Journal articles: 'Length of queue'

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Raj Jhunjhunwala, Prakirt, and Siva Theja Maguluri. "Heavy Traffic Joint Queue Length Distribution withoutResource Pooling." ACM SIGMETRICS Performance Evaluation Review 51, no. 4 (2024): 16–17. http://dx.doi.org/10.1145/3649477.3649487.

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This paper studies the Heavy Traffic (HT) joint distribution of queue lengths in an Input-queued switch (IQ switch) operating under the MaxWeight scheduling policy. IQ switchserve as representative of SPNs that do not satisfy the socalled Complete Resource Pooling (CRP) condition, and consequently exhibit a multidimensional State Space Collapse (SSC). Except in special cases, only mean queue lengths of such non-CRP systems is known in the literature. In this paper, we develop the Transform method to study the joint distribution of queue lengths in non-CRP systems. The key challenge is in solving an implicit functional equation involving the Laplace transform of the HT limiting distribution. For the general n x n IQ switch that has n2 queues, under a conjecture on uniqueness of the solution of the functional equation, we obtain an exact joint distribution of the HT limiting queue-lengths in terms of a non-linear combination of 2n iid exponentials.

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Jhunjhunwala, Prakirt Raj, and Siva Theja Maguluri. "Heavy Traffic Queue Length Distribution without Resource Pooling in an Input-Queued Switch." ACM SIGMETRICS Performance Evaluation Review 50, no. 4 (2023): 26–28. http://dx.doi.org/10.1145/3595244.3595254.

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This paper studies the heavy-traffic joint distribution of queue lengths of an input-queued switch operating under the MaxWeight scheduling policy. Input-queued switch acts as a representative of SPNs that do not satisfy the so-called complete resource pooling (CRP) condition, and consequently exhibit a multidimensional state space collapse. Except in special cases, only mean queue lengths of such non-CRP systems have been obtained in the literature. In this paper, we develop the transform method to study the steady state distribution of non-CRP systems. The key challenge is in solving an implicit functional equation involving the Laplace transform of the heavy-traffic limiting distribution. We then consider the general n - n input-queued switch that has n2 queues. Under a conjecture on uniqueness of the solution of the functional equation, we obtain an exact joint distribution of the heavy-traffic limiting queue-lengths in terms of a nonlinear transformation of 2n iid exponentials.

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Long, Gary. "Start-Up Delays of Queued Vehicles." Transportation Research Record: Journal of the Transportation Research Board 1934, no. 1 (2005): 125–31. http://dx.doi.org/10.1177/0361198105193400113.

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Start-up delays of queued vehicles have been studied in past research for evaluation of their impacts on saturation flow rates at downstream traffic signals. A more crucial issue, however, can be the effect of start-up delays of queued vehicles at upstream locations where queued vehicles back up from a traffic signal across a railroad crossing. The relationship between queue start-up delays and track clearance times is important in establishing traffic signal preemption settings. This paper presents models that are developed for prediction of the expected maximum time required to mobilize a queue of any length. The models consider not only the average delay times but also the limiting delay times that are expected to accommodate high proportions of queues. For design convenience, queue lengths are converted into distance from the leading edge of a queue rather than being described only by the number of vehicles in a queue. Because the variations in start-up times, in addition to the average times reported in the literature, are needed, two sets of field studies were used to obtain data for model calibration and to investigate various traffic operation effects. Other factors that might be expected to influence queue start-up times are also analyzed.

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Prahara, Eduardi, and Rio Dandy Arsyad. "Lane Reduction and Queue Length Relationship on Arterial and Collector Roads." IOP Conference Series: Earth and Environmental Science 1324, no. 1 (2024): 012008. http://dx.doi.org/10.1088/1755-1315/1324/1/012008.

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Abstract Geometric diversity of roads for an example is the narrowing of road segments. The purpose of this research is to determine whether lane reduction leads to significant queue lengths, observe the behaviour of drivers on those road segments, and compare the actual queue length to the queue length generated by PTV Vissim. The data used in this study consists of direct observations during peak hours in the morning, afternoon, and evening, along with simulations using PTV Vissim. The queue results obtained from PTV Vissim were validated using two types of tests. The research findings indicate a significant relationship between queue length and lane reduction during peak hours on workdays. However, during the evening peak hours on weekends, the queue length is not significantly affected by lane reduction. As a potential solution, widening each road segment in PTV Vissim was tested, which increased road capacity and slightly reduced the queues that occurred.

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Deng, Yonglu, and Jiqing Tan. "Priority queueing model with changeover times and switching threshold." Journal of Applied Probability 38, A (2001): 263–73. http://dx.doi.org/10.1239/jap/1085496608.

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The paper studies a single-server two-queue priority system with changeover times and switching threshold. The server serves queue 1 exhaustively and does not remain at an empty queue if the other one is non-empty. It immediately switches from queue 2 to queue 1 when the length of the latter reaches some level M. Whenever service is changed from one queue to the other a changeover time is required. Arrivals are Poisson, service times and changeover times are independent and exponentially distributed. Using an analytic method we obtain the steady-state joint probability generating function of the lengths of the two queues. By means of this probability generating function some performance measures of the system such as mean length of queue and mean delay can be calculated.

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Deng, Yonglu, and Jiqing Tan. "Priority queueing model with changeover times and switching threshold." Journal of Applied Probability 38, A (2001): 263–73. http://dx.doi.org/10.1017/s0021900200112847.

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The paper studies a single-server two-queue priority system with changeover times and switching threshold. The server serves queue 1 exhaustively and does not remain at an empty queue if the other one is non-empty. It immediately switches from queue 2 to queue 1 when the length of the latter reaches some level M. Whenever service is changed from one queue to the other a changeover time is required. Arrivals are Poisson, service times and changeover times are independent and exponentially distributed. Using an analytic method we obtain the steady-state joint probability generating function of the lengths of the two queues. By means of this probability generating function some performance measures of the system such as mean length of queue and mean delay can be calculated.

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Boon, M. A. A., and E. M. M. Winands. "HEAVY-TRAFFIC ANALYSIS OF K-LIMITED POLLING SYSTEMS." Probability in the Engineering and Informational Sciences 28, no. 4 (2014): 451–71. http://dx.doi.org/10.1017/s0269964814000096.

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In this paper, we study a two-queue polling model with zero switchover times and k-limited service (serve at most ki customers during one visit period to queue i, i=1, 2) in each queue. The arrival processes at the two queues are Poisson, and the service times are exponentially distributed. By increasing the arrival intensities until one of the queues becomes critically loaded, we derive exact heavy-traffic limits for the joint queue-length distribution using a singular-perturbation technique. It turns out that the number of customers in the stable queue has the same distribution as the number of customers in a vacation system with Erlang-k2 distributed vacations. The queue-length distribution of the critically loaded queue, after applying an appropriate scaling, is exponentially distributed. Finally, we show that the two queue-length processes are independent in heavy traffic.

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Daines, Tanner J., Grant G. Schultz, and Gregory S. Macfarlane. "Evaluating Real Time Ramp Meter Queue Length and Wait Time Estimation." Future Transportation 2, no. 4 (2022): 807–27. http://dx.doi.org/10.3390/futuretransp2040045.

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Models to predict ramp meter queue length from traffic detector data are potentially useful tools in improving traffic operations and safety. Existing research, however, has been based on microscopic simulation or relied on extensive calibration of Kalman filter and related models to produce reliable queue length estimates. This research seeks to develop methodologies for improving and simplifying the calibration process of existing queue length models by applying loop detector data including volume, occupancy, and the metering rate data for ramp meters along I-15 in Utah. A conservation model and several variations of a Kalman filter model generated estimated queues that were compared to observed queue lengths in 60 s bins. A modified Kalman filter model and a new heuristic model derived from cluster analysis—the models that yielded the best results—provided queue length estimates that were generally within approximately eight vehicles of the observed queue length. Using the ramp metering rate, the queue length estimates were converted into wait times that were generally within approximately 30 s of the actual wait time, producing a viable method to predict wait time from up-to-the-minute traffic detection information with relatively little required calibration. The implementation of the ramp meter queue length and wait time estimation algorithms presented in this research will allow departments of transportation to better assess freeway and ramp conditions, which can then aid in reducing congestion throughout the freeway network.

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Flatto, Leopold. "The Longer Queue Model." Probability in the Engineering and Informational Sciences 3, no. 4 (1989): 537–59. http://dx.doi.org/10.1017/s0269964800001376.

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Two queues forming two independent Poisson processes are served by one server with exponential service time. The server always works on the longer queue and, in case that they are of equal length, chooses either one with probability ½. Let πij be the probability that the two queue lengths equal i andj at equilibrium and π(z, w) = ∑πi j Ziwj. We determine π(z, w) and derive from this asymptotic formulas forπij as i, j → ∞. These asymptotic formulas are used to study the interdependence of the queue lengths. In particular, we obtain limit laws for the queue lengths conditioned on each other.

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Qu, Wenrui, Tao Tao, Bo Xie, and Yi Qi. "A State-Dependent Approximation Method for Estimating Truck Queue Length at Marine Terminals." Sustainability 13, no. 5 (2021): 2917. http://dx.doi.org/10.3390/su13052917.

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As international trade and freight volumes increase, there is a growing port congestion problem, leading to the long truck queues at US marine terminal gates. To address this problem, some countermeasures have been proposed and implemented for reducing truck queue length at marine terminals. To assess the effectiveness of these countermeasures, a method for accurately estimating terminal gate truck queue length is needed. This study developed a new method, named the state-dependent approximation method, for estimating the truck queue length at marine terminals. Based on the simulation of the truck queuing system, it was found that it takes several hours for the truck queue length to reach its steady state, and neglecting the queue formation (queue dispersion) processes will cause overestimation (underestimation) of truck queue length. The developed model can take into account the queue formation and dispersion processes, and it can be used to estimate the truck queue length caused by short-term oversaturation at marine terminals. For model evaluation, a simulation-based case study was conducted to evaluate the prediction accuracy of the developed model by comparing its results with the simulated queue lengths and the results of other four existing methods, including the fluid flow model, the M/M/S queuing model, and a simulation-based regression model developed a previous study. The evaluation results indicate that the developed model outperformed the other four modeling methods for different states of queue formation and dispersion processes. In addition, this new method can accurately estimate the truck queue length caused by the short-term system oversaturation during peak hours. Therefore, it will be useful for assessing the effectiveness of the countermeasures that are targeted at reducing the peak-hour congestion at marine terminals.

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11

Le Gall, Pierre. "The queue-length in GI/G/s queues." Mathematical Problems in Engineering 6, no. 1 (2000): 1–11. http://dx.doi.org/10.1155/s1024123x00001228.

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The distribution of the queue-length in the stationary symmetrical GI/G/s queue is given with an application to the M/G/s queue, particularly in the case of the combination of several packet traffics, with various constant service times, to dimension the buffer capacity.

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Ross, J. V., T. Taimre, and P. K. Pollett. "Estimation for queues from queue length data." Queueing Systems 55, no. 2 (2007): 131–38. http://dx.doi.org/10.1007/s11134-006-9009-2.

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Ratrout, Nedal T., and Maen Abdullatif Abu Olba. "Adequacy of TRANSYT-7F and Synchro models along a major arterial in Saudi Arabia." Canadian Journal of Civil Engineering 36, no. 1 (2009): 95–102. http://dx.doi.org/10.1139/l08-120.

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The TRANSYT-7F and Synchro models are used in developing optimal timing plans in the city of Al-Khobar, Saudi Arabia. This paper evaluates the adequacy of both TRANSYT-7F and Synchro under local traffic conditions by comparing queue lengths observed along a major arterial in the study area with simulated queues. The models were then calibrated to produce simulated queue lengths which are as close as possible to the observed ones. A clear difference was found between queue lengths estimated by Synchro and TRANSYT-7F. A queue length calibration process was accomplished for TRANSYT-7F by using platoon dispersion factor values of 20 and 35 for through and left-turning traffic, respectively. Synchro calibration was unsatisfactory. The simulated queue lengths could not be calibrated in a meaningful way to resemble the observed queue lengths. Regardless of this, both models produced comparable optimal signal timing plans.

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Al Hanbali, Ahmad, Roland de Haan, Richard J. Boucherie, and Jan-Kees van Ommeren. "DELAY IN A TANDEM QUEUEING MODEL WITH MOBILE QUEUES: AN ANALYTICAL APPROXIMATION." Probability in the Engineering and Informational Sciences 28, no. 3 (2014): 363–87. http://dx.doi.org/10.1017/s0269964814000059.

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In this paper, we analyze the end-to-end delay performance of a tandem queueing system with mobile queues. Due to state-space explosion, there is no hope for a numerical exact analysis for the joint-queue-length distribution. For this reason, we present an analytical approximation that is based on queue-length analysis. Through extensive numerical validation, we find that the queue-length approximation exhibits excellent performance for light traffic load.

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Cheung, Sing-Kong, Hans van den Berg, and Richard J. Boucherie. "Decomposing the queue length distribution of processor-sharing models into queue lengths of permanent customer queues." Performance Evaluation 62, no. 1-4 (2005): 100–116. http://dx.doi.org/10.1016/j.peva.2005.07.009.

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Viloria, Fadhely, Kenneth Courage, and Donald Avery. "Comparison of Queue-Length Models at Signalized Intersections." Transportation Research Record: Journal of the Transportation Research Board 1710, no. 1 (2000): 222–30. http://dx.doi.org/10.3141/1710-26.

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Several measures of effectiveness (MOEs) are associated with the queuing process at traffic signals, including delay, number of stops, fuel consumption, emissions, and queue length. The focus in this study is on queue length in general and on the storage requirements for left turns in particular. Queue length is an important MOE because queues that overflow the available storage space have an adverse effect on the overall operation of the intersection. Many traffic models now provide queue-length estimates, but the procedures used by these models are based on different queue definitions and have different computational approaches that lead to different results. A classification framework is developed for the existing models, their behavior is compared with that of the proposed Highway Capacity Manual (HCM) 2000 queue model, and queue conversion factors are provided for translating the various model outputs to their HCM 2000 equivalent. The proposed HCM 2000 model and its parent model from the Signalized and Unsignalized Intersection Design and Research Aid (SIDRA) provide a comprehensive treatment of the queuing process, accounting for control parameters such as controller type and progression quality as well as for the random and overflow effects associated with traffic flow. As such, the queue-length estimates from these models are more analytically defensible than those of the simpler theoretical models. The SIDRA and HCM 2000 queue estimates are generally higher than those of most other models and are somewhat higher than what conventional wisdom would suggest. It is suggested as a result of the comparisons presented that the queue estimates from some models are unduly optimistic when demand approaches capacity and that a goal of 90 percent confidence in the adequacy of left-turn storage lanes may be difficult to achieve under these conditions.

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Respati, Sara, Mohamad Isram, Fatmawati Fatmawati, and Sri Kusrini. "Estimasi Panjang Antrian Pada Simpang Bersinyal Dengan Menggunakan Artificial Neural Network." Jurnal Ilmiah Ilmu Terapan Universitas Jambi|JIITUJ| 6, no. 2 (2022): 201–11. http://dx.doi.org/10.22437/jiituj.v6i2.22958.

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Signalized intersections are nodes in the transportation network where vehicles in different directions meet and are critical points for congestion. Vehicle queue length is one of the performance parameters of a signalized intersection. Long queues of vehicles are at high risk of accidents involving many vehicles. Feedback signal control (actuated signal control) can be used to improve intersection performance. One of the variables that can be used as a feedback input is the length of the vehicle queue. Traffic in Indonesia is mixed traffic where various types of vehicles use the same road lanes and with low lane discipline. This causes the traffic system to become complex and to be stochastic and non-linear. Queue length modeling using a static linear algorithm is unable to capture the phenomenon of this complex traffic system. Therefore, this study aims to build a queue length model based on machine learning, that is, using an artificial neural network (ANN). This model studies traffic systems with historical data so that through the training process it can model queue lengths with a good degree of accuracy. An estimation model was built and applied to a section of the Muara Rapak signalized intersections, Balikpapan. Data on queue length for 10 days, 2 hours/day, obtained using CCTV and direct field surveys. The results of the model test show that ANN has a good level of accuracy with MAE, RMSE and MAPE of 3.8 m, 4.9 m and 6%, respectively.

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Lieberman, Edward B., Jinil Chang, and Elena Shenk Prassas. "Formulation of Real-Time Control Policy for Oversaturated Arterials." Transportation Research Record: Journal of the Transportation Research Board 1727, no. 1 (2000): 77–88. http://dx.doi.org/10.3141/1727-10.

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The formulation of a real-time traffic control policy designed expressly for oversaturated arterials is presented, and the operating protocol is described. Its objectives are to ( a) maximize system throughput, ( b) fully use storage capacity, and ( c) provide equitable service. This control policy, known as RT/IMPOST (real-time/internal metering policy to optimize signal timing), is designed to control queue growth on every saturated approach by suitably metering traffic to maintain stable queues. Consistent with this approach, bounds on queue lengths and signal offsets are determined. A mixed-integer linear program (MILP) tableau is formulated to yield optimal values of signal offsets and queue length for each approach. A nonlinear (quadratic) programming formulation adjusts the arterial green-phase durations of each signal cycle so that the actual arterial queue lengths on each saturated approach will continually closely approximate the optimal queue lengths computed by the MILP formulation. The policy principles are as follows: ( a) the signal phase durations “meter” traffic at intersections servicing oversaturated approaches to control and stabilize queue lengths and to provide equitable service to competing traffic streams; and ( b) the signal coordination (i.e., offsets) controls the interaction between incoming platoons and standing queues in a way that fully uses the available storage capacity, keeps intersections clear of queue spillback, and maximizes throughput.

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Boriboon, Anupon, and Siriwhaddhanah Pongpadpinit. "The HSBQ Algorithm with Triple-play Services for Broadband Hybrid Satellite Constellation Communication System." International Journal of Advances in Telecommunications, Electrotechnics, Signals and Systems 5, no. 2 (2016): 108. http://dx.doi.org/10.11601/ijates.v5i2.169.

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The HSBQ algorithm is the one of active queue management algorithms, which orders to avoid high packet loss rates and control stable stream queue. That is the problem of calculation of the drop probability for both queue length stability and bandwidth fairness. This paper proposes the HSBQ, which drop the packets before the queues overflow at the gateways, so that the end nodes can respond to the congestion before queue overflow. This algorithm uses the change of the average queue length to adjust the amount by which the mark (or drop) probability is changed. Moreover it adjusts the queue weight, which is used to estimate the average queue length, based on the rate. The results show that HSBQ algorithm could maintain control stable stream queue better than group of congestion metric without flow information algorithm as the rate of hybrid satellite network changing dramatically, as well as the presented empiric evidences demonstrate that the use of HSBQ algorithm offers a better quality of service than the traditionally queue control mechanisms used in hybrid satellite network.

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Al-Deek, Haitham M., Roger L. Wayson, C. David Cooper, et al. "Queueing Algorithm for Calculating Idling Emissions in FLINT—the FLorida INTersection Air Quality Model." Transportation Research Record: Journal of the Transportation Research Board 1587, no. 1 (1997): 128–36. http://dx.doi.org/10.3141/1587-15.

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The theoretical development of the queueing model used in the FLINT (FLorida INTersection) air quality model is described. FLINT is an area source model used to predict carbon monoxide concentrations for under-saturated and oversaturated traffic conditions at signalized intersections. In the FLINT model, deterministic queueing is used to estimate the queue length for cases of undersaturated conditions. In oversaturated cases, a cycle failure method has been developed to estimate queue length. In addition, a new concept is presented for calculating idling time for each vehicle’s position in the queue during both the red and the green phases of the traffic signal cycle. A limited set of undersaturated cases from monitoring data in Melrose Park, Illinois, was used to compare the predicted queue lengths with the measured queue lengths for several air quality models. It was found that FLINT predicted the queue length within one vehicle of the observed queue length. The same cases were tested using CAL3QHC, TEXIN2 intersection air quality models, and the American Automobile Manufacturers Association (AAMA) simulation model. It was found that predictions of the AAMA and the FLINT models were very close to the measured queue lengths in cases of undersaturated conditions. Moreover, although the FLINT and the AAMA models use a different approach to estimate queue length, their predicted queue lengths were very close in oversaturated cases. However, the predicted queue lengths of CAL3QHC were too long for oversaturated cases.

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Atar, Rami, Isaac Keslassy, and Gal Mendelson. "Subdiffusive Load Balancing in Time-Varying Queueing Systems." Operations Research 67, no. 6 (2019): 1678–98. http://dx.doi.org/10.1287/opre.2019.1851.

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The degree to which delays or queue lengths equalize under load-balancing algorithms gives a good indication of their performance. Some of the most well-known results in this context are concerned with the asymptotic behavior of the delay or queue length at the diffusion scale under a critical load condition, where arrival and service rates do not vary with time. For example, under the join-the-shortest-queue policy, the queue length deviation process, defined as the difference between the greatest and smallest queue length as it varies over time, is at a smaller scale (subdiffusive) than that of queue lengths (diffusive).

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Miyazawa, Masakiyo, and Ronald W. Wolff. "Symmetric queues with batch departures and their networks." Advances in Applied Probability 28, no. 1 (1996): 308–26. http://dx.doi.org/10.2307/1427923.

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Batch departures arise in various applications of queues. In particular, such models have been studied recently in connection with production systems. For the most part, however, these models assume Poisson arrivals and exponential service times; little is known about them under more general settings. We consider how their stationary queue length distributions are affected by the distributions of interarrival times, service times and departing batch sizes of customers. Since this is not an easy problem even for single departure models, we first concentrate on single-node queues with a symmetric service discipline, which is known to have nice properties. We start with pre-emptive LIFO, a special case of the symmetric service discipline, and then consider symmetric queues with Poisson arrivals. Stability conditions and stationary queue length distributions are obtained for them, and several stochastic order relations are considered. For the symmetric queues and Poisson arrivals, we also discuss their network. Stability conditions and the stationary joint queue length distribution are obtained for this network.

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Miyazawa, Masakiyo, and Ronald W. Wolff. "Symmetric queues with batch departures and their networks." Advances in Applied Probability 28, no. 01 (1996): 308–26. http://dx.doi.org/10.1017/s0001867800027385.

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Batch departures arise in various applications of queues. In particular, such models have been studied recently in connection with production systems. For the most part, however, these models assume Poisson arrivals and exponential service times; little is known about them under more general settings. We consider how their stationary queue length distributions are affected by the distributions of interarrival times, service times and departing batch sizes of customers. Since this is not an easy problem even for single departure models, we first concentrate on single-node queues with a symmetric service discipline, which is known to have nice properties. We start with pre-emptive LIFO, a special case of the symmetric service discipline, and then consider symmetric queues with Poisson arrivals. Stability conditions and stationary queue length distributions are obtained for them, and several stochastic order relations are considered. For the symmetric queues and Poisson arrivals, we also discuss their network. Stability conditions and the stationary joint queue length distribution are obtained for this network.

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Zheng, Guan, Yang Zhijun, Qian Wenhua, and He Min. "On Two-Level State-Dependent Routing Polling Systems with Mixed Service." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/109325.

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Based on priority differentiation and efficiency of the system, we consider anN+1queues’ single-server two-level polling system which consists of one key queue andNnormal queues. The novel contribution of the present paper is that we consider that the server just polls active queues with customers waiting in the queue. Furthermore, key queue is served with exhaustive service and normal queues are served with 1-limited service in a parallel scheduling. For this model, we derive an expression for the probability generating function of the joint queue length distribution at polling epochs. Based on these results, we derive the explicit closed-form expressions for the mean waiting time. Numerical examples demonstrate that theoretical and simulation results are identical and the new system is efficient both at key queue and normal queues.

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Wei, Lu, Jin-hong Li, Li-wen Xu, Lei Gao, and Jian Yang. "Queue Length Estimation for Signalized Intersections under Partially Connected Vehicle Environment." Journal of Advanced Transportation 2022 (May 2, 2022): 1–11. http://dx.doi.org/10.1155/2022/9568723.

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Queue length is a crucial measurement of traffic signal control at urban intersections. Conventional queue length estimation methods mostly still rely on fixed detectors. The development of connected vehicles (CV) provides massive amounts of vehicle trajectory data, and the queue length estimation based on CV data has received considerable attention in recent years. However, most existing CV-based methods require the prior knowledge of the penetration rate of CV and vehicle arrivals, but the estimation of these prior distributions has not been well studied. To address this issue, this paper proposes a cycle-based queue length estimation method under partially connected vehicle (CV) environment, with the prior vehicle arrivals being unknown. The empirical Bayes method is adopted to estimate the arrival rate by leveraging the observed queued CV information such as the number and positions. The hyperparameter estimation problem of the prior distribution is solved by the maximum likelihood estimation (MLE) method. To validate the proposed queue length estimation method, a simulation environment with partially connected vehicles is established using VISSIM and Python for data generating. The results in terms of normalized mean absolute errors (NMAE) and normalized root mean square errors (NRMSE) show that the proposed method could produce accurate and reliable estimated queue length under various CV penetration rates.

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Li, Jun, and Yiqiang Q. Zhao. "ON THE PROBABILITY DISTRIBUTION OF JOIN QUEUE LENGTH IN A FORK-JOIN MODEL." Probability in the Engineering and Informational Sciences 24, no. 4 (2010): 473–83. http://dx.doi.org/10.1017/s0269964810000112.

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In this article, we consider the two-node fork-join model with a Poisson arrival process and exponential service times of heterogeneous service rates. Using a mapping from the queue lengths in the parallel nodes to the join queue length, we first derive the probability distribution function of the join queue length in terms of joint probabilities in the parallel nodes and then study the exact tail asymptotics of the join queue length distribution. Although the asymptotics of the joint distribution of the queue lengths in the parallel nodes have three types of characterizations, our results show that the asymptotics of the join queue length distribution are characterized by two scenarios: (1) an exact geometric decay and (2) a geometric decay with the prefactor n−1/2.

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Akçelik, Rahmi. "Progression Factor for Queue Length and Other Queue-Related Statistics." Transportation Research Record: Journal of the Transportation Research Board 1555, no. 1 (1996): 99–104. http://dx.doi.org/10.1177/0361198196155500113.

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A method is presented that extends the U.S. Highway Capacity Manual (HCM) delay progression factor method to the prediction of queue length, queue clearance time, proportion queued (stopped), and queue move-up rate. These predictions are achieved by the introduction of an additional progression factor and adoption of the HCM overflow term adjustment factor, providing a simple method to allow for the effects of platooned arrivals on the performance of coordinated signalized intersections. The method is useful at the level of basic capacity and performance analysis of a single intersection where detailed platooned arrival patterns generated at upstream signal stop lines are not available. The arrival types defined by the HCM as the basic input to define the characteristics of platooned arrivals are adopted for use in calculating the additional progression factor in the same way as the original HCM progression factor for delay. It is assumed that the reader has a good knowledge of the subject area.

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Neuts, Marcel F. "A new informative embedded Markov renewal process for the PH/G/1 queue." Advances in Applied Probability 18, no. 2 (1986): 533–57. http://dx.doi.org/10.2307/1427311.

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We consider a new embedded Markov chain for the PH/G/1 queue by recording the queue length, the phase of the arrival process and the number of services completed during the current busy period at the successive departure epochs. Algorithmically tractable matrix formulas are obtained which permit the analysis of the fluctuations of the queue length and waiting times during a typical busy cycle. These are useful in the computation of certain profile curves arising in the statistical analysis of queues. In addition, informative expressions for the mean waiting times in the stable GI/G/1 queue and a simple new algorithm to evaluate the waiting-time distributions for the stationary PH/PH/1 queue are obtained.

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Neuts, Marcel F. "A new informative embedded Markov renewal process for the PH/G/1 queue." Advances in Applied Probability 18, no. 02 (1986): 533–57. http://dx.doi.org/10.1017/s0001867800015871.

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We consider a new embedded Markov chain for the PH/G/1 queue by recording the queue length, the phase of the arrival process and the number of services completed during the current busy period at the successive departure epochs. Algorithmically tractable matrix formulas are obtained which permit the analysis of the fluctuations of the queue length and waiting times during a typical busy cycle. These are useful in the computation of certain profile curves arising in the statistical analysis of queues. In addition, informative expressions for the mean waiting times in the stable GI/G/1 queue and a simple new algorithm to evaluate the waiting-time distributions for the stationary PH/PH/1 queue are obtained.

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Yang, Guangchuan, Rui Yue, Zong Tian, and Hao Xu. "Modeling the Impacts of Traffic Flow Arrival Profiles on Ramp Metering Queues." Transportation Research Record: Journal of the Transportation Research Board 2672, no. 15 (2018): 85–92. http://dx.doi.org/10.1177/0361198118782253.

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An adequate queue storage length is critical for a metered on-ramp to prevent ramp queue spillback to the upstream signalized intersection. Previous research on queue length estimation or queue storage length design at metered ramps has not taken into account the potential impact of various on-ramp traffic flow arrival profiles on ramp queue lengths. This paper depicts the traffic flow arrival profiles and queue generation processes at three different metered ramp categories. Based on a large number of microscopic simulation runs, it is found that, under a given demand-to-capacity scenario, the queue at a metered ramp with two on-ramp feeding movements is more likely to be cleared in a cycle than at a metered ramp with three on-ramp feeding movements. Also, the platoon dispersion effect significantly reduces the ramp queue length, and hence the queue storage needs at a metered ramp. In addition, this paper reveals that ramp queue length tends to increase linearly with upstream signal cycle length. The design of queue storage length for a metered on-ramp hence needs to fully consider the various ramp configurations and upstream signal timing settings.

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Fakharian Qom, Somaye, Mohammed Hadi, Yan Xiao, and Haitham Al-Deek. "Queue Length Estimation for Freeway Facilities: Based on Combination of Point Traffic Detector and Automatic Vehicle Identification Data." Transportation Research Record: Journal of the Transportation Research Board 2616, no. 1 (2017): 19–26. http://dx.doi.org/10.3141/2616-03.

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Queue length is a critical performance measure for assessing and managing transportation network performance. Two new methods that integrate data from point traffic detectors and automatic vehicle identification (AVI) readers to estimate the queue length of freeway segments for both off-line and real-time applications are developed in this study. One method estimates the queue length between two detectors by using linear interpolation between the travel time measurement based on AVI data when the link is fully queued and when no queue is present. In the second method, a segment with a partial queue is divided into two subsegments: the first is assumed to be similar to upstream traffic conditions and the second to downstream traffic conditions. Then, the length of each part is calculated from AVI speed data. The performance of these methods is assessed and compared in two case studies that are based on simulation data and real-world data. The results show that using a combination of point detector data and AVI data produces accurate estimates of queue length. The queue estimation method based on cumulative volumes collected with point detectors alone also produces reasonably good estimates but requires additional ramp detection and assumptions regarding moving queue density. The two combination methods produce results that are close to each other based on simulation data and real-world data. The segmentation method produces better results based on real-world data.

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Shin, Yang Woo, and Chareles E. M. Pearce. "The BMAP/G/1 vacation queue with queue-length dependent vacation schedule." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 40, no. 2 (1998): 207–21. http://dx.doi.org/10.1017/s0334270000012479.

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AbstractWe treat a single-server vacation queue with queue-length dependent vacation schedules. This subsumes the single-server vacation queue with exhaustive service discipline and the vacation queue with Bernoulli schedule as special cases. The lengths of vacation times depend on the number of customers in the system at the beginning of a vacation. The arrival process is a batch-Markovian arrival process (BMAP). We derive the queue-length distribution at departure epochs. By using a semi-Markov process technique, we obtain the Laplace-Stieltjes transform of the transient queue-length distribution at an arbitrary time point and its limiting distribution

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Luo, Huidan, Mingjun Deng, and Jia Chen. "Queue Length Estimation Based on Probe Vehicle Data at Signalized Intersections." Journal of Advanced Transportation 2023 (July 17, 2023): 1–15. http://dx.doi.org/10.1155/2023/3241207.

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Queue length is one of the important indexes to evaluate the operation efficiency of signalized intersection and also the key parameter of intersection signal control optimization. Traditional queue length estimation models are mostly based on fixed detection equipment, and the models assumptions are too harsh; there are certain limitations. Based on the probe vehicle data, this paper establishes a model of queue length estimation for signalized intersection based on shockwave theory. First, based on the speed and location data of the probe vehicle, the vehicle density is calculated to estimate the intersection stop line. A real-time calculation method of vehicle arrival rate is proposed to improve the applicability of the model. Then, based on the shockwave theory, the meeting time of the queue forming wave and the queue discharging wave are calculated after the green light is on. Finally, the queue length is summed in sections, including the distance between the last queued probe vehicle and the stop line during the red light period, the length of the subsequent vehicles arriving during the residual red light time, and the newly increased queue length within the queue discharging time. This paper uses the VISSIM software to simulate the actual intersection. The simulation results show that when the penetration of probe vehicle is 50%, 25%, and 10%, their corresponding mean absolute relative error are 11.27%, 27.77%, and 39.12%, respectively. It can be seen that with the increase of penetration, the error gradually decreases. The average absolute relative error is within the acceptable range. After analyzing the existing similar methods, although the accuracy of the method proposed in this paper does not reach the highest level, it has the advantages of simple operation, less computation, and good real-time computation. Relevant research results can provide support for traffic control at signalized intersections.

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Ma, Dongfang, Dianhai Wang, Yiming Bie, Feng Sun, and Sheng Jin. "A Method for Queue Length Estimation in an Urban Street Network Based on Roll Time Occupancy Data." Mathematical Problems in Engineering 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/892575.

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A method estimating the queue length in city street networks was proposed using the data of roll time occupancy. The key idea of this paper is that when the queue length in front of the queue detector becomes longer, the speeds of the following vehicles to pass through the detector will become smaller, resulting in higher occupancy with constant traffic intensity. Considering the relationship between queue lengths and roll time occupancy affected by many factors, such as link length, lane width, lane number, and bus ratio, twelve different conditions were designed, and the traffic data under different conditions was obtained using VISSIM simulation. Based on the analysis of simulation data, an S-type logistic model was decided to develop for the relationship between queue lengths and roll time occupancy, and the fitting equations were obtained under the twelve simulation situations. The average model for the relationship between queue lengths and roll time occupancy was presented by successive multiple linear regression with the fitting equation parameters and simulation parameters, and the estimation model for queue length was presented through analyzing the equation of the average relation model.

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Lin, Cheng-Han, Ce-Kuen Shieh, Wen-Shyang Hwang, and Dai-Ying Liu. "Throughput-Based Mapping Algorithm for Video Streaming over IEEE 802.11e WLAN." Wireless Communications and Mobile Computing 2021 (October 22, 2021): 1–14. http://dx.doi.org/10.1155/2021/8852095.

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IEEE 802.11e utilizes the Enhanced Distributed Channel Access (EDCA) protocol to provide quality of service (QoS) support over WLANs. However, under EDCA, all video data are allocated to the same access category (AC) queue, irrespective of their coding importance. Consequently, the quality of the transmitted video may be severely degraded under heavy traffic load conditions. The literature contains several queue mapping mechanisms based on the settings of the AC queues, such as contention window size, for improving the video transmission quality over IEEE 802.11e WLANs. However, these mechanisms fail to consider the effect of the dequeuing time on the video delivery performance. Accordingly, the present study proposes a new queue mapping algorithm, designated as the throughput-based mapping algorithm (TMA), for improving the video transmission quality and reducing the video delay by dynamically allocating the video data packets to different AC queues based on their length and throughput such that the probability of the dequeuing time being reduced is increased. In implementing the proposed approach, the throughputs of the AC queues are analyzed using two Markov chain models. The simulation results show that TMA outperforms previously proposed static and dynamic queue mapping schemes in terms of a reduced AC queue length, an improved PSNR (peak signal-to-noise ratio), and a shorter transmission delay.

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Akgun, Osman T., Rhonda Righter, and Ronald Wolff. "Partial Flexibility in Routeing and Scheduling." Advances in Applied Probability 45, no. 3 (2013): 673–91. http://dx.doi.org/10.1239/aap/1377868534.

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We consider partial customer flexibility in service systems under two different designs. In the first design, flexible customers have their own queue and each server has its own queue of dedicated customers. Under this model, the problem is a scheduling problem and we show under various settings that the dedicated customers first (DCF) policy is optimal. In the second design, flexible customers are not queued separately and must be routed to one of the server's dedicated queues upon arrival. We extend earlier results about the ‘join the smallest work (JSW)’ policy to systems with dedicated as well as flexible arrivals. We compare these models to a routeing model in which only the queue length is available in terms of both efficiency and fairness and argue that the overall best approach for call centers is JSW routeing. We also discuss how this can be implemented in call centers even when work is unknown.

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Akgun, Osman T., Rhonda Righter, and Ronald Wolff. "Partial Flexibility in Routeing and Scheduling." Advances in Applied Probability 45, no. 03 (2013): 673–91. http://dx.doi.org/10.1017/s0001867800006534.

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We consider partial customer flexibility in service systems under two different designs. In the first design, flexible customers have their own queue and each server has its own queue of dedicated customers. Under this model, the problem is a scheduling problem and we show under various settings that the dedicated customers first (DCF) policy is optimal. In the second design, flexible customers are not queued separately and must be routed to one of the server's dedicated queues upon arrival. We extend earlier results about the ‘join the smallest work (JSW)’ policy to systems with dedicated as well as flexible arrivals. We compare these models to a routeing model in which only the queue length is available in terms of both efficiency and fairness and argue that the overall best approach for call centers is JSW routeing. We also discuss how this can be implemented in call centers even when work is unknown.

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Pender, Jamol, Richard Rand, and Elizabeth Wesson. "A Stochastic Analysis of Queues with Customer Choice and Delayed Information." Mathematics of Operations Research 45, no. 3 (2020): 1104–26. http://dx.doi.org/10.1287/moor.2019.1024.

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Many service systems provide queue length information to customers, thereby allowing customers to choose among many options of service. However, queue length information is often delayed, and it is often not provided in real time. Recent work by Dong et al. [Dong J, Yom-Tov E, Yom-Tov GB (2018) The impact of delay announcements on hospital network coordination and waiting times. Management Sci. 65(5):1969–1994.] explores the impact of these delays in an empirical study in U.S. hospitals. Work by Pender et al. [Pender J, Rand RH, Wesson E (2017) Queues with choice via delay differential equations. Internat. J. Bifurcation Chaos Appl. Sci. Engrg. 27(4):1730016-1–1730016-20.] uses a two-dimensional fluid model to study the impact of delayed information and determine the exact threshold under which delayed information can cause oscillations in the dynamics of the queue length. In this work, we confirm that the fluid model analyzed by Pender et al. [Pender J, Rand RH, Wesson E (2017) Queues with choice via delay differential equations. Internat. J. Bifurcation Chaos Appl. Sci. Engrg. 27(4):1730016-1–1730016-20.] can be rigorously obtained as a functional law of large numbers limit of a stochastic queueing process, and we generalize their threshold analysis to arbitrary dimensions. Moreover, we prove a functional central limit theorem for the queue length process and show that the scaled queue length converges to a stochastic delay differential equation. Thus, our analysis sheds new insight on how delayed information can produce unexpected system dynamics.

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May, Marvin Carl, Alexander Albers, Marc David Fischer, Florian Mayerhofer, Louis Schäfer, and Gisela Lanza. "Queue Length Forecasting in Complex Manufacturing Job Shops." Forecasting 3, no. 2 (2021): 322–38. http://dx.doi.org/10.3390/forecast3020021.

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Currently, manufacturing is characterized by increasing complexity both on the technical and organizational levels. Thus, more complex and intelligent production control methods are developed in order to remain competitive and achieve operational excellence. Operations management described early on the influence among target metrics, such as queuing times, queue length, and production speed. However, accurate predictions of queue lengths have long been overlooked as a means to better understanding manufacturing systems. In order to provide queue length forecasts, this paper introduced a methodology to identify queue lengths in retrospect based on transitional data, as well as a comparison of easy-to-deploy machine learning-based queue forecasting models. Forecasting, based on static data sets, as well as time series models can be shown to be successfully applied in an exemplary semiconductor case study. The main findings concluded that accurate queue length prediction, even with minimal available data, is feasible by applying a variety of techniques, which can enable further research and predictions.

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40

König, Dieter, and Volker Schmidt. "Stationary queue-length characteristics in queues with delayed feedback." Journal of Applied Probability 22, no. 2 (1985): 394–407. http://dx.doi.org/10.2307/3213782.

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A class of two-node queueing networks with general stationary ergodic governing sequence is considered. This means that, in particular, a non-Poissonian arrival process and dependent service times, as well as a non-Bernoulli feedback mechanism are admitted. A mixing condition ensures that the limiting distributions of the number of customers in the nodes observed in continuous time as well as at certain embedded epochs can be expressed by the Palm distributions of appropriately chosen marked point processes. This gives the possibility of connecting the classical concept of embedding with a general point-process approach. Furthermore, it leads to simple proofs of relationships between the limiting distributions. An example is given to illustrate how these relationships can be used to derive explicit formulas for various stationary queueing characteristics.

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41

Myers, Daniel S., and Mary K. Vernon. "Estimating queue length distributions for queues with random arrivals." ACM SIGMETRICS Performance Evaluation Review 40, no. 3 (2012): 77–79. http://dx.doi.org/10.1145/2425248.2425268.

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42

Walraevens, Joris, Dieter Claeys, and Tuan Phung-Duc. "Asymptotics of queue length distributions in priority retrial queues." Performance Evaluation 127-128 (November 2018): 235–52. http://dx.doi.org/10.1016/j.peva.2018.10.004.

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43

Cai, Nanlian, and Yaohui Zheng. "Increasing convex ordering of queue length in bulk queues." Operations Research Letters 36, no. 1 (2008): 123–26. http://dx.doi.org/10.1016/j.orl.2007.02.011.

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44

König, Dieter, and Volker Schmidt. "Stationary queue-length characteristics in queues with delayed feedback." Journal of Applied Probability 22, no. 02 (1985): 394–407. http://dx.doi.org/10.1017/s0021900200037852.

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A class of two-node queueing networks with general stationary ergodic governing sequence is considered. This means that, in particular, a non-Poissonian arrival process and dependent service times, as well as a non-Bernoulli feedback mechanism are admitted. A mixing condition ensures that the limiting distributions of the number of customers in the nodes observed in continuous time as well as at certain embedded epochs can be expressed by the Palm distributions of appropriately chosen marked point processes. This gives the possibility of connecting the classical concept of embedding with a general point-process approach. Furthermore, it leads to simple proofs of relationships between the limiting distributions. An example is given to illustrate how these relationships can be used to derive explicit formulas for various stationary queueing characteristics.

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45

Rabehasaina, Landy, and Bruno Sericola. "Transient Analysis of Averaged Queue Length in Markovian Queues." Stochastic Models 21, no. 2-3 (2005): 599–613. http://dx.doi.org/10.1081/stm-200056225.

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46

Lee, Kyu-Seok, and Hong Shik Park. "Approximation of The Queue Length Distribution of General Queues." ETRI Journal 15, no. 3 (1994): 35–45. http://dx.doi.org/10.4218/etrij.94.0194.0003.

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47

Daley, D. J., and L. D. Servi. "Approximating last-exit probabilities of a random walk, by application to conditional queue length moments within busy periods of M/GI/1 queues." Journal of Applied Probability 31, A (1994): 251–67. http://dx.doi.org/10.2307/3214960.

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Certain last-exit and first-passage probabilities for random walks are approximated via a heuristic method suggested by a ladder variable argument. They yield satisfactory approximations of the first- and second-order moments of the queue length within a busy period of an M/D/1 queue. The approximation is applied to the wider class of random walks that arise in studying M/GI/1 queues. For gamma-distributed service times the queue length distribution is independent of the arrival rate. For other distributions where the arrival rate affects the queue length distribution, we have to use conjugate distributions in order to exploit a local central limit property. The limit underlying the approximation has the nature of a Brownian excursion.The source of the problem lies in recent queueing inference work; the connection with Takács' interests comes from both queueing theory and the ballot theorem.

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48

Daley, D. J., and L. D. Servi. "Approximating last-exit probabilities of a random walk, by application to conditional queue length moments within busy periods of M/GI/1 queues." Journal of Applied Probability 31, A (1994): 251–67. http://dx.doi.org/10.1017/s0021900200107107.

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Certain last-exit and first-passage probabilities for random walks are approximated via a heuristic method suggested by a ladder variable argument. They yield satisfactory approximations of the first- and second-order moments of the queue length within a busy period of an M/D/1 queue. The approximation is applied to the wider class of random walks that arise in studying M/GI/1 queues. For gamma-distributed service times the queue length distribution is independent of the arrival rate. For other distributions where the arrival rate affects the queue length distribution, we have to use conjugate distributions in order to exploit a local central limit property. The limit underlying the approximation has the nature of a Brownian excursion. The source of the problem lies in recent queueing inference work; the connection with Takács' interests comes from both queueing theory and the ballot theorem.

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Yin, Juyuan, Jian Sun, and Keshuang Tang. "A Kalman Filter-Based Queue Length Estimation Method with Low-Penetration Mobile Sensor Data at Signalized Intersections." Transportation Research Record: Journal of the Transportation Research Board 2672, no. 45 (2018): 253–64. http://dx.doi.org/10.1177/0361198118798734.

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Queue length estimation is of great importance for signal performance measures and signal optimization. With the development of connected vehicle technology and mobile internet technology, using mobile sensor data instead of fixed detector data to estimate queue length has become a significant research topic. This study proposes a queue length estimation method using low-penetration mobile sensor data as the only input. The proposed method is based on the combination of Kalman Filtering and shockwave theory. The critical points are identified from raw spatiotemporal points and allocated to different cycles for subsequent estimation. To apply the Kalman Filter, a state-space model with two state variables and the system noise determined by queue-forming acceleration is established, which can characterize the stochastic property of queue forming. The Kalman Filter with joining points as measurement input recursively estimates real-time queue lengths; on the other hand, queue-discharging waves are estimated with a line fitted to leaving points. By calculating the crossing point of the queue-forming wave and the queue-discharging wave of a cycle, the maximum queue length is also estimated. A case study with DiDi mobile sensor data and ground truth maximum queue lengths at Huanggang-Fuzhong intersection, Shenzhen, China, shows that the mean absolute percentage error is only 11.2%. Moreover, the sensitivity analysis shows that the proposed estimation method achieves much better performance than the classical linear regression method, especially in extremely low penetration rates.

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Hanqin, Zhang, Hsu Guanghui, and Wang Rongxin. "Strong approximations for multiple channel queues in heavy traffic." Journal of Applied Probability 27, no. 3 (1990): 658–70. http://dx.doi.org/10.2307/3214549.

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We prove strong approximations for multiple channel queues in heavy traffic. Strong approximations are given for the waiting time and queue length processes, and for embedded sequences associated with the length process.

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Journal articles on the topic 'Length of queue'

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