A M/Dx/1 vacation queue model for a signalized intersection

Hu, Xinping; Tang, Loon Ching; Ong, H. L.

doi:10.1016/s0360-8352(97)00240-4

Cited by 24 publications

(13 citation statements)

References 4 publications

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“…While a larger value (upto S max = 60 secs) could have been chosen for this scheduling period (green time) for better "efficiency"' (i.e., less loss of scheduling time due to lag effects), we observe that a larger scheduling time worsens the performance substantially at low traffic load. Furthermore, a larger scheduling period also increases the scheduling average latency defined in (3). Note that even though the scheduling period is set to 15 secs, the actual green time for which a chosen collision-free set Γ k is served can be more, if that set is chosen in consecutive scheduling period by MWS.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…In this signaling scheme a specific amount of time is specified for each traffic lane to allow the vehicles pass through the intersection successively with the aim of collision prevention. Intersection traffic control based on information on different types of statistics (available or estimated) on vehicular traffic has been studied for a long period of time [1], [2], [3], [4], [5]. In 1958, Webster gave equations A. Ghavami and K. Kar for the optimal cycle length and the green phase time assignment, which are the basis of fixed-time control which has been widely used [2].…”

Section: Introductionmentioning

confidence: 99%

“…Alpha and Neuts suggest that discrete time Markovian arrival process (MAP) captures the platoon nature of the traffic stream process [12]. The queuing model proposed in [3] models the fixed time traffic control with fixed number of green and red periods for each traffic phase based on an M/G/1 queuing model. Mirchandani and Zou develop a stochastic queuing model for a two-phase simplified adaptive control strategy [13].…”

Section: Introductionmentioning

confidence: 99%

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Delay analysis of signal control policies for an isolated intersection

Ghavami

Kar

Ukkusuri

2012

2012 15th International IEEE Conference on Intelligent Transportation Systems

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In this paper, we analyze the delay performance of three traffic signal control algorithms that can attain maximum system throughput, for a single four-way intersection. The first is a static (state-independent) fixed-time scheduling (FTS) policy which is followed in current practice. The second is a dynamic maximum weight (backlog) scheduling (MWS) policy that determines the traffic signal phase (the set of collision-free lanes chosen to be scheduled) based on the backlogs (number of queued vehicles) in the different lanes of the intersection, but the schedule length (green time) is kept fixed. The third is adaptive length MWS (aMWS), a variant of MWS in which the schedule length (green time of the phase) is also adjusted based on the backlogs, in addition to the phases. We show that while the dynamic signal control policies (MWS and aMWS) outperform the static (FTS) policy in general, the performance of a fixedlength schedule like MWS can be seriously affected when loss of scheduling time due to "lag effects" is considered. However, with adaptive adjustment of the schedule lengths (green times), a dynamic signal control policy (like aMWS) can outperform the FTS policy at all traffic loads.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Delay analysis of signal control policies for an isolated intersection

Ghavami

Kar

Ukkusuri

2012

2012 15th International IEEE Conference on Intelligent Transportation Systems

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“…[9]. Apart from Markovian queuing systems non-Markovian queuing systems can be found on signalized intersections [10]. Key spot in these solutions is presented in the form of shared-short Lanes for the left turn [11,12].…”

Section: Introductionmentioning

confidence: 99%

“…The exception is state X 0,0 whose intensities are expressed as the product of the probabilities of each state in a geometric series (10).…”

mentioning

confidence: 99%

New Analytic Solutions of Queueing System for Shared–Short Lanes at Unsignalized Intersections

et al. 2019

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Designing the crossroads capacity is a prerequisite for achieving a high level of service with the same sustainability in stochastic traffic flow. Also, modeling of crossroad capacity can influence on balancing (symmetry) of traffic flow. Loss of priority in a left turn and optimal dimensioning of shared-short line is one of the permanent problems at intersections. A shared–short lane for taking a left turn from a priority direction at unsignalized intersections with a homogenous traffic flow and heterogeneous demands is a two-phase queueing system requiring a first in–first out (FIFO) service discipline and single-server service facility. The first phase (short lane) of the system is the queueing system M(pλ)/M(μ)/1/∞, whereas the second phase (shared lane) is a system with a binomial distribution service. In this research, we explicitly derive the probability of the state of a queueing system with a short lane of a finite capacity for taking a left turn and shared lane of infinite capacity. The presented formulas are under the presumption that the system is Markovian, i.e., the vehicle arrivals in both the minor and major streams are distributed according to the Poisson law, and that the service of the vehicles is exponentially distributed. Complex recursive operations in the two-phase queueing system are explained and solved in manuscript.

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Application of a Particular Class of Markov Chains in the Assessment of Semi-actuated Signalized Intersections

Macedo

Milheiro–Oliveira²,

Pacheco

et al. 2017

Analytical and Stochastic Modelling Techniques and Applications

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We investigate a queuing model for a signalized intersection regulated by semi-actuated control in a urban traffic network. Modelling the queue length and the delay of vehicles for this type of traffic, characterized by variable durations of the green signal, is crucial to evaluate the performance of traffic intersections. Additionally, determining the size of the extensions of the green signal is also relevant. The traffic systems addressed in the paper have the particularity that the server remains active (green signal) for a period of time that depends on the number of vehicles waiting at the intersection. This gives rise to an M/D/1 queuing system with a server that occasionally takes vacations (red signal), for which we compute the long-run mean delay of vehicles, mean queue length and mean duration of the green signal. We consider a case study and compare the results obtained from the proposed queueing model with those obtained by using a microsimulation model. The formulas derived for the performance measures are of interest for traffic engineers, since the existing alternative formulas are subject to strong criticism.

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A M/Dx/1 vacation queue model for a signalized intersection

Cited by 24 publications

References 4 publications

Delay analysis of signal control policies for an isolated intersection

Delay analysis of signal control policies for an isolated intersection

New Analytic Solutions of Queueing System for Shared–Short Lanes at Unsignalized Intersections

Application of a Particular Class of Markov Chains in the Assessment of Semi-actuated Signalized Intersections

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