Methodology for calculation of minimum transfer time in the transport hub

. The most important element in railway passenger transport is a customer – traveller, who requires the transport from one place to another. A basic precondition for accomplishing the main requirement – transport, is making the complete offer which provides not only transport, but also other associated services. Practically, there are many associated criteria of transport, for example safety, duration, price, reliability, comfort and complementary services. Passenger transport is generally considered as an activity, which arises as the consequence of spatial division of places, where people are in exact time and their need to move. Motivators for moving could be commuting – job or education, dealing with personal or working matters, travelling for vacation – hiking, sport, health, cultural and social facilities, visiting relatives and friends. Requirements for transport of passengers originate in the need to move, while the passenger transport is dependent on the willingness of travelling. In passenger transport, there are mostly individual passengers, so it is difficult to determine all transport requirements. The paper is focused on one of the key factors of passenger transportation - connectivity of trains. Connectivity of passenger trains and other means of transport can be distinguished also from temporal and spatial point of view. Temporal connectivity is such sequence of arrivals and departures of different passenger trains and other means of transport, which allows changing the different passenger vehicles easily in regard to necessary time. Spatial connectivity means the distance between two passenger vehicles, among which the passenger is moving. In the paper, there is described the general methodology for calculation of minimum transfer time in the railway station. Railway passenger station is some kind of transport hub – a starting and finishing point for flows of passengers. Passengers have the opportunity to change the train type from long-haul train to regional train or contrariwise or simply enter or leave the system of railway transport. In the methodology, all necessary aspects are taken into account.


Introduction
Transport network consists of transport routes and transport hubs [1,2]. The transport hub is important part of passenger transport process. In the transport hub, a vehicle could be changed in the same or different type of transport [3]. It is necessary to ensure suitable constructional layout, which would provide safe, fast and comfortable transfer of passengers among vehicles of the same or different type of transport [4,5]. Additional services for passengers are also one of the significant factors [6,7] because passengers could use them while they are waiting. In the transport process, it is very important to minimize waiting time from temporal point of view, but all conditions for safe transfer and sufficient time for it must be kept [8,9]. The paper is focused on a methodology, which can exactly stipulate the minimum transfer time in the transport hub among various vehicles and types of passenger transport. Currently, transfer times are set empirically or by estimation. When some lack is identified, transfer times are operationally adapted to passengers' requirements [10]. General methodology for solving transfer problems in transport hubs is described in the paper.

Characteristics of passenger transport chain
In the passenger transport system, the element is an object, which cannot be divided into smaller parts during transport process. Transport requirements represent the relocation of passengers therefore the object of transport is the passenger. All passenger transport systems could be characterized by [11]: • Places of getting on, getting off and getting among vehicles, • Transport hubs, • Sections between pairs of transport hubs, which are performed always with one vehicle, • Mutual aim of fast, safe, comfortable and reliable transportation. Appropriate methodology of temporal elements quantification could detect some bottle necks of transportation process, which must be subsequently modified for purpose of improving quality and efficiency of public passenger transport.  15 15 Analysis of constructional layout in the transport hub Creation of transport hub network graph

Calculation of elements modules
Setting the minimum transfer time

The methodology for setting the minimum transfer time in transport hub
The proposed methodology is based on exactly established approaches, which must be abided for reaching the aim -determination of necessary minimum transfer time in transport hub for various groups of passengers.

Analysis of constructional layout in the transport hub
Constructional layout in the transport hub significantly influences the minimum transfer time, which are necessary for passengers in case of changing the vehicle or mode of transport in the transport hub [12].

Fig. 2. Constructional layout parts which influence the transfer time
Access paths should connect all public spaces in the transport hub with way, which must be as short as possible. They should be signed by visual tools for better orientation and their surface should be anti-skid. In the analysis, it is necessary to identify all access paths, which could be used by passengers. Also it is necessary to identify access paths for PRM passengers. Identification of access paths length is necessary for calculation of elements (modules) in the transport hub. Another part, what impacts the transfer time, is a staircase. [13,14] In the analysis, it is important to determine their location in the transport hub (different passenger frequency) and number of stairs. The elevator is a transport device for vertical transport of passengers. In the analysis, it is necessary to determine the location of elevators in the transport hub, because the frequency of passengers could be different. Then, it is important to determine the time of opening doors, transport velocity of elevator and floor size, because these indicators directly influence the transport capacity of passengers. Escalators and walkways are devices for horizontal and vertical transport of passengers in the building. Their advantage is higher transport capacity than elevators. It is necessary to analyse their location in the transport hub, transport velocity and constructional length. Ticket offices and machines situated in the transport hub ensure travel tickets selling for passengers. In the analysis, it is important to determine the number of them (number of desks, machines etc.) and their opening hours.

Creation of transport hub network graph
The network graph presents a unique way of mathematical expression for temporal or technological sequence of partial operations. In the proposed methodology, the network graph of transport hub is evaluated by vertices and edges. Edges of network graph represent oriented lines between vertices. Edges in the graph show access paths in the transport hub. The evaluation of edges is time t which is necessary for getting across the access paths by passengers. Vertices of network graph represent activities, which must be accomplished by passenger during transfer in the transport hub. [15] For instance: getting off the vehicle, buying travel tickets, etc. Vertices in the graph are carriers of information called modules.

Calculation of elements (modules)evaluation of vertices in the network graph
Vertices in the network graph are carriers of information about duration of each activity while transferring in the transport hub -modules. Partial indicators are: • Buying travel ticket time.

Getting off the vehicle time
Getting where:

Going on stairs time
It is necessary to divide going on stairs time into: -Going upstairs, -Going downstairs. The reason of passengers' going on stairs time division into going upstairs and going downstairs is that velocity of going upstairs is lower than velocity of going downstairs. For verification of this hypothesis, the measurement in the transport hub Zilina was done. Passengers were divided into three groups: • Group 1 -students, • Group 2 -productive ages, • Group 3 -pensioners.
The reason of this division is that passengers in each group are going very similar time. Entire number of measurements, which were done in each group, is 100 measurements. Number of stairs was set to 23 stairs.
The formula for calculation of going on stairs time is: where:

Transport on escalators time
Entire transport time depends on individual constructional layout of the escalator in the transport hub. It means that there are these dependent parameters: transport velocity and constructional length of the escalator. For calculation of entire transport on escalators time is necessary to count all passengers, who are going on the escalator in the same time.
The calculation of transport on escalators time should be: 1. passenger: t1 2. passenger: t 1 + t i 3. passenger: t 1 + 2 * t i n. passenger: t 1 + (n-1) * t i Transport on escalators time of the first passenger is set by formula: where: If there is possible to stand of more passengers next to each other on the escalator, order of the passengers (1. passenger, 2. passender, 3. passenger,..., n. passenger) means order of the m-tuble of the passengers on the escalator, where m is number of passengers who can stay next to each other on the escalator.

Transport in elevators time
The entire transport in elevators time depends on individual constructional layout of the transport hub. Getting off the elevator time starts after the elevator stops on the floor. It is set by formula: Getting on the elevator time starts after all getting off the elevator passengers are out of the elevator. It is set by formula: Entire transport in elevator time is set by formula: where: T e entire transport in elevator time [s], T e in transport in elevator time [s].

Walkways module
Walkways are suitable for mass transport of people in shopping centres and transport hubs. In general, transport on walkways time is set by the same formula as for transport on escalator.

Buying travel ticket time
A place, where passengers can buy ticket is a typical example of Queueing theory systems. Basic model is system M/M/n/∞ with n possibilities for buying the travel ticket. Arrivals of passengers are described with Poisson's distribution with λ frequency and duration of service has got exponential distribution with average duration 1/μ. All buying possibilities are equally productive. Passengers are served in the same order as they came to the system. The entire time in the system -average duration in the system is a sum of average time of waiting in the queue and time of buying the travel ticket. It is set by formula:

Calculation of elements (modules)valuation of edges in the network graph
Edges in the network graph represent oriented lines between vertices (passengers' activities in transport hub during the transfer). Vertices are access paths in the transport hub.

Walking on access paths time
Access paths would connect all public spaces in the transport hub by way which is as short as possible.
Another module for valuation of transport connectivity in public transport system is setting necessary time for reach these distances. In this measurement, passengers were divided into three groups again, similarly as it was in the measurement of going on stairs time. Entire number of measurements was 100 and the distance was 45,5 meters. According results of these measurements, average time and velocity of walking was set for each group of passengers. The formula for calculation of walking on access paths:

Setting the minimum transfer time
The result of the network graph application in the transport hub and by counting the modules is setting the minimum transfer time in all combinations of edges and vertices, which could be possible while passengers are transferring in the transport hub.

Conclusions
1. Proposal of the network graph in the transport hub with valuation of edges and vertices 2. Calculation of transferring passenger partial activities 3. Possibility of constructional layout integration in the transport hub 4. Possibility of constructional layout integration in vehicles 5. Simplification of timetables in integrated transport systems 6. Optimization of transfer times according to passengers' needs