Waiting times at periodically switched one-way traffic lanes - A periodic, two-queue polling system with random setup times

Matthijs C. van der Heijden, Aart van Harten, Mark Ebben

Research output: Working paperProfessional

6 Citations (Scopus)
21 Downloads (Pure)

Abstract

We study vehicle waiting times at a traffic lane that is shared by traffic from two directions. In contrast to crossovers, we focus on instances where the vehicle passing time of the shared infrastructure can be large. The motivation for this model arises from our research on underground transportation systems. We examine vehicle waiting times under periodic control rules, i.e. the driving direction on the infrastructure is switched between two directions according to a fixed time schedule. We analyse both symmetric and asymmetric systems (I.e., vehicle arrival rates as well as effective green and red periods may be different for both directions). In fact, we are dealing with a single server, two-queue polling system with random set-up times and periodic (non-exhaustive) service discipline. We develop approximations for the mean waiting time and we show by comparison to simulation results that the accuracy is usually in the range of 1-2% for Poisson arrivals. Also, we indicate how our approximations can be generalised to compound Poisson arrivals.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Research School for Operations Management and Logistics (BETA)
Number of pages31
Publication statusPublished - 2001

Publication series

NameBETA Working Paper
PublisherUniversity of Enschede, BETA
No.WP-56

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Keywords

  • METIS-310350
  • IR-95696

Cite this

van der Heijden, M. C., van Harten, A., & Ebben, M. (2001). Waiting times at periodically switched one-way traffic lanes - A periodic, two-queue polling system with random setup times. (BETA Working Paper; No. WP-56). Enschede: University of Twente, Research School for Operations Management and Logistics (BETA).
van der Heijden, Matthijs C. ; van Harten, Aart ; Ebben, Mark. / Waiting times at periodically switched one-way traffic lanes - A periodic, two-queue polling system with random setup times. Enschede : University of Twente, Research School for Operations Management and Logistics (BETA), 2001. (BETA Working Paper; WP-56).
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abstract = "We study vehicle waiting times at a traffic lane that is shared by traffic from two directions. In contrast to crossovers, we focus on instances where the vehicle passing time of the shared infrastructure can be large. The motivation for this model arises from our research on underground transportation systems. We examine vehicle waiting times under periodic control rules, i.e. the driving direction on the infrastructure is switched between two directions according to a fixed time schedule. We analyse both symmetric and asymmetric systems (I.e., vehicle arrival rates as well as effective green and red periods may be different for both directions). In fact, we are dealing with a single server, two-queue polling system with random set-up times and periodic (non-exhaustive) service discipline. We develop approximations for the mean waiting time and we show by comparison to simulation results that the accuracy is usually in the range of 1-2{\%} for Poisson arrivals. Also, we indicate how our approximations can be generalised to compound Poisson arrivals.",
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van der Heijden, MC, van Harten, A & Ebben, M 2001 'Waiting times at periodically switched one-way traffic lanes - A periodic, two-queue polling system with random setup times' BETA Working Paper, no. WP-56, University of Twente, Research School for Operations Management and Logistics (BETA), Enschede.

Waiting times at periodically switched one-way traffic lanes - A periodic, two-queue polling system with random setup times. / van der Heijden, Matthijs C.; van Harten, Aart; Ebben, Mark.

Enschede : University of Twente, Research School for Operations Management and Logistics (BETA), 2001. (BETA Working Paper; No. WP-56).

Research output: Working paperProfessional

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AB - We study vehicle waiting times at a traffic lane that is shared by traffic from two directions. In contrast to crossovers, we focus on instances where the vehicle passing time of the shared infrastructure can be large. The motivation for this model arises from our research on underground transportation systems. We examine vehicle waiting times under periodic control rules, i.e. the driving direction on the infrastructure is switched between two directions according to a fixed time schedule. We analyse both symmetric and asymmetric systems (I.e., vehicle arrival rates as well as effective green and red periods may be different for both directions). In fact, we are dealing with a single server, two-queue polling system with random set-up times and periodic (non-exhaustive) service discipline. We develop approximations for the mean waiting time and we show by comparison to simulation results that the accuracy is usually in the range of 1-2% for Poisson arrivals. Also, we indicate how our approximations can be generalised to compound Poisson arrivals.

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van der Heijden MC, van Harten A, Ebben M. Waiting times at periodically switched one-way traffic lanes - A periodic, two-queue polling system with random setup times. Enschede: University of Twente, Research School for Operations Management and Logistics (BETA). 2001. (BETA Working Paper; WP-56).