E VALUATION OF INFLUENCE OF MOBILITY MANAGEMENT INSTRUMENTS IMPLEMENTED IN SEPARATED AREAS OF THE CITY ON THE CHANGES IN MODAL SPLIT

The article presents results of research aimed at construction of the model for evaluation of potential impact of mobility management instruments implemented in areas of high volume of work related trips. The model helps forecast the impact of the instruments application on the changes in modal split. In proposed approach the potential decrease in the car share depends on the improvement of public transport accessibility of the area and its current private transport accessibility. Due to the specific nature of the analyzed problem the elements of fuzzy set theory have been used to construct the model. To determine unknown volumes of decreases results achieved during implementation of mobility plans in the European workplaces with high number of employees have been taken under consideration. Approximation of the surface received as a result of fuzzy inference has been conducted using formula of multiple linear regression. Prepared model has been applied on the example of Cracow to evaluate of potential impact of mobility plans on the change in modal split.


Introduction
Because of the growing size of negative occurrences related to the mobility different measures in order to reduce its scale are undertaken (Banister, 2005;Jacyna et al. 2014).One of very promising approaches indicates changes in travel behaviour, including decrease in the number of private car trips as a tool of mitigation of negative impact of travelling in cities (COM, 2007;COM, 2011;Garling and Steg, 2007;Starowicz, 2011;Rudnicki et al. 2010).Concept focused on change of transport behavior is called mobility management and is aimed at shaping demand for alternative transport modes to private cars, including public transport means, pedestrian and bicycle trips (Loukopoulos, 2007;Meyer, 1999;Starowicz, 2007;Stradling et al. 2000; Taylor and Ampt, 2003).In the transport policy the European Commission indicates necessity of implementation of measures oriented towards changes of transport behavior of people travelling to work.In the "Green Paper" (COM, 2007) and "Action plan on urban mobility" (COM, 2009) the significant role of enterprises and public sector entities is underlined since their promobility strategy may contribute with shaping transport behaviors of their employees.It is necessary to encourage companies, especially those of high number of employees to create so called mobility plans (Bojczuk, 2011;Nosal, 2009;Valiente, 2012) and implement of mobility management instruments (Loukopoulos, 2007).Exceptionally significant is cooperation of companies with transport managers and operators also in the scope of improvement of quality of public transport services and improvement of transport accessibility to workplaces.Special case are selected areas of the city, such as: business, industrial or other zones which everyday generate and absorb many trips related to work, including private cars (MoMa.BIZ; Sandyford Smarter Travel, 2012).Implementation of mobility management instruments in those zones may be a chance to convince drivers to resign of use of cars and gradually raising of competitiveness of other transport means may encourage current users to continuing.The article presents results of research aimed at construction of the model for evaluation of potential impact of sets of mobility management instruments implemented in areas (transportation zones) of high volume of trips related to work to decrease share of car trips.Prepared model has been used to evaluate of potential impact of implementation of sets of mobility management instruments on changes in modal split in selected transport zones in Cracow as well as in trips on relations "Home-Work" in the urban area.

Assumptions of defining model
While constructing model for evaluation of potential impact of mobility management instruments implemented in the areas absorbing high volume of trips related to work following assumptions and annotations have been taken under consideration: 1.In trips related to work mainly public transport means may be the most competitive alternative for cars so it is assumed that implemented instruments should mainly be based on improvement of travel conditions provided in public transport and, mainly this transport mean will take over trips which so far have been carried out by car. 2. It is assumed that instruments will be implemented by employers located in the analyzed zone and by transport managers and operators cooperating with employers.Employers will mainly apply measures encouraging to travelling by public transport, including financial, information, promotional and educational instruments.Besides they will also use instruments connected with organization of parking a car, work times and encouraging for travel by other sustainable transport means.As a result of cooperation with transport managers and operators mobility management instruments devoted to improvement of accessibility of the area by the public transport means, e.g.: introduction of new public transport lines and direct connections, change of public transport routes or stops locations in order to improve access to the area or employees' places of residence as well as introduction of intermediate stops, providing separated bus lines, increasing frequency of lines' courses.It was assumed that only integrated measures contributes with increase of accessibility with public transport means and other tools may bring expected effect finally leading to the decrease in car share in trips.

Elaboration of structure of model of fuzzy interference evaluating the volume of decrease in car share in trips
Elements of theory of fuzzy sets have been used for modelling of volume of decrease in car share in trips depending on improvement of accessibility to the area by public transport and current accessibility to the area by private transport.Process of inference was supported by toolbox Fuzzy Logic Design -Matlab software (Wath Works, 2012), which enables to use Mamdani layout (Mamdani, 1977).Two input data (predecessor of the rule) and one output data (successor of the rule) described by suitable fuzzy sets are assumed.First input data (predecessor of the rule) refers to the evaluation of current volume of indicator of accessibility to the area by public transport means and is the linguistic variable called TZ accessibility.Although input data refers to the current volume of indicator of accessibility to the area by public transport means, it is assumed that as a result of implementation of mobility management instruments improvement of current volume of indicator will be achieved to a higher level.Decrease in share of car trips will be dependent on improved transport accessibilitynot on the current one.Second input data (predecessor of the rule) refers to the evaluation of current volume of indicator of accessibility by private transport and will be the linguistic variable: TI accessibility.It is assumed that any changes of current volume of accessibility by private transport will not appear and it is assumed as input data to provide reference to considerations about possible decrease in car share in trips caused by implementation of measures aimed at improvement of accessibility of the area by public transport.Although mobility management instruments implemented by employers haven't been accepted as input data in the model of fuzzy inference directly, it is assumed that they strengthen effectiveness of measures aimed at improvement of accessibility of the area by public transport means.Output data (successor of the rule) is evaluation of volume of relative decrease in car share in trips which may be achieved with implementation of mobility management instruments (described as a linguistic variable: decrease).General concept of created inference model is presented in figure 1 and its schematic diagramin figure 2. The following set of the linguistic terms for input data (predecessor of the rule) and output data (successor of the rule) is assumed:  predecessor of the rule: "TZ accessibility" = {"very low", "low", average", "high", "very high"},  predecessor of the rule: "TI accessibility" = {"very low", "low", average", "high", "very high"},  successor of the rule: "Decrease" = {"very low", "low", average", "high", "very high"}."TZ accessibility" = {"very low", "low", average", "high", "very high"} "TI accessibility" = {"very low", "low", average", "high", "very high"} Membership functions defined for all terms describing linguistic variable TZ accessibility are presented in figure 3, whereas functions for terms describing linguistic variable TI accessibilityin figure 4.   Results of sensitivity analysis proved that average differences appearing in the volumes of decreases calculated with use of model with basic functions and accepted scenarios of modifications of function are very small and does not exceed 0,26 of percentage point.It is to be expected that even bigger modification of shapes of membership function then determined for sensitivity analysis wouldn't cause significant differences in the calculated volumes of decreases.It has confirmed possibility to use of determined membership functions for the purposes of created model.

Elaboration of inference rules and determination of the scope of possible results of the model describing volume of expected decrease in car share
The last component of created model of fuzzy inference is block of inference rules, including set of rules type: IF...THEN.For the requires of current research semantics of rules is fixed with conjunction AND in predecessor of inference rules and then set of all possible rules has been created.Number of all possible inference rules is: R=5*5*5 =125 (five terms describing linguistic variable TZ accessibility, five terms describing linguistic variable TI accessibility and five terms describing linguistic variable decrease).Among generated rules those illogical and those which seemed to be improbable have been rejected.Finally 25 inference rules have been accepted.Constructing rules has been based on the assumption that current accessibility to the area with public transport would be improved as a result of implementation of mobility management instruments (fig.1).For example, even if current TZ accessibility is "low", implementation of instruments will bring some improvement so that TZ accessibility becomes "average".While taking into account current "low" TI accessibility the effect of "average" decrease car share in trips to work in this area may be expected.For all rules value of 1,0 was assumed so that they are treated in the same way in the whole process of inference.Next phase of the fuzzy inference process implemented with the Matlab software (Wath Works, 2012), was related to the aggregation and defuzzification of the output data.Those operations are resulted with the output data as figure numerical value of relative decrease in car share in trips.Inclusion of the inference system in the Matlab software enables to receive a set of results as the surface of solutions for each possible set of input data (TZ accessibility indicator and TI accessibility indicator).This surface, created in the threedimensional spatial arrangement, present connection between current public transport accessibility indicator of the transportation zone (assuming that the indicator is the subject of improvement as a result of implementation of mobility management instruments), current private transport accessibility indicator to the zone and expected relative decrease in car share in trips to work in the zone (fig.6).Fig. 6.Surface of the fuzzy inference model.
While analyzing received surface it may be noted that in the process of fuzzy inference extreme volumes of decreases have been eliminated, very close 1,8% and very close 30%.Volumes of potential decreases of car share in trips to work range between 3,5% in the least favorable conditions (value of indicator of public transport accessibility is on the lowest level) and 27,7% in the most favorable conditions (value of indicator of public transport accessibility is on the highest level and indicator of individual transport accessibilityon the lowest level).

Approximation of the resulting surface of the model of fuzzy inference describing volume of expected decrease in car share
Application of the elaborated model in practice requires mathematical description of received resulting surface.Looking for suitable formula following activities have been undertaken: from the created inference system coordinates of points which create surface presented in the figure 6  Volumes of potential decreases in car share in trips, possible to determine with accepted model range between -2,0% and 27,2%, so it may be noted that adaptation of approximated equation on the base of received resulting surface causedcomparing to the results of fuzzy inference systemslight increase including volumes of expected decreases.It seems that it made real the results, especially for the least beneficial cases which volumes of decreases may take negative value.
Possibility to receive negative values points out significant regularityin situation when individual transport accessibility to the area is very high and public transport accessibility very low even its slight growth may not cause required changes if it is not accompanied by additional activities.3), public and private transport accessibility indicators for separate analyzed zones have been determined and using accepted model (4)volume of relative decreases in car share in trips to zones achievable as a result of implementation of set of mobility management instruments have been determined.Determined values of indicators and calculated volume of decreases for exemplary ten zones have been listed in the table 2. Those values are differential and visibly dependent on accepted values of accessibility indicators.Average value of relative decrease for all analyzed 80 transportation zones in Cracow was 14,95%, the minimum value -9,89%, the maximum value -19,86%.Data concerning indicated decreases has been used for testing scenarios related to potential changes in modal split achievable in dependence on percentage of employers implementing mobility management set of instruments (independently and in cooperation with transport managers and operators).5 scenarios have been assumed:  V20 -20% of employers located in the transportation zone implement instruments independently and in cooperation with transport managers and operators,  V40 -40% of employers located in the transportation zone implement instruments independently and in cooperation with transport managers and operators,  V60 -60% of employers located in the transportation zone implement instruments independently and in cooperation with transport managers and operators,  V80 -80% of employers located in the transportation zone implement instruments independently and in cooperation with transport managers and operators,  V100 -100% of employers located in the transportation zone implement instruments independently and in cooperation with transport managers and operators.
Results received for specific scenarios concerning volume of car share in trips to selected 10 zones are presented in the table 2. Also differences between volumes of shares indicated for base scenario V0 where non instruments are implemented and for considered scenarios V20-V100 (differences are expressed in percentage points) are presented in this table.It is noticeable that together with percentage of employers implementing instruments, effectiveness of measures undertaken in the area is growing.Bearing in mind assumed scenarios impact of sets has been also considered in the relation to the potential number of transportation zones where instruments would be implemented (assuming that instruments would be implemented firstly in zones of the highest number of trips related to work).Results of calculation concerning potential changes in car share in all internal trips in the morning peak hours in the relation Home-Work are presented in the table 3. Analyzing results listed in the table 3 it is noticed thatin the least favorable situation, if instruments are implemented in only 10 transportation zones by 20% employers (independently and in cooperation with transport managers and operators) car share in internal trips in the relation Home-Work in the morning peak hours could decrease from 48,9% to 48,7% (decrease in 0,2 percentage point).In the most favorable situation (80 transportation zones, 100% employers implementing instruments) car share could be decreased from 48,9% to 43,7% (5,2 percentage point).Thus even the smallest intervention with mobility management instruments in the areas absorbing large traffic flows related to work contributes with beneficial changes in modal split in the city scalein trips in the relation Home-Work in the morning peak hours.workplaces with high number of employees have been taken under consideration.Affiliation functions of input data and given output have been elaborated and final adoption of those functions has been enabled by results of sensitivity analysis not revealing significant differences in the case of modification of shape function.
Approximation of the surface received as a result of fuzzy inference has been conducted using formula of multiple linear regression which enabled adoption of model describing analyzed phenomenon.Interpretation of importance of accepted formula requires to take into account its contractual nature indicating expected decrease in care share in trips to work.Application of accepted model on the example of Cracow has confirmed the influence of sets of mobility management instruments on the changes in modal split in zones where they are implemented as well as in trips in the city.Results of the research prove that mobility management instruments have multidimensional effectiveness and contribute with improvement of accessibility of urban areas with public transport means and confirm legitimacy its application by public and private sector entities.Although construction of the model has been based on Cracow data, it is possible to apply it in conditions of different cities using suitable healing indicators, created by the authors but not described in the article due to its size.Next phase of the research on the effectiveness of mobility management instruments implemented in the areas absorbing large traffic flows related to work will be an attempt at verification of the created model.

Fig 4 .
Fig 4. Membership functions for terms describing linguistic variable "TI accessibility".Indicating membership functions for output data it is necessary to bear in mind restriction connected with the lack of detailed data about volume of decrease in share private car in trips to work in the area.Information about implementation of those type of initiatives may be found in the European sources (CiViTAS ARCHIMEDES; CiViTAS MODERN; INVOLVE; LEPT; Valiente, 2012).Although they refer to different aspects of implementation they do not include detailed data concerning achieved/expected decreases.Few examples found in available sources inform about results of implementation of the instruments and achieved relative decrease in car in trips on the level of 27% 2002) and 7% (OECD, 2014).Each example illustrates implementation of instruments which consequently has provided growth of public transport accessibility to the areas.Acceptation of the membership function just on the basis of those two examples has been not sufficient so that the results of 18 mobility plans for the European workplaces employing more than 1000 employees (number of travelers to work in the area comparable with number of employees in large workplaces) have been used as well.In the scope of those plans instruments for improvement of workplace accessibility by the means of public transport.For each of 20 examples for variable related to the relative decrease in car
have been determined, then using the Statgraphics program (StatPoint Inc.), attempt of approximation of the function which described this has been undertaken.After many attempts model of linear, multiple regression and formula describing relation between volume of expected decrease in car share in trips and current public transport accessibility indicator of the transportation zone (assuming that improvement of the indicator is a result of mobility management instruments) and current private transport accessibility indicator is: relative decrease in car share in work related trips to the transportation zone i, received as a result of the mobility management instruments implementation [%], i wd TZ -current public transport accessibility indicator for the transportation zone i [h -1 ], i wd TI -current private transport accessibility indicator for the transportation zone i [h -1 ].Evaluation of the quality of the model has been conducted on the level of significance 0,05.Quality of received results of approximation of resulting surface is described with parameters: R² = 93,13 [%], Rs²= 93,01 [%], SEE = 1,8 [%], MAE = 1,4 [%].It seems that taking under consideration the subject of analysis values of received parameters are the most sufficient.Scope of model application is limited to the values of defined indicators of accessibility to the transportation zones in Cracow.In the case of public transport accessibility indicator the scope of model application is between 0,5 and 3,7 [h -1 ], and for individual transport accessibility indicatorfrom 1,5 to 5,2 [h -1 ].

7.
Application of the model for evaluation of implemented sets of instruments impact in the selected areas in Cracow on changes in modal split 80 transportation zones in Cracow absorbing the biggest internal traffic flows related to work in the morning peak hours have been selected to apply created model for evaluation of instruments impact on changes in modal split.Selection of zones was based on the results of the Comprehensive Traffic Research 2013 (Konsorcjum Wykonawców, 2014).Using formulas (2) and (

Table 1 .
Percentiles and mean value for variable: relative decrease in car share in trips for 20 analyzed cases of mobility plans.standard deviation ), both for input and output data.

Table 2 .
Potential volume of car share in Home-Work trips (internal traffic) to the chosen 10 transportation zones, received as a result of the mobility management instruments implementation.

Table 3 .
Potential volume of car share in Home-Work trips in morning peak hour (internal traffic), received as a result of instruments implementation in chosen transportation zones in Cracow.