Arabian Journal for Science and Engineering

, Volume 43, Issue 10, pp 5499–5516 | Cite as

Optimal Configuration of the Metro Rail Transit Station Service Facilities by Integrated Simulation-Optimization Method Using Passengers’ Flow Fluctuation

  • Afaq Khattak
  • Jiang Yangsheng
  • Malik Muneeb Abid
Research Article - Civil Engineering


This paper proposes an integrated discrete-event simulation (DES) using phase-type (PH) distribution and optimization method for the performance assessment, as well as optimal configuration of metro rail transit (MRT) station service facilities. The MRT facilities (including ticket facilities and elevator) are represented as a queuing network system with the passengers’ arrival flow and the service time based on the PH distribution, which considers the flow and service time fluctuation. The necessary performance measures include facility utilization, mean number of passengers and waiting time of passengers in the facilities are obtained by PH-based DES model of service facilities. The model is then coupled with a genetic algorithm that works simultaneously to give the optimal configuration of service facilities. The results of PH-based DES model are first verified by existing PH-based analytical models and then compared with other existing exponential-based and deterministic-based queuing models. The results reveal that increase in squared coefficient of variation of arrival interval causes an increase in the performance measure values and high number of ticket facilities compared to existing models. The existing models therefore underestimate the results. The squared coefficient of variation is an important parameter and cannot be ignored in analysis and design of service facilities. This research provides a more realistic and novel PH-based DES, as well as PH-based simulation-optimization method that will assist the planners and designers of MRT stations to make intelligent decisions regarding analysis and design.


Metro rail transit Discrete-event simulation Phase-type distribution Simulation-optimization Ticket facilities Elevator facility 

List of symbols


Number of facility

\(\lambda _{a,i} \)

Passengers’ arrival rate to the ith facility


Passengers’ arrival interval

\(\varepsilon \)

Peak-hour factor

\(c_{a,i}^2 \)

Squared coefficient of variation of arrival interval of the ith facility

\(\mu _{s,i} \)

Mean service rate of the ith facility

\(c_{s,i}^2 \)

Squared coefficient of variation of service time of the ith facility


Number of servers in each facility


Peak-hour volume (ped/h)


Ground floor

− 1F

Lower ground floor

\(\alpha \)

Sub-stochastic vector for the passengers’ arrival process


Sub-generator matrix for the passengers’ arrival process

\(\beta \)

Sub-stochastic vector for service process of the service facility


Sub-generator matrix for service process of the service facility

\(\rho \)

Utilization of the facility


Mean number of passengers in the queue of the facility


Mean waiting time of passengers in the queue of the facility


Number of passengers in the facility


Degree of Erlang Distribution


Uniformly distributed random number


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We would like to express our sincere acknowledgement to National Natural Science Foundation of China (Serial Nos. 51578465 and 71402149), Basic Research Project of Sichuan Province, the Chinese government for the funding of doctoral program at Southwest Jiaotong University and the colleagues of National United Engineering Laboratory of Integrated and Intelligent Transportation at Southwest Jiaotong University, Chengdu for their support and valuable advices.


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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  • Afaq Khattak
    • 1
    • 2
  • Jiang Yangsheng
    • 1
  • Malik Muneeb Abid
    • 2
  1. 1.School of Transportation and LogisticsSouthwest Jiaotong UniversityChengduChina
  2. 2.Department of Civil EngineeringInternational Islamic UniversityIslamabadPakistan

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