Travel Time Model Research Articles

Sharpness of the hemispherical boundary in the inner core beneath the northern Pacific

The hemispherical nature of heterogeneities of the isotropic velocity and attenuation of the inner core has been extensively studied by seismic observations, but consensus on the character of the boundary between two hemispheres has not yet been achieved. To investigate the hemispherical boundary in detail, we analyze core phase data whose ray paths propagate beneath the northern Pacific. We employ a waveform inversion approach based on simulated annealing to measure the differential traveltime and the attenuation parameter of the core phases. Measured differential traveltimes for data from European stations for events in the Fiji-Tonga region show positive anomalies consistent with the eastern hemisphere model, while those from USArray for events in Indonesia show relatively small values. Ray-theory based forward modeling of the differential traveltimes is conducted by varying the shape and the transition width of the boundary. An arc-like shape boundary that connects points (0°N, 159°W) on the equator and (79°N, 110°E) in far north with a transition width of ∼600 km best explains the observed differential traveltimes rather than a sharp boundary. This model also accounts for the observed variation of attenuation parameters.

Travel time models for a three-dimensional compact AS/RS considering different I/O point policies

This paper studies a three-dimensional automated storage and retrieval system that uses conveyors for depth transportation and a crane for both horizontal and vertical transportation. While previous studies put input and output points together at the system bottom, we consider separating and elevating them by proposing four I/O point policies: input and output points at two sides, input and output points elevated at one side, input and output points elevated at two sides, input and output points elevated at a midpoint. We build travel time models to analyse these policies and use simulation for validation. We theoretically find the optimal system structure and compare these I/O point policies, in terms of expected S/R machine travel time. The results show that the square-in-time structure is optimal in most cases and the mid-point elevation I/O point policy performs the best in terms of expected travel time. Moreover, we compare our I/O point policies with the lower mid-point policy. The results show that the mid-point elevation I/O point policy outperforms the I/O point at the lower mid-point by about in terms of expected travel time, while other I/O point policies are dominated by the I/O point at the lower mid-point.

Travel time models for the rack-moving mobile robot system

The rack-moving mobile robot (RMMR) system is a special parts-to-picker automated warehousing system that uses hundreds of rack-moving machines to accomplish the repetitive tasks of storing and retrieving parts by lifting and transporting unit racks autonomously. This paper investigates the operation cycle of the rack-moving machine for storage and retrieval from the perspective of the lane depth, especially exploring the particularity of the RMMR system in multi-deep lanes, and proposes expected travel time models of the rack-moving machine for single- and multi-deep layouts of the RMMR system. To validate the effectiveness of the proposed models, an experimental simulation was conducted with a 1–4-deep layout under six scenarios of different numbers of aisles and layers, and results were compared with results obtained using proposed models. The paper presents useful guidelines for the configuration of the RMMR system layout including the determination of the optimal lane depth.

Modeling Travel Time with Travelers’ Experience

This paper presents results from analysis of travel time model of Bus Rapid Transit (BRT) system. It meant to consult BRT operators and other parties concerning vehicles scheduling and maintenance, customer care, customer service, and structural improvement in future with regards to travelers’ perceptions. It used descriptive survey research design and survey questionnaire to collect data on the six routes of Dar es Salaam BRT system. It applied Microsoft Excel spreadsheet to organize and analyze the data. Analysis of travelers’ responses shows that, travel demand volume is low on Sunday and is high on Monday and Friday. The travel time total calculated from these responses ranges from lowest travel time to highest travel time. Certainly, through Kimara - Kivukoni route, the travel time total ranges between 53 to 112 minutes, Kimara - Morocco 47 to 101 minutes, Kimara - Gerezani 49 to 103 minutes, Morocco - Kivukoni 40 to 87 minutes, Morocco - Gerezani 36 to 78 minutes, and Gerezani - Kivukoni 29 to 64 minutes. The time that a traveler should add to an average travel time when planning for a trip in a dense traffic in order to ensure on time arrival through any of these routes are as follows: Through Kimara - Kivukoni route, a traveler has to add at least 17 minutes, while through Kimara - Morocco 13 minutes. Likewise, through Kimara - Gerezani 16 minutes, Morocco - Kivukoni 11 minutes, and Morocco - Gerezani 9 minutes. The planning time a traveler should allow in a dense traffic to ensure on time arrival varies from one route to another and at a point in time. Through Kimara - Kivukoni route, a traveler has to plan at least 65 minutes, Kimara - Morocco 48 minutes, Kimara - Gerezani 61 minutes, Morocco - Kivukoni 41 minutes, and Morocco - Gerezani 34 minutes. Some underlying factors that influences high travel time variations and delays on the BRT system include inadequate number of express-articulated buses, inappropriate vehicles scheduling and maintenance plans, imbalance between travel demand volumes and availability of travel facilities, inadequate on/off-boarding systems, failure to adhere to set schedules, and other reckless behaviors by some drivers. Among the measures that the responsible parties should put on board to mitigate these underlying factors include having in place proper maintenance plan, introducing new buses with equitable carrying capacity, and developing flexible scheduling plans that comply with the changing travel demand volumes. Other measures are improving ticketing services even outsides the existing facilities and establishing direct routes that strategically connect all terminals on the system. Keywords: Travel Time Reliability, 90 th or 95 th Percentile, Buffer Time Index and Planning Time Index DOI : 10.7176/MTM/9-8-05 Publication date : August 31st 2019

A generalized Rytov approximation for accurate calculation of phase variation in strong perturbation media

SUMMARY In the case of long-range propagation of forward scattering, due to the accumulation of phase changes caused by the velocity perturbations, the validity of the Born approximation will be violated. In contrast, the phase-change accumulation can be handled by the Rytov approximation, which has been widely used for long-distance propagation with only forward scattering or small-angle scattering involved. However, the weak scattering assumption (i.e. small velocity perturbation) in the Rytov approximation limits its scope of application. To address this problem, we analyse the integral kernel of the Rytov transform using the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation and we demonstrate that the integral kernel is a function of velocity perturbation and scattering angle. By applying a small scattering angle approximation, we show that the phase variation has a linear relationship with the slowness perturbation, no matter how strong the magnitude of perturbation is. Therefore, the new integral equation is then referred to as the generalized Rytov approximation (GRA) because it overcomes the weak scattering assumption of the Rytov approximation. To show the limitations of the Rytov approximation and the advantages of the proposed GRA method, first we design a two-layer model and we analytically calculate the errors introduced by the small scattering angle assumption using plane wave incidence. We show that the phase (traveltime) variations predicted by the GRA are always more accurate than the Rytov approximation. Particularly, the GRA produces accurate phase variations for the normal incident plane wave regardless of the magnitude of velocity perturbation. Numerical examples using Gaussian anomaly models demonstrate that the scattering angle has a crucial impact on the accuracy of the GRA. If the small scattering angle assumption holds, the GRA can produce an accurate phase approximation even if the velocity perturbation is very strong. On the contrary, both the first-order Rytov approximation and the GRA fail to get satisfying results when the scattering angle is large enough. The proposed GRA method has the potential to be used for traveltime modelling and inversion for large-scale strong perturbation media.

Seismic investigation of an active ocean–continent transform margin: the interaction between the Swan Islands Fault Zone and the ultraslow-spreading Mid-Cayman Spreading Centre

SUMMARY The Swan Islands Transform Fault (SITF) marks the southern boundary of the Cayman Trough and the ocean–continent transition of the North American–Caribbean Plate boundary offshore Honduras. The CAYSEIS experiment acquired a 180-km-long seismic refraction and gravity profile across this transform margin, ∼70 km to the west of the Mid-Cayman Spreading Centre (MCSC). This profile shows the crustal structure across a transform fault system that juxtaposes Mesozoic-age continental crust to the south against the ∼10-Myr-old ultraslow spread oceanic crust to the north. Ocean-bottom seismographs were deployed along-profile, and inverse and forward traveltime modelling, supported by gravity analysis, reveals ∼23-km-thick continental crust that has been thinned over a distance of ∼70 km to ∼10 km-thick at the SITF, juxtaposed against ∼4-km-thick oceanic crust. This thinning is primarily accommodated within the lower crust. Since Moho reflections are not widely observed, the 7.0 km s−1 velocity contour is used to define the Moho along-profile. The apparent lack of reflections to the north of the SITF suggests that the Moho is more likely a transition zone between crust and mantle. Where the profile traverses bathymetric highs in the off-axis oceanic crust, higher P-wave velocity is observed at shallow crustal depths. S-wave arrival modelling also reveals elevated velocities at shallow depths, except for crust adjacent to the SITF that would have occupied the inside corner high of the ridge-transform intersection when on axis. We use a Vp/Vs ratio of 1.9 to mark where lithologies of the lower crust and uppermost mantle may be exhumed, and also to locate the upper-to-lower crustal transition, identify relict oceanic core complexes and regions of magmatically formed crust. An elevated Vp/Vs ratio suggests not only that serpentinized peridotite may be exposed at the seafloor in places, but also that seawater has been able to flow deep into the crust and upper mantle over 20–30-km-wide regions which may explain the lack of a distinct Moho. The SITF has higher velocities at shallower depths than observed in the oceanic crust to the north and, at the seabed, it is a relatively wide feature. However, the velocity–depth model subseabed suggests a fault zone no wider than ∼5–10 km, that is mirrored by a narrow seabed depression ∼7500 m deep. Gravity modelling shows that the SITF is also underlain, at >2 km subseabed, by a ∼20-km-wide region of density >3000 kg m−3 that may reflect a broad region of metamorphism. The residual mantle Bouguer anomaly across the survey region, when compared with the bathymetry, suggests that the transform may also have a component of left-lateral trans-tensional displacement that accounts for its apparently broad seabed appearance, and that the focus of magma supply may currently be displaced to the north of the MCSC segment centre. Our results suggest that Swan Islands margin development caused thinning of the adjacent continental crust, and that the adjacent oceanic crust formed in a cool ridge setting, either as a result of reduced mantle upwelling and/or due to fracture enhanced fluid flow.

Seismic structure of the northwestern margin of the South China Sea: implication for asymmetric continental extension

Evolution of the continental margins of the South China Sea (SCS) is one of the open questions when discussing continental breakup and seafloor spreading. We processed data from a wide-angle seismic profile (OBS2011-1), which passes through the northwestern margin of the SCS, and performed travel time modelling to obtain the seismic velocity structures. The modelling results show a stepwise variation of the crustal thicknesses from continental margin to oceanic basin. Stretching factor of the upper crust is nearly double the estimate of the lower crust along the Zhongsha Trough. The lower crust shows asymmetrical upwelling towards the trough center, accompanied by similar to 0.3 kms(-1) of the velocity increase due to magmatic addition. The upper and lower crusts have almost the same stretching factor beneath continental blocks, indicating a uniform extension. Crustal structures of the conjugate margins of the Southwest Subbasin show similar velocity range and different thickness distribution, supporting the common origin and asymmetric extension of these two margins. The Ocean-Continent Transition zones (OCT) are much wider in the southern part (similar to 50 km) than the northern part (similar to 25 km) crossing the margins. We propose a tectonic model for the asymmetry of both the conjugate margins and the OCTs, favoring the highly stretched upper crust and accompanied by rising of the ductile middle-lower crust controlled by major low-angle faults. The rigid blocks may also act as a kind of hindrance for further evolution of the failed rifts and affect the shape of the OCT.

The October 14, 1908 MW 6.6 earthquake in the Barents and Kara sea region of the Arctic: Relocation based on instrumental data

A magnitude Mw (ISC) = 6.6 earthquake on October 14, 1908 in the Barents-Kara Sea region was the strongest in this region for the entire observation period. We performed earthquake relocation based on our compilation of all available seismological bulletins of the time that included data from the ISC-GEM (International Seismological Centre–Global Earthquake Model) project, the EuroSeismos project, the Geophysical Survey of the Russian Academy of Sciences and the Russian State Library. The relocation was performed using a modified generalized beamforming method based on the BARENTS travel time model. The epicenter was located in the estuarial part of the Franz Victoria Graben at the continent-ocean transition zone. According to our justification, an earthquake of such magnitude could well have occurred in the area of Franz Victoria Graben.

Simulation study of vehicle travel time on route with signals considering comprehensive influencing factors

Vehicle travel time is widely regarded as an important performance of the road traffic as well as a significant decision factors for travelers. While the travel time is variable because of the stochastic factors such as traffic flow, signals, and some other emergency conditions. Considering the dynamic characteristics of road traffic flow and the importance of shortening travel time for emergency transport task, in this paper, a basic vehicle travel time model based on empirical velocity–density function is established, in which the travel time is divided into road running time and signal waiting time. Simulations based on the basic model are conducted to investigate the comprehensive effect of the multiple factors on the travel time, such as traffic density, number of signals, circle time, green ratio and offset time between adjacent signals. A green-wave traffic objective-oriented method is also explored to achieve the shortest travel time. The results demonstrate that plateaus and sloped plateaus would appear under the comprehensive influence of both traffic density and traffic light number or signal parameters. It is found there is a minimum traffic time with a certain offset time under different traffic density when the traffic lights on a route do not change synchronously. The fitting formula and theoretical formula for the optimal offset time are also proposed, which can be used to achieve green-wave traffic in a practical case.

Dynamic headway control for high‐frequency bus line based on speed guidance and intersection signal adjustment

AbstractTo prevent bus bunching, a dynamic headway control method in the V2I (vehicle to infrastructure) environment for a high‐frequency route with bus lane is developed. Bus operating speed guidance on the mid‐blocks and intersection signal adjustment are two main strategies in the proposed method. A forecasting model of bus travel time under the dynamic control method is developed. The objective function is set up by taking into account differences between actual bus headways and dispatching headways, and the scaling ratios of intersection cycle lengths. The optimization model is solved using genetic algorithm. The proposed method is applied to a real bus route in Meihekou city, China, and compared with the current control plan as well as holding strategy. Results show that the proposed method can reduce bus headway deviations in all investigating periods; negative impacts on cars can be limited by setting reasonable values for the parameters.

Warehouse Design Model for Shuttle Based Storage and Retrieve System

Recently, SBS / RS system has been widely used and studied. This paper presents a mathematical model of travel time and cost for shuttle based storage and retrieve systems (SBS/RS), through which we can decide the optimized configuration and picking efficiency of the warehouse. By considering the operating characteristics, such as acceleration and deceleration and assuming that the storage units are uniform distributed and using probability theory, we obtain a time and cost function for a dual command storage and retrieve procedure. Finally, we validate our analysis by numerical examples and sensitivity analysis. The results show that the optimal configuration and efficiency of the warehouse are mainly affected by several key indicators, such as the width of each storage unit, the height of each shelf, etc.

MODELLING TRAVEL TIME DISTRIBUTION AND ITS INFLUENCE OVER STOCHASTIC VEHICLE SCHEDULING

Due to the paucity of well-established modelling approaches or well-accepted travel time distributions, the existing travel time models are often assumed to follow certain popular distributions, such as normal or lognormal, which may lead to results deviating from actual ones. This paper proposes a modelling approach for travel times using distribution fitting methods based on the data collected by Automatic Vehicle Location (AVL) systems. By this proposed approach, a compound travel time model can be built, which consists of the best distribution models for the travel times in each period of a day. Applying to stochastic vehicle scheduling, the influence of different travel time models is further studied. Results show that the compound model can fit more precisely to the actual travel times under various traffic situations, whilst the on-time performance of resulting vehicle schedules can be improved. The research findings have also potential benefit for the other research based on travel time models in public transport including timetabling, service planning and reliability measurement.

Sustainable Highway Maintenance: Optimization of Existing Highway Vertical Alignment Considering Pavement Condition

Any change in the geometric configuration of the existing road affects other dependent elements such as travel time, fuel consumption, and existing pavement. This paper quantifies these effects and finds an optimum geometric configuration. Three separate models are developed in this research: (1) the travel time model which predicts vehicles flow speed on the specified geometric condition, traffic composure, and evaluates the imposed costs to the road users; (2) the fuel consumption model, which estimates needed propulsive force and anticipated fuel for vehicles passing through the road; and (3) the pavement rehabilitation cost model considering two main constraints of existing pavement condition and project line elevation. The developed pavement rehabilitation model proposes the best solution for pavement rehabilitation practice and computes associated costs. Particle Swarm Optimization (PSO) is used to find the optimum solution in a minimization problem search space. The proposed model is applied to a real-world case study. Results show that there is an extremely less tendency for change, even with the existence of adverse geometric conditions, when there is a relatively good pavement condition. In the case of deteriorated pavement conditions, economic justification for geometric modification is required.

Updated data on the current seismicity of the White Sea and the Karelian region during the period 2005–2016

This article is the result of previous studies to clarify the seismicity of the White sea, supplemented by similar studies on the continental part of the Republic of Karelia. The relocated catalog of earthquakes was created for the period from 2005 to 2016 for White Sea and the Karelian region. With the help of proven methods, the parameters of the epicenters of identified earthquakes were relocated and a map of current seismicity was obtained. The parameters of the epicenters were specified using BARENTS travel-time model, a single methodological approach (using Generalized beamforming) and all currently available source data and bulletins of Russian and foreign seismic stations. The obtained seismic catalog allowed us to identify the main patterns of the distribution of current seismicity in the White Sea region. Seismicity of the White sea and the Karelian region is characterized as low-magnitude (generally of low magnitude with ML<2.0). Most earthquakes in the White Sea are characterized by a focal depths up to 20 km. Analysis of catalog shows that the majority of earthquakes are concentrated in the north-western part of the defined area, in the continental part of Karelia and Kandalaksha graben. Some earthquakes were recorded in the eastern and central part of the White sea.

Optimising two dwell point policies for AS/RSs with input and output point at opposite ends of the aisle

Automated storage and retrieval systems (AS/RSs) are widely used for storing and retrieving products in all types of warehouses. Dwell point policy is a vital control policy that can greatly affect the performance of AS/RSs. In this paper, we study dwell point policies in AS/RSs with input and output stations at opposite ends of the aisle. We first propose two dwell point policies. We find that five existing dwell point policies in the literature are special cases of exactly one of our policies. We then develop expected travel time models for the proposed policies, solve these models with the objective of minimising expected travel time, and obtain closed-form solutions for the optimal dwell location(s). We prove that one proposed policy dominates the other in terms of expected travel time. Numerical experiments are performed to quantify the percentage gap of expected travel time between the proposed policies and policies in the literature. We find that, in some situations, the better proposed policy can achieve up to 8%–10% reduction in expected travel time in comparison with the best literature policy. A real-data case study validates that these situations arise with high probability in typical daily warehouse operations.

Reliable vehicle routing problem in stochastic networks with correlated travel times

This study is motivated by the fact that travel times on road networks are correlated. However, all existing studies on the vehicle routing problem share a common simplifying assumption that arc travel times are independently distributed. In this paper, we address a variant of the vehicle routing problem with soft time windows in which travel times are treated as correlated random variables. To this end, correlations among arc travel times are modeled by a variance–covariance matrix. We use a mathematical model in which penalties are incurred for early and late arrival at each customer (violation of time window constraints). A Max–Min ant colony system is hybridized with a tabu search algorithm to solve the model. Results show that ignorance of correlations among arc travel times can significantly lead to inefficient solutions to the vehicle routing problem in stochastic networks. We also conduct an exploratory analysis of real travel time data. The results of the analysis demonstrate that travel times are significantly correlated and the shifted log-normal distribution is an appropriate candidate for modeling travel time uncertainty.

Determining time-dependent minimum cost paths under several objectives

As the largest contributor to greenhouse gas (GHG) emissions in the transportation sector, road freight transportation is the focus of numerous strategies to tackle increased pollution. One way to reduce emissions is to consider congestion and being able to route traffic around it. In this paper we study time-dependent minimum cost paths under several objectives (TDMCP-SO), in which the objective function comprises GHG emissions, driver and congestion costs. Travel costs are impacted by traffic due to changing congestion levels depending on the time of the day, vehicle types and carried load. We also develop time-dependent lower and upper bounds, which are both accurate and fast to compute. Computational experiments are performed on real-life instances that incorporate the variation of traffic throughout the day, by adapting Dijkstra’s label-setting algorithm according to different cost computation methods. We show that explicitly considering first-in, first-out (FIFO) consistency using time-varying speeds allows the efficient computation of tight time-dependent bounds. Our computational results demonstrate that the TDMCP-SO is more difficult to solve to optimality but the proposed algorithm is shown to be robust and efficient in reducing the total cost even for large instances in an environment of varying speeds, outperforming those based on the link travel time model and on the smoothing method according to each optimization objective, flexible departure times, and different load patterns.

Distance and Travel Time Modeling in High-Level Picker-To-Part Systems (3-D Warehouses)

This article describes new minimum travel time formulations for the picker routing problem (PRP) in 3-D warehouses based on real operating conditions, such as height reference levels, to leave aisles and to pick devices with simultaneous and sequential movements. This study validated the proposed formulations through an experimental design, statistical analysis based on ANOVA, and comparison of means. This research proposal allows for improving order picking models for 3-D warehouses by including appropriate travel time formulations related to vertical and horizontal movements and height reference levels to leave aisles, which affect the objective functions involving travel time.

Modelling Travel Time After Incidents on Freeway Segments in China

The reduction in incident-induced delays on freeways is a main objective of transportation management. The use of travel time estimation model for freeway segments is an important method for estimating delays resulting from incidents on freeways. In this study, freeways with temporary partial lane closures were considered to simulate traffic accidents occupying lanes. Travel time, traffic volumes, and speeds under various traffic conditions on a few typical Chinese freeway segments under regular and simulated accident conditions were investigated through field experiments. The collected traffic data collected were used to establish travel time models based on the Bureau of Public Roads (BPR) function for basic freeway segments under both regular and accident conditions, and to obtain the model parameters. The results demonstrate that the calibrated BPR models established in this study fit the data well. In addition, this study proposes an application method for the established travel time models by which variations in travel time can be estimated rapidly and easily. The results of this study can be used to reduce travel time for road users and contribute to decision making of transportation management systems to improve traffic efficiency after incidents.

Analyzing distributions for travel time data collected using radio frequency identification technique in urban road networks

Travel time distribution studies are fundamental for supporting transportation system reliability studies, particularly for urban road networks. However, such studies are generally based on travel time data sets with limited sample sizes, which provide inconsistent findings. In this paper, a large amount of travel time data collected from the emerging radio frequency identification (RFID) technique are used to conduct empirical investigations and estimations of travel time distributions, and three major findings are determined. First, travel time data are shown to have a complex statistical structure: the travel time distribution is in general peaky, multi-modal, and skewed to the right, which cross validates findings shown in previous publications. Second, unimodal distribution models are shown to be unable to capture the complex statistical dynamics embedded in the travel time data; therefore, a multistate distribution model is more appropriate for modeling travel time distributions. In this respect, a three-component gaussian mixture model (GMM) is tested and results consistently outperform those of unimodal distribution models. Finally, the aggregation time interval is shown to have a trivial effect on the shape of travel time distributions: the travel time distribution is stable under different aggregation time intervals. Future work is recommended to investigate further travel time variabilities and travel time distribution estimations.