Application of Multi-Server Queuing Theory to Estimate Vehicle Travel Times at Freeway Electronic Toll-Collection Systems

고속도로 자동요금징수시스템의 차량 통행시간 산정을 위한 다중서비스 대기행렬이론 연구

  • 성현진 (서울시립대학교 교통공학과) ;
  • 최재성 (서울시립대학교 교통공학과) ;
  • 김상엽 (서울시립대학교 교통공학과)
  • Received : 2011.01.05
  • Accepted : 2011.03.25
  • Published : 2011.04.30


This paper presents the investigation results of a research on how engineers can analyze the economic effect of the ETCS(Electronic Toll Collection System) installed to minimize the vehicle delays on freeway tollgates during toll payments. This research considered this economic effect to occur in the form of vehicle passing time reductions at the ETCS, and the multi-service queuing theory was applied to estimate these values. This research found: 1) When vehicles approaching tollgates show Poisson distribution and the service time of the ETCS shows Exponential distribution, the multi-service queuing theory would be applicable for estimating vehicle passing times at toll-gates, 2) Despite the ETCS placement, exit sections of tollgates give a greater reduction of vehicle passing times than entering sections due to more delays at conventional toll payments, and 3)The ETCS would not guarantee vehicle passing time reductions all the time, because in such a case as many vehicles were queuing at the ETCS, the total delay level for a toll gate would increase greatly. In addition, in order to examine the accuracy of the estimated vehicle passing values, this research compared the values from the multi-service queuing theory with the observed values from a set of field survey values at freeway toll-gates, and found that the two values were in a good agreement with a very low error range of 1-3 seconds per vehicle. Based on this result, the multi-service queuing theory was recommended for practice.


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