations having more than

average demand. These destinations were Dun Laoghaire College (2), Sallynogin (3), Monkstown (4),

Deans Grange (5), Stillorgan (8) and Loughlinstown (12). Selection of these nodes as potential

destinations developed six routes with 12.85% unsatisfied demand. Selection of five nodes i.e. Dun

Laoghaire College (2), Sallynogin (3), Deans Grange (5), Stillorgan (8) and Lough Linstown (12) also

gave 12.85% unsatisfied demand with five feeder routes. Therefore these five destinations were selected

as potential destinations and five k-paths as indicated in table 2 were developed for each of these potential

destinations originating from the DART station. These k – paths were used with LibGA software of

Genetic Algorithms in Linux and feeder routes with frequencies leading to coordinated schedules were

developed simultaneously. The following feeder routes were obtained (with codes as given in table 1).

   Nodes in feeder routes                            Length in terms of travel time in „minutes‟

        1–2                                                        8

        1–3                                                        7

        1–4–5                                                      15

        1–6–7–8                                                    25

        1 – 3 – 17 – 11 – 12                                       30

Since the developed feeder route network does not satisfy 100% demand, the next stage of further

modification of feeder routes using node selection and insertion strategies is adopted. The frequencies

associated with feeder routes in the earlier stage are discarded since fresh frequencies are required to be

determined due to the modification of routes. The travel time on the first two feeder routes is even less

than ten minutes (minimum specified length of 2.5 km) Hence the first two routes are discarded and node

„2‟ which leads to unsatisfied demand is selected for the insertion process in the next stage for

modification of routes along with other unsatisfied nodes. Thus the 3rd, 4th and 5th routes were selected for
                                                                                                         11

modification and nodes having unsatisfied demand are inserted priority-wise using a heuristic approach.

Finally, the following three feeder routes, as indicated in figure 3 were developed.

Nodes in feeder routes                                 Length in „km‟

 1 – 4 – 2 – 5 – 10 – 9 – 16                              10.76

 1 – 6 – 7 – 8 – 15 – 14 – 13                             14.60

 1 – 3 – 17 – 11 – 12                                     7.72

It can be seen that the developed feeder routes are well within the specified minimum (2.5 km) and

maximum (15 km) lengths of routes. These lengths of routes are decided based on locations of nodes to

which demand exists as identified in typical traffic survey. The upper limit of the length of routes can be

revised and shorter lengths can be adopted if a similar exercise of coordination is repeated at other DART

stations also. This is due to the fact that a particular node may have connectivity with more than one

DART station which may lead to shorter and better routes from one station, as compared to another one.

For example, nodes 13, 14 and 15 are very close to the Blackrock DART station as compared to Dun

Laoghaire. Thus feeder routes for these destinations from Blackrock will be shorter.

        In the next stage for determination of coordinated schedules for feeder buses for the existing

schedules of DARTs these feeder routes were used. Genetic Algorithms are implemented for determining

optimal frequencies and coordinated schedules were derived from these frequencies. Table 3 shows

details of coordinated schedules of feeder buses for the existing schedules of DARTs and load factors. It

can be seen in the table that the average load factor on each route is more than 0.40 and the overall load

factor (average of load factors on all the three routes) is 0.47. The load factors on the routes and overall

load factor have much improved values against the existing scenario in which the load factor hardly

increases above 0.3.

         In the case study the capacity of feeder buses is taken as 74 (Scott Wilson, 2000) which is on

higher side as compared to the number of DART commuters transfer to buses. The load factor will be

more (greater than „1‟) if coordinating buses are held for longer time. Commuters from later DART trains

will be able to seek transfer to a particular bus due to a longer holding period. Longer holding increases
                                                                                                          12

transfer time between DARTs and feeder buses which is not desirable to users and will also increase the

value of the objective function. Thus the two contradictory conditions regarding higher load factors in

favor of the operator and the lower transfer time for users are satisfied by striking a balance between the

two. As the load factor decreases below „1‟ penalties are imposed because the constraint for the minimum

load factor is violated. Thus the load factors obtained in the study are less than „1‟ but transfer time

remains within desirable limits. Busses with lower seating capacity will improve the load factor. Also the

load factor will be higher if the model is implemented to places where higher numbers of train commuters

seek transfer to buses.

        Thus the decision of bus dispatch time not only depends on arrival time of DARTs but also on the

number of passengers transferring from DARTs to buses. As discussed above, the dispatch time of buses

is decided upon by means of striking a balance between transfer time and the acceptable value of the load

factor. If the load factor is lower, then buses are held for more time so as to acquire more commuters from

later DART trains. Other factors influencing the schedule of buses are the available fleet size and the

percentage demand satisfied. The coordinated buses are dispatched only after five minutes of scheduled

arrival of DART at station because it takes about five minutes for passengers to reach bus stops after

arriving on a DART train. It can be seen in table 3 that the first bus is at 8.07 which is five minutes after

the arrival of the south bound DART scheduled at 8.02; on route number 1, the second bus is at 8.13

which is five minutes after the arrival of the first north bound DART at 8.08. Some buses are scheduled

later than five minutes after the arrival of a DART train. This is done in order to compromise with the

load factor by holding the bus, as discussed above. The other coordinated schedules can be explained on

the basis of the above reasoning.

        Table 4 gives a comparison between existing and proposed route network. It can be seen that on

average 89 % of the total demand is satisfied within 5 minutes of effective waiting time and 99% of

demand is satisfied within 10 minutes of effective waiting time. Only 1 % of commuters are required to

wait up to 15 minutes. Route wise details indicate that 100 % demand on route 1 is satisfied within 5

minutes of effective waiting time and on route 2 and 3, 96 % of demand is satisfied within 10 minutes of
                                                                                                      13

effective waiting time. Only 4 % of commuters have to wait up to 15 minutes. Thus if a monetary value is

assigned to a saving in transfer time then about a 70% saving can be expected in transfer time due to the

proposed system. In the existing scenario there are 6 bus routes travelling through identified nodes

whereas in the proposed model three bus routes cover identified demand nodes. The saving in in-vehicle

time and operating cost can be expected to be 50% due to the proposed model against the existing

scenario. Table 4 briefly summarises the above discussions.

CONCLUSIONS

In the proposed research, feeder routes are developed using a hybrid approach which makes use of the

benefits of optimisation using genetic algorithms and a heuristic approach.     For the development of

feeder routes, priority is given to nodes having higher demands. In view of this, nodes having higher

demand (more than average) are considered as potential destinations and optimisation is carried out by

GAs. Nodes having lower demand are attached to (or inserted in) developed routes keeping the length (or

deviation) within reasonable limits. Coordinated schedules are determined by genetic algorithms.     The

following conclusions can be drawn from the proposed modelling exercise.

1. It has been observed that for the given influence area of a DART train station a combination of

    genetic algorithms and the proposed heuristic approach develops an improved feeder route structure.

    In the influence area of the railway station destinations closer to the railway stations have higher

    demands and other destinations are well-scattered with limited connectivity between them. By using

    this approach, a lower number of feeder routes is developed as compared to earlier approaches for the

    same influence area and demand. The proposed model also provides improved load factors with a

    higher percentage of demand satisfaction and lower waiting time.

2. The lengths of feeder routes are well controlled in the model. They are checked after the first stage

    i.e. after simultaneous development of routes and schedules using GAs and also using the heuristic

    approach route lengths are controlled by the „maximum demand deviation shorter path time criterion‟

    and the „path extension time criterion‟.
                                                                                                       14

3. The model strikes a balance between user need and operator requirements. The objective function

   incorporates user costs in terms of time spent in buses and the transfer time between DARTs and

   buses; the operators cost is the vehicle operation cost which is directly proportional to the distance

   travelled by buses. Similarly constraints are also as per the requirements of users and operators. The

   load factor constraint is kept within minimum and maximum values so as to maintain a better level of

   service for users and economic operation to satisfy operators. The fleet size constraint is also a

   realistic constraint from the operator‟s point of view. The constraint for unsatisfied demand increases

   the probability of availability of seats to commuters though it is not very important when the load

   factor remains less than a minimum value as has been experienced for the study area.

4. The same modelling exercise can be carried out at other DART stations with large scale data

   collection for the whole day. A fully integrated system with DART as the main line haul carrier and

   buses as feeder services can be developed. Schedules and thus the requirement of buses can be found

   for peak and off-peak periods of the day. Even the route structure can be appropriately designed as

   per demand at various destinations for different periods of the day.

5. The application of all three algorithms i.e. K – Path, Genetic and Heuristic Algorithms makes this

   approach acceptable for all types of networks i.e. networks with well connected nodes and networks

   in which all the nodes have limited connectivity. Planners have limited options available in the

   formation of alternative routes in the case of networks with limited connectivity. Combinations of

   Genetic Algorithms and K –Path algorithms have been successfully implemented for well connected

   networks. The heuristic approach is developed keeping in mind networks in which nodes are not well

   connected. Thus this method can be implemented for a network which is well connected and also for

   a network in which nodes do not posses better connectivity with other nodes. Thus this methodology

   is not developed only for a given case study but it can be implemented to other networks also. If the

   higher demand destinations are located away from the origin (railway station), well scattered and well

   connected then optimised feeder routes and coordinated schedules will be developed in the first stage

   of model in which optimisation of feeder routes and coordinated schedules is done simultaneously
                                                                                                  15

   using Genetic Algorithms. Thus the proposed model can be used for any influence area if demands at

   various destinations and network connectivity details are known.

REFERENCES

1. Baaj M.H. and Mahmassani H.S. (1995). Hybrid Route Generation Heuristic Algorithm for the

   Design of Transit Networks, Transpn. Res.C, 3, 1, 31 – 50.

2. Eppstein, David (1994).     Finding the    k shortest paths. Tech. Report 94-26, Department of

   Information        and    Computer        Science,     University    of      California,    USA.

   http://www.ics.uci.edu/~eppstein/pubs/Epp-TR-94-26.pdf accessed on 25.09.2004

3. Geok K, and Jossef P. (1988). Optimization of feeder bus routes and bus stop spacing. Journal of

   Transportation Engineering, 114, 3, ASCE, Reston, VA, 341-354.

4. Chambers, L. (1995). “Practical Handbook of Genetic Algorithms Applications. Volume I”, CRC

   Press, 555.

5. Reklaitis, G.V. Ravindran, A. and Ragsdell K.M. (1983), “Engineering Optimization – methods and

   applications”, Wiley, New York, N.Y.

6. Scott Wilson (2000). “Final Report on Bus Network Strategy Appraisal Report for Greater Dublin

   Area”. www.dublinbus.ie/about_us/pdf/swilson.pdf Accessed May 13, 2004.

7. Shrivastava P. and Dhingra S.L (2000). An overview of bus routing and scheduling techniques.

   Highway Research Bulletin, 62, 65 – 90.

8. Shrivastava P. and Dhingra S.L. (2001), Development of feeder routes for suburban railway stations

   using heuristic approach Journal of Transportation Engineering, ASCE, USA, July/August 2001,

   127, 4, 334-341.

9. Shrivastava P., Dhingra S.L. and Gundaliya P.J. (2002), Application of Genetic Algorithm for

   Scheduling and Schedule co-ordination problems. Journal of Advanced Transportation. 36, 1, Winter

   2002, 23 – 41.

10. Shrivastava P. and O‟Mahony M. (2006), A Model for Development of Optimized Feeder Routes and

   Coordinated Schedules – A Genetic Algorithms Approach, Transport Policy, 13, 5, 413-425.
                                                                                                 16

11. Shrivastava P. and O‟Mahony M. (2007), Design of Feeder Route Network Using Combined Genetic

   Algorithm and Specialized Repair Heuristic, Journal of Public Transport, 10, 2, 99-123

12. Wirasinghe, S.C. (1980), Nearly optimal parameters for a rail feeder bus system on a rectangular

   grid. Transp. Sci. 14A (1), 33-40.

13. Zhao F. and Ubaka I. (2004), Transit network optimization – minimizing transfers and optimizing
   route directness, Journal of Public Transportation, 7, 67 – 82
                                                                                 17




Table 1 Potential Demand to Various Destinations

  Node             Destinations                Potential demand to various
   No.                                                 destinations
 (code)                                  7 – 8 a.m.    8 – 9 a.m.     7-9 a.m.
1         Dun Laoghaire DART Station          0             0             0
2         Dun Laoghaire College              39           202           241
3         Sallynoggin                        17           103           120
4         Monks town                         10            63            73
5         Deans Grange                       16            93           109
6         Temple Hill                         2             6             8
7         Black Rock                          8            46            54
8         Stillorgan                         13            77            90
9         Leopards town                       2             8            10
10        Foxrock                             2             8            10
11        Maple Manor / Cabinteely            2             4             6
12        Lough Linstown                     13            78            91
13        Mount Merrion                       2            15            17
14        University College of Dublin        4            23            27
15        Dundrum                             6            31            37
16        Sandyford                           3            15            18
17        Rouches Town Avenue                 2             4             6
                                                                              18


Table 2 Developed ‘K’ paths between DART station and Potential Destinations

Origin   Potential Destination          Nodes in „k‟ paths     Travel time
                                            ( k=5 )                 min
  1               2              1, 2                          8
                                 1,3,2                         10
                                 1,4,2                         15
                                 1,6,4,2                       20
                                 1,4,5,2                       20
  1               3              1,3                           7
                                 1,2,3                         11
                                 1,4,2,3                       18
                                 1,4,5,2,3                     23
                                 1,2,5,3                       23
  1               5              1,2,5                         13
                                 1,3,2,5                       15
                                 1,4,5                         15
                                 1,2,4,5                       16
                                 1,3,5                         17
  1               8              1,6,8                         21
                                 1,7,8                         24
                                 1,6,7,8                       25
                                 1,7,6,8                       26
                                 1,2,5,8                       26
  1               12             1,3,17,12                     23
                                 1,2,3,17,12                   27
                                 1,3,11,12                     28
                                 1,2,17,12                     30
                                 1,3,17,11,12                  30
                                                                                                      19

Table 3 Details of Bus Schedules with Load Factors



    Train Timings                 Bus Timings                     Load Factors               Over
                                                                                           all load
                                                                                            factor
   North       South
  Bound       Bound       Route    Route        Route    Route     Route         Route
  DARTS       DARTS         1        2            3        1         2             3

 8.08         8.02       8.07     8.07       8.07        0.46    0.23       0.22
 8.15         8.09       8.13     8.19       8.19        0.16    0.31       0.30
 8.23         8.20       8.19     8.31       8.31        0.46    0.62       0.60
 8.29         8.25       8.25     8.43       8.43        0.62    0.70       0.67
 8.33         8.31       8.31     8.55       8.55        0.62    0.39       0.38            0.47
 8.38         8.36       8.37        -                   0.62         -
 8.43         8.45       8.43        -                   0.78         -     Load factor
 8.49         8.53       8.49        -       Buses to    0.16         -     for Buses
 8.58            -       8.55        -       be          0.62         -     to        be
                         Buses to be         scheduled   Load factor for    scheduled
  Trains after 9 a.m.    scheduled after     after 9     Buses     to    be after 9 a.m.
                         9 a.m.              a.m.        scheduled after
                                                         9 a.m.
 Average load factors on individual routes               0.50    0.45       0.43
                                                                                                20




        Table 4: Comparison between existing and proposed Route Network


    Property for comparison        Existing Route network in the   Proposed route network for the
                                             study area                       study area
      Type of route network         Not a feeder route network          Feeder route network
Average load factor on routes              Less than 0.3          Greater than 0.4 on all routes,
                                                                  over all load factor is 0.47
Waiting time / percentage Average waiting time is more 89% demand is satisfied with in
demand satisfaction           than 20 minutes                     5 minutes, 99 % with in 10
                                                                  minutes and 100 % is satisfied
                                                                  with in 15 minutes of effective
                                                                  waiting.
Transfer Cost                 About 70% saving in transfer cost can be achieved per head due to
                              proposed network and coordinated scheduling
In vehicle cost and Operating There will be about 50 % saving in in-vehicle cost and operating cost
Cost
Total Cost                    The total saving can be expected to be more than 50%
                                                                                              21


                                 Identification of data requirement




                             Details of existing bus and DART network
                              - Coded bus and DART network
                              - Link lengths & link travel time
                              - Characteristics of Dublin buses


                                          TRAFFIC SURVEYS


                         Surveys for assessing             Assessment of potential
                         existing distribution of          demand to different
                         DART Commuters on                 destinations from DART
                           Different Modes                 station using willingness
                                                           to shift surveys




                     Existing Road Network              Potential O - D Matrix



                         SHRIVASTAVA – O‟MAHONY HYBRID FEEDER
                              ROUTE GENERATION ALGORITHM
                                       (SOHFRGA)



                                              Feeder routes
                                            for DART station




                                SCHEDULE OPTIMISATION MODEL
                  Minimisation of distance travelled by Dublin buses (Operator Cost) and
                 Transfer time between DART and coordinating feeder public buses (User
                     cost) with the constraints related to load factor, transfer time and
                                                                                            Existing
                                            unsatisfied demand.                              DART
                                                                                            timings


                                 Coordinated Schedules of Public Buses


Figure 1: Proposed Methodology for development of feeder routes and coordinated
         Schedule
                                                                                              22

Figure 2: Proposed Shrivastava – O’Mahony Hybrid Feeder Route Generation Algorithm
       (SOHFRGA)

                                                      Demand Matrix obtained
                  Existing Road Network                 by Traffic surveys


                                                        Selection of Potential
                  Link connectivity matrix
                                                        destinations based on
                                                          average demand

                                   Development of K –paths
                                  between DART station and
                                     potential destinations

                  Optimization of penalized objective function using Genetic Algorithms
                  Objective function: Minimization (Transfer time between DARTs and
                  Buses + in Vehicle time + Vehicle operating cost)
                  Constraints: Related to Minimum and Maximum load factors, fleet
                  size and unsatisfied demand


     Existing
      DART                            Optimized Feeder routes and
                                        coordinated schedules
     timings
                                                       Yes
                                                                             No
                                         Is entire demand
                                             Satisfied?

                                                          Yes
                                                                                          A

                                          Are the lengths of
                                         feeder routes with in
                                          acceptable limits?




                                   Print optimized feeder routes and
                                         coordinated schedules
                                                                                                               23




                                                              A


                                 Discard the routes having less than minimum
                                                    specified
                                 Length / Travel time (2.5 km / 10 min for case
                                                     study).
                                       Available routes for modification


                                Sort all the available nodes due to following in decreasing
                                order of demand:
                                 Could not be used by developed feeder routes and
                                    give rise to unsatisfied demand
                                 Available due to discarding of smaller feeder routes.



                                    Select first node among arranged in decreasing order of
                                                           demand


                    Stop,            Yes
                                                     Is last node has been
                 Print Routes                               inserted?

                                                                             No

Node selection and                  Find out the route in which selected node has to be
insertion strategies              inserted /attached as per node selection and insertion
                                   strategies and Insert / attach the selected node in the
                                                      identified route.



                                                                                              Select next
                                                  Is route length with in                        route
                                                      specified limit?




                                      Insert the node in selected route and delete from
                                                           node list                          Take next node



 Figure 2 : Proposed Shrivastava – O’Mahony Hybrid Feeder Route Generation Algorithm
          (SOHFRGA) (Continued)
                                                                                          24


Figure 3 is available on request from the authors


List of Tables


Table 1 Potential Demand to Various Destinations

Table 2 Developed „K‟ paths between DART station and Potential Destinations

Table 3 Details of Bus Schedules with Load Factors

Table 4 Comparison between existing and proposed Route Network




List of Figures

Figure 1 Proposed Methodology for development of feeder routes and coordinated schedule

Figure 2 Proposed Shrivastava – O‟Mahony Hybrid Feeder Route Generation Algorithm

(SOHFRGA)

Figure 2 Proposed Shrivastava – O‟Mahony Hybrid Feeder Route Generation Algorithm

(SOHFRGA) (Continued)

Figure 3 Developed feeder route network for Dun Laoghaire DART station

				
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