Design of passengers’ circulation areas at the transfer station: An automated hybrid simulation-differential evolution framework

Abstract

The capacity design of passengers’ circulation areas at the transfer stations is a crucial issue from the designers’ point of view. An adequate design reflects the better performance while inadequacy leads to the congestion issues at the transfer stations. To overcome the shortcomings in the design guide (TCRP-165 Report) and existing exponential-based (M/G(n)/N/N) design model, this paper reports a novel Discrete-Event Simulation (DES) model based on the Phase-Type (PH)-distributed random variates for the circulation areas (passageways and stairways), integrated with the Differential Evolution (DE) optimization approach. This hybrid simulation-optimization model is an automated framework that simultaneously works to provide optimal widths of the passengers’ circulation areas, under a desirable Level-of-Service (LOS) and blocking probability criteria. The passengers’ arrival and service time pattern of the circulation areas in the DES model is described by the PH distribution, which accurately takes into account the variation of passengers’ arrival at different instants as well as randomness and state-dependent service time of the circulation areas. The comparison of proposed model with exponential-based (M/G(n)/N/N) model and TCRP-165 Report reveals that: (1) the optimal widths of circulation areas obtained by proposed model are greater than both M/G(n)/N/N and TCRP-100 Report; (2) the optimal width increases with the increase in squared coefficient of variation for all the passengers’ arrival rates, LOS and lengths of the circulation areas; (3) the optimal width values drop from LOS B towards D; (4) our proposed simulation-DE optimization outperforms the simulation-GA optimization approach in term of the speed of convergence. This novel hybrid simulation-DE optimization framework is an effective tool for the designers of transfer stations in decision making process and analyzing the complex facilities with ease.

Introduction

The transfer stations (also known as interchange stations) are the urban rail transit stations that are located at the intersection of two or more Lines (routes), often located at the Central Business Districts (CBD) or intensively developed part of the city. They allow passengers to transfer from one Line to another with minimum waiting, often without leaving the station or to pay an extra fare. The design of the transfer stations is a great challenge for the civil engineers as they are tightly constraint by existing buildings, highways and public utilities. The Transit Cooperative Research Program (TCRP) Report-165 [1] presents the analysis and design approach for the passengers’ circulation areas (including passageways and stairways) at the transfer stations. The passageways or concourses are the connection points between two or more Lines while stairways are the mean of vertical transportation in the transfer stations. Design factors that affect the performance of passengers’ circulation areas at the transfer stations include passengers’ walking speed, passengers’ density, and dimensional features (lengths and widths of the circulation area). Among aforementioned factors, width of the circulation areas is thought to be the most significant one [2], [3], [4]. According to TCRP-165 Report, the computation of passageways’ width is based on the desirable Level of Service (LOS). The LOS of circulation areas at the transfer station is an indicator of passengers’ level of comfort and freedom to maneuver without conflict. The TCRP-165 Report computes the width of the circulation areas by using the ratio of passenger’ arrival rate and service rate per unit width of the circulation areas under a desirable LOS. It shows that the TCRP-165 Report assumes the constant arrival flow of passengers and service rate of circulation area. If ‘D’ represent the deterministic arrival and service and ‘N’ is the capacity of a single circulation area, then TCRP-165 Report design approach is analogous to the D/D/N/N queuing model [2]. However in reality, the passengers’ flow as well as service rate in the interchange station is highly random.

Therefore, the width design approach of the TCRP-165 Report neglects several essential conditions such as: variation in the passengers’ arrival flow at different instants to the circulation areas. In reality, the passengers’ arrival flow to the circulation areas is not constant but random. The walking speed of passenger is assumed constant while in reality; the walking speed is the function of the number of passengers ‘n’ (state) present in the circulation areas. Practically, the passengers’ walking speed decreases with increase in the number of passengers and affects the passengers’ dwell time in the passageway. This phenomenon is known as state-dependent walking speed. The TCRP-165 Report ignores the blocking phenomenon that may occur when the number of passengers in the circulation areas equals to the capacity of the circulation areas.

As a result of these shortcomings, the circulation areas at transfer stations designed by the TCRP Report-165 approach are always blocked during peak and off-peak hours. The optimal design of circulation areas at the transfer station, taking into account all the practical conditions is therefore of an utmost importance. It is necessary to design the circulation areas at the transfer stations in accordance to the passengers’ arrival pattern to ensure that the capacity of circulation areas adequately matches the number of passengers. The proper design would lead to the efficient utilization of resources as well as avoid unnecessary delays.

Given the limitation TCRP Report-165, several researchers have tried to develop and improve the queuing model as well as simulation models for the analysis and design of both passengers and vehicular facilities. Researchers have employed queuing analytical modeling and simulation approach to carry out studies on: passengers’ facilities in the airport terminals [5], [6], [7], [8], [9], pedestrian flow in residential and commercial buildings [10], [11], [12], [13], for the performance evaluation and design of urban rail transit stations [14], [15], [16], [17], [18], [19], [20], [21], for the passengers’ flow at the BRT stations or bus terminals [22], [23], [24]. Similarly, some researchers focused on the vehicular traffic facilities on the highways [25], [26], [27].

Recent developments in computer technologies put the research applications of simulation- optimization approach in the field of applied sciences and engineering forward. The simulation-optimiation approach is a valuable tool in those conditions where the explicit mathematical formulae (analytical queuing models) are too complex to be solved [28], [29], [30]. For the simultaneous analysis and design of passengers and vehicular facilities, several researchers used simulation-optimization approach for the transportation facilities design [31], [32], [33], [34].

The major downside of several queuing and simulation models is fitting Poisson's and exponential distributions to the pedestrian and vehicular arrival flow and service processes, respectively, which is appropriate only when there is free flow of passengers in the facility. The exponential distribution has squared coefficient of variation $\left(c_{v,a}^2\right)$ equal to 1, which ignores randomness in the flow of passengers/pedestrian and vehicles, but in reality, uncertainty and fluctuations exist in the flow. The Poisson's and exponential distributions have been replaced by the Phase-Type (PH) distribution in various domains. It is more generalized distribution and can fit any positive random number with different values of$c_v^2$, while keeping the Markovian characteristics.

The $c_v^2$ of arrival interval is the randomness factor that depicts the real situation and takes into account the fluctuating demand in the: modeling of computer and communication systems [35], industrial and manufacturing [36] and passenger flow modeling at urban rail transit stations. [37]

In the domain of urban rail transit station design, the stochastic analytical models with the considerations to passengers’ fluctuation factors in the urban rail transit station were developed by Hu et al. [2]. The Phase-Type Distribution was introduced that described the randomness of passengers’ flow and service time of corridors and stairs at urban rail transit station. However, the drawback of this model is the complications associated with the closed form solution of explicit mathematical expressions. The computation of expressions for performance measures of a single corridor is based upon Quasi-Birth-Death (QBD) process [38] and Matrix Geometric Method (MGM), whose computational complexity depends upon the number of passengers available in the corridor facility. The computational complexity enhances as the number of passengers increases. Moreover, this analytical model does not take into account the passengers’ blocking when number of passengers exceed the capacity of the corridor.

To limit the scope of our study, here we only consider the flow of passengers in the circulation areas of the transfer stations. The flow of passengers in the circulation areas comprise a type of unique queuing system with diversified passengers’ arrival rate distributions, circulation areas varying service time distributions (passengers’ walking speed is the function of number of passengers ‘n’ present in it) and having limited capacity. Therefore, simultaneously taking the advantage of the queuing systems as well as eliminating the need to solve explicit mathematical expressions, the Discrete-Event Simulation (DES) of passenger’ circulation areas is developed. The circulation areas are first described as an open-finite capacity queuing network system and then translated into the DES models in the SimEvents^® software module. The DES model is taken as an efficient simulation approach with a wide range of applications. The DES model does not require the specific physical environment and entities, making it more efficient and easier to calibrate than the microscopic simulation models. Another advantage that makes the DES model superior than the microscopic simulation model is its convenient coupling with the optimization technique to develop a simulation-optimization framework. In this research, we integrate the Differential Evolution (DE) optimization technique [39] with DES model to develop an automated hybrid simulation-optimization approach for the optimal width design of passengers’ circulation area at the transfer stations. This proposed model offsets the limitations of TCRP-165 Report and depicts the passengers flow more accurately due to the introduction of PH distribution. The parallel implementation of the DES model based on the PH-distributed random variates and DE optimization is an automated framework that provides optimal widths under a desirable LOS. The framework of the proposed model is illustrated in Fig. 1.

The rest of the paper is organized as follows. In Section 2 the list of symbols is presented. Then, the details of hybrid Simulation-DE optimization for the optimal width design are discussed in Section 3. The computational experiments under different design parameters are conducted in Section 4. Finally, the conclusions are drawn from the research findings and reported in Section 5.