FIELD OF THE INVENTION

The present disclosure relates to traffic control systems, particularly to a system for predicting traffic flow patterns and associated features.

BACKGROUND

Traffic congestion poses serious challenges for city infrastructure facilities and also affects the socio-economic lives of residents due to time wasted whilst waiting in traffic. The problem of traffic optimization is challenging, with increasing impact due to the increase in the number of vehicles on the roads and congestion on the streets, which may cause major economic losses and high levels of pollution in cities.

Fixed time allocation systems are still used to control traffic lights in some cities. However, these systems may lead to inefficient operations when there is a low throughput of vehicles passing, which may cause traffic jams. The major disadvantage of these systems is that they do not account for how the environment evolves.

Many approaches for modelling traffic have been studied, with the aim of optimizing traffic congestion based on traffic patterns. Although some of the models and solutions that have been proposed are complex and sophisticated, traffic is typically very agile and the behaviour changes rapidly, particularly when there are events, such as accidents, on the road. Moreover, each intersection in a city will typically have a different layout and/or throughput, which limits the deployment of specific solutions. For these reasons, most solutions to optimize traffic and control the traffic lights times to reduce traffic jams or increase the throughput are not effective. Adaptive traffic control systems are deployed in many cities to adjust signal timing based on real-time traffic conditions at a single intersection or multiple neighbouring intersections. More recent adaptive traffic light management systems adjust signal timing (cycle length, phase split and offset) based on real-time traffic conditions at a single or multiple neighbouring intersections. This is done using traffic data from various sensors (such as cameras, embedded induction loops and speed sensors).

SCATS, as described at www.scats.com.au/files/an_introduction_to_scats_6.pdf, is an example of a decentralized dynamic control system that adjusts offsets between adjacent intersections belonging to the same subgroup. Each subgroup of intersections is coordinated by one critical intersection and each intersection adjusts its signal phase independently based on local traffic conditions. SCATS is a two-level hierarchical adaptive traffic signal platform that adjusts three main parameters: cycle length, phase split and offset based on changes in traffic flow from the previous cycle. The adjustment regional computers receive traffic measurements from induction loop detectors and compute degrees of saturation and link flows used in the adjustment.

SCOOT, as described at www.ukiOads.org/wcbfilcs/tal04-95.pdf, is a model-based adaptive traffic control system. It uses an online traffic behavior model to build cyclic flow profiles using on-street detector data. The model output is the input for three optimizers that make small adjustments on phase split, offset and cycle time in a way that disturbance to traffic is minimal.

UTOPIA, as introduced in V. Mauro and C. Di Taranto, “UTOPIA”, IFAC Control, Computers, Communications in Transportations (1989), is a self-calibrating traffic control system that has a hierarchical distributed architecture. The higher level central system is responsible for setting the network control strategies. The lower level (local intersection controllers deploying SPOT software), constrained by the network control strategy from the higher level, implements signal timings using real-time local traffic flow based on detectors installed upstream and downstream of the traffic intersections.

However, adjusting traffic signal timing based on observed traffic flow parameters from previous cycles at a single intersection, or even at neighbouring intersections, may not provide an optimal solution because adjusting the timing of traffic lights at one intersection may highly influence the traffic flow at other intersections, creating traffic jams. Such a system needs to have real-time insight of the traffic at the city-level by online analysis of streams of traffic data received from sensors to extract major flow patterns, compute traffic metrics, predict future flow patterns, and detect non-recurrent events such as accidents that might highly influence the traffic. This can be expensive in terms of the processing resources required. It is desirable to develop a method for traffic prediction that overcomes these problems.

SUMMARY

According to a first aspect there is provided a system for determining and/or predicting flow patterns of traffic and forming outputs dependent thereon in dependence on data received from a plurality of sensors each configured to acquire data at a respective location in a spatial region having a known road layout, wherein the system is configured to: receive data from the sensors; aggregate the received data with historical data from the sensors in the spatial region in dependence on the road layout; in dependence on the aggregated data, determine and/or predict traffic flow patterns at the locations; and analyse the received data to identify deviations between the received data and the determined and/or predicted traffic flow patterns, and/or analyse the determined and/or predicted traffic flow patterns to identify vehicle-level features therein; and output the said deviations and/or vehicle level features.

The system may be configured to perform one or more of traffic anomaly detection, delay computation, traffic jam detection and offset computation in dependence on the output deviations and/or vehicle level features. This may allow events, such as accidents, to be detected and their impact on the traffic in the region to be reduced.

The vehicle-level features may comprise the number of vehicles at a location and/or a queue length of vehicles at a location. This may provide an insight into future traffic conditions. The data received from each of the sensors may comprise a dataseries of values. The data received from each of the sensors may comprise a timeseries of values This may allow for analysis of the received data with time and/or traffic prediction over an arbitrary horizon.

The system may be configured to predict traffic flow patterns by implementing a learned artificial intelligence model. This may allow for more accurate flow prediction in a particular region.

The system may be configured to aggregate the received data with historical data from the sensors hierarchically across respective sub-regions of different size within the spatial region. This may allow for more accurate flow prediction. The respective locations may be respective traffic intersections. Each intersection may comprise at least three intersecting vehicle pathways and traffic flow patterns may be predicted in further dependence on at least one of: the number of cars entering an intersection in each direction, the stopping probability of vehicles at the intersection, and the probability of vehicles going in each direction at the intersection. This may allow the influence that intersections have on each other in a spatial region to be included in the traffic predictions.

The determined and/or predicted traffic flow patterns may be used to determine traffic lights plans for traffic signals located at the intersections. The system may therefore be used to control traffic signals at multiple locations, which may help to avoid traffic congestion in the region.

The system may be further configured to determine traffic light plans for traffic signals located at the intersections by optimizing at least one traffic metric at the intersection. The at least one traffic metric may be one or more of traffic throughput, queue length and wasted green time of the traffic signals. This allows traffic flow in the region to be optimised, which may help to avoid traffic jams.

The system may be further configured to predict the pathways of at least two vehicles in the region and, if these predictions indicate that the vehicles will pass through the same location at the same time, adjust the timings of traffic signals to temporally interleave the pathways. This may help to avoid traffic jams that might be caused when these vehicles meet each other.

The system may be deployed across more than one cloud-based entity. Components of the system may therefore be split between public and private clouds.

Each of the sensors may comprise one of a camera, a weather sensor, a pollution sensor, a noise sensor and an induction loop. This may allow the number of vehicles at a particular location to be measured directly or inferred.

According to a second aspect there is provided a method for implementation at a system for determining and/or predicting flow patterns of traffic and forming outputs dependent thereon in dependence on data received from a plurality of sensors each configured to acquire data at a respective location in a spatial region having a known road layout, wherein the method comprises: receiving data from the sensors; aggregating the received data with historical data from the sensors in the spatial region in dependence on the road layout; in dependence on the aggregated data, determining and/or predicting traffic flow patterns at the locations and analysing the received data to identify deviations between the received data and the determined and/or predicted traffic flow patterns, and/or analysing the determined and/or predicted traffic flow patterns to identify vehicle-level features therein; and outputting the said deviations and/or vehicle level features.

BRIEF DESCRIPTION OF THE FIGURES

The present disclosure will now be described by way of example with reference to the accompanying drawings. In the drawings:

Figure 1 shows an overview of an example of a traffic reasoner system. Figure 2 illustrates a functional example of online multi-metric traffic optimization.

Figure 3 shows an overview of a smart traffic management system incorporating the traffic reasoner as described with reference to Figure 1.

Figure 4 illustrates the deployment of the system across public and private clouds.

Figure 5 shows a method for implementation at a system for predicting flow patterns of traffic and forming outputs dependent thereon.

Figure 6 shows the dominant flows at two different time instants, tl and t2.

Figure 7 shows an example of a dominant flow use case.

Figure 8 shows online multi-metric traffic light optimization gains. DETAIFED DESCRIPTION OF THE EMBODIMENTS

The present disclosure relates to a system and method which can be used to optimize traffic lights plans in a spatial region, ranging from a single location or intersection up to a city level. The system may advantageously use a cloud-based big data distributed stream processing solution. The system can determine and/or predict flow patterns of traffic and form outputs dependent on the flow patterns by receiving data from a plurality of sensors each configured to acquire data at a respective location in a spatial region having a known road layout. The system aggregates the received sensor data with historical data from the sensors in the spatial region in dependence on the road layout of the region. From this aggregated data, the system can determine and/or predict traffic flow patterns at the locations and analyse the received data to identify deviations between the received data and the determined and/or predicted traffic flow patterns. This allows the system to detect anomalies in the patterns, such as accidents, which may cause traffic jams. The system can also analyse the determined and/or predicted traffic flow patterns to identify vehicle-level features, such as the number of vehicles at a location or intersection, or the queue length of vehicles at a location or intersection, in the future.

Figure 1 presents the overall architecture of the traffic reasoner system 100.

Traffic metrics are received as data streams, shown generally at 101, which are sequences of events (for example, tuples containing various types of data, such as the number of cars, speed of cars etc.) that are collected from various sources. For example, data may be collected from sensors in cars, or from sensors such as cameras and induction loops embedded on the roads, or from other data sources such as WiFi-access points, pollution sensors and noise sensors, in a chronologically ordered fashion.

Data streams may be received from sensors at a location or intersection in a sector of the spatial region under consideration. Such sectors are illustrated at 102, 103 and 104 in Figure 1. The data received from each of the sensors therefore comprises a dataseries of values, which may in some examples be a timeseries. Video cameras and inductions loops may measure traffic flow (i.e. the number of cars passing a location in a certain time period) directly. Traffic flow may be inferred from the parameters measured by other types of sensors, such as pollution sensors, which may measure the amount of CO, NC or NO, which may be related to the number of vehicles at the location of the sensor.

The roads layout service 105 provides detailed information about the layout of the roads and intersections in the spatial region under consideration. This may include the type of intersection, the number of lanes per direction, the length of roads or lanes, the maximum speed on each lane, and the number of allowed driving directions for each lane or road. It also provides layout details of intersections, such as incoming and outgoing roads and the neighbouring intersections for each intersection. ‘Neighbouring’ refers to the explicit connection (via roads or edges) between two intersections. An intersection that is directly adjacent to an intersection of reference is neighbouring at space lag 1 (1 hop away). The further an intersection from the intersection of reference, the higher the spatial lag. The roads and intersections layout can be represented using Extensible Markup Language (xml) format. The road layout service can be built using Java or C++ to load the xml fdes and build and initialize a data structure representing the layout.

Each intersection comprises at least three intersecting vehicle pathways. The road layouts service may indicate that an intersection at a particular location is a highway intersection (for example, 4 directions, 5-6 lanes per direction), a T-type intersection (for example, 3 directions, 3-4 lanes per direction), or a regular intersection (for example, 4 directions, 3-4 lanes per direction).

The aggregation service 106 collects the data from the traffic sensors. The received data is aggregated with historical data from the locations, shown at 107, and processed to provide real time and historic intersection and city-level traffic insights and analytics to the other traffic reasoner components. As shown in Figure 1, the aggregator 106 has a hierarchical structure, with aggregation at the sector, region, and global level. These sub-regions have different sizes (respectively increasing sizes for sector, region and global level) within the spatial region under consideration (i.e. a sector is smaller than a region and a region is smaller than the global level). The sector aggregators receive traffic data and other data streams in real time from deployed sensors by subscribing to Apache Kafka or a similar low-latency data feed platform. The received data may be aggregated at the lane, road and intersection levels based on connection data from roads layout service. The sector aggregators forward the computed data to the global aggregator directly or through region aggregators to compute a global aggregation at the city level. The service can be built using Java or C++ with RPC support to communicate with the traffic intelligence agent 110 and the added value services 109. The aggregation service 106 may therefore aggregate the received data with historical data from the sensors hierarchically across respective sub-regions (i.e. sectors, regions) of increasing size within the spatial region under consideration (i.e. the global level). If the spatial region under consideration is small, with a small number of intersections, the global aggregator may suffice and the hierarchical aggregation is not performed. In this case, data is aggregated for the spatial region as a whole. The system can therefore be deployed on a small set of locations or intersections, in an area of a city, or at the city level.

The online flow detection service 108 extracts flow patterns from the aggregated data in real time. Flow patterns represent vehicles following the same route or path for a certain period of time or for a certain distance. Detecting the dominant traffic flow patterns is very useful for cross intersection city-level traffic optimization because multiple flow patterns might overlap at some point or constrain each other on an intersections, which may result in a traffic jam. Computed flow patterns are also useful in city-level traffic optimization and to analyze the overall performance of the traffic optimization system. Flow patterns also allow for the adjustment of traffic light offsets to create green waves (i.e., when a series of traffic lights are coordinated to allow continuous traffic flow over several intersections). The online flow detector service can be implemented by extending the classical architecture of a stream operator, such as a Flink process function. The stream operator can receive the number of vehicles arriving at each intersection from all of the neighbouring intersections in real time, computes the probability for stopping and continuing in each direction, and updates the previously observed flow patterns.

Added value services, shown at 109, compute traffic features and patterns based on the data received from the aggregation service 106. This component of the system may perform, for example, online anomaly detection that detects non-recurrent events such as accidents. It may also predict vehicle-level features, such as the number of vehicles and/or queue length in the following cycles, based on real-time updates from the aggregation service. In dependence on the aggregated data and predicted traffic flow patterns at the locations, the system can identify deviations between the received data and the predicted traffic flow patterns and/or analyse the predicted traffic flow patterns to identify the vehicle-level features from the flow patterns. The system can output the said deviations and/or vehicle level features to provide the added value services shown at 109.

Traffic flow patterns may be predicted in further dependence on at least one of the number of cars entering an intersection in each direction, the stopping probability of vehicles at the intersection, and the probability of vehicles going in each direction at the intersection. In some implementations, the system may be configured to predict traffic flow patterns by implementing a learned artificial intelligence model, using known techniques.

The traffic flow patterns may represent vehicles which follow the same trajectory for some time. In the system described herein, traffic flow patterns may be predicted by estimating likelihoods of paths. Traffic flow patterns can be computed based on the number of cars entering an intersection from all the directions in addition to probability of vehicles stopping and the probability of vehicles going in each direction. These traffic flows patterns can be used for cross intersection traffic light optimization to avoid jams caused by different overlapping flow patterns or flow patterns of different vehicles that constrain each other at intersections. These traffic flow patterns are important for traffic optimization because traffic congestion can be considered as a result of major overlapping flow patterns across the city (for example, from vehicles commuting from residential to commercial or work areas). Understanding such flows enables optimization techniques going beyond per- intersection methods.

In one implementation, the system can predict the traffic flow patterns for at least two vehicles in the region and, if these predictions indicate that the vehicles will pass through the same location at the same time, adjust the timings of traffic signals to temporally interleave the pathways of the vehicles (i.e. ensure that the pathways of the vehicles do not meet at the same place at the same time). This may help to avoid traffic jams that might be caused when these vehicles meet each other.

The aggregation of real time and historical traffic data in the aggregation service 106 and the extraction of traffic flow patterns in the flow detector 108 therefore enable the deployment of a range of intelligent traffic services, such as AI analytics, delay computation, event or anomaly detection (such as the detection of accidents) and traffic predictions, which may be used in a traffic lights simulator (shown at 112 in Figure 1), or in an autonomous driving simulator.

The traffic intelligence agent, shown at 110, optimizes in real time the offline optimized plans based on a global traffic optimization strategy. This can be done using city-level traffic data updates from the aggregation service and flow detection in addition to local and global perspectives and correlations from the added value services, such as region correlation and classification, intersection clustering, green waves and anomaly detection. The traffic intelligence agent can adjust the optimized offline traffic plan in real time based on single traffic metrics (such as throughput, queue length or wasted green time). Anomaly patterns detected in real time by the added value services 109, such as accidents and jams, can also be used to adjust the plans.

The optimization of offline plans based on multiple metrics may further improve performance. The online multi-metric optimizer 111 collects traffic metrics, models them in search states, makes predictions about the future traffic flow and selects from the search states the control sequence to enhance the road traffic flow. The online multi-metric traffic optimizer adjusts the offline optimized plans based on multi-metrics such as maximizing throughput, minimizing queue length and minimizing wasted green time of traffic lights. Therefore, the optimization of the traffic can be performed continuously and in real-time from an incoming stream of traffic metrics to adjust the offline optimized plans based on multiple metrics.

Figure 2 illustrates an example of the function of the online multi-metric traffic optimization module 200. In this example, queue length 201 and vehicle count 202, in addition to the output of the flow detection service, shown at 203, are used by the online multi-metric traffic optimizer to adjust traffic light plans (shown as final green plan). Here, the online multi-metric component is implemented starting from a process function operator in Flink. This component is aided by a source to read the data from the aggregation component and by a sink to output the adjusted plans. These components together for the stream topology that executes the logic for optimizing the traffic online. The internal logic of the online multi metric is composed of multiple modules that can be called based on user configuration, each applying a logic for modelling the traffic metric, making a forecast based on it and proposing a plan independently. The proposed plans are then merged based on a user defined strategy.

The system can therefore optimize traffic light plans for traffic signals located at the locations or intersections by optimizing at least one traffic metric at the location or intersection.

Figure 3 shows an overview of a smart traffic management system incorporating the traffic reasoner of Figure 1. As shown in Figure 3, using traffic data collected from a region 302, the traffic intelligence agent and the online multi-metric traffic optimization components of the traffic reasoner system 100 communicate the refined perspective of traffic light timing with online controller agents 301 to adjust and deploy a new traffic light plan to the region 302. The city level traffic insights created by the traffic reasoner 100 can also be used by traffic analytics visualization tools and dashboards, as shown at 303, to give traffic authorities both a detailed and big picture of the traffic situation in the city. The output of the aggregation service of the system 100 may also be provided to a third party data consumer, shown at 304. The traffic reasoner, with its aggregation service, flow detector, and added value services can therefore provide real time city level traffic insights for traffic analytics visualization tools and dashboards in addition to third party traffic data consumers.

The traffic reasoner can be deployed on a centralized system, a distributed architecture, or alternatively may be split between more than one cloud-based entity. Advantageously, the components of the proposed traffic reasoner can be deployed and split between public cloud and governmental clouds that control the traffic lights. In one example, the sector and region aggregators are deployed on the governmental cloud and the global aggregator on the public cloud. As shown in Figure 4, the governmental cloud 401 may collect the data from the traffic sensors and cameras, and may deploy the sector and region aggregators, in addition to the online traffic intelligence agent and multi-metric optimizers used to optimize the traffic light plans. The public cloud 402 may then hold the global aggregator service, flow extraction and management service and the added value services. Other components may be deployed and split between more than one cloud-based entity (such as public and governmental clouds) as appropriate. The system may therefore be implemented online.

Figure 5 shows a method for implementation at a system for predicting flow patterns of traffic and forming outputs dependent thereon in dependence on data received from a plurality of sensors each configured to acquire data at a respective location in a spatial region having a known road layout. At step 501, the method comprises receiving data from the sensors. At step 502, the method comprises aggregating the received data with historical data from the sensors in the spatial region in dependence on the road layout. At step 503, the method comprises, in dependence on the aggregated data, predicting traffic flow patterns at the locations and analysing the received data to identify deviations between the received data and the predicted traffic flow patterns and/or analysing the predicted traffic flow patterns to identify vehicle-level features therein. At step 504, the method comprises outputting the said deviations and/or vehicle level features.

The traffic reasoner therefore implements a method that collects traffic data in real time from sources such as embedded induction loops in roads and cameras in addition to other data sources, such as noise and pollution sensors. The aggregator computes detailed intersection and city level traffic insights based on the layout of roads in the region under consideration. The system enables online detection of traffic flow patterns, which can be used for real-time adjustment of offline optimized traffic light plans at a city-level, for example by creating green waves. The system enables online adaptability of the scheduling control based on real time up-to-date view of the environment and a multi-metric optimization algorithm.

The system may comprise a processor and a non-volatile memory. The system may comprise more than one processor and more than one memory. The memory may store data that is executable by the processor. The processor may be configured to operate in accordance with a computer program stored in non-transitory form on a machine readable storage medium. The computer program may store instructions for causing the processor to perform its methods in the manner described herein. As discussed above, the system may advantageously be implemented in the cloud.

In order to assess the capabilities of the system described herein, the results of two case scenarios are shown in Figures 6 to 8. Simulation of Urban Mobility (SUMO, version 0.32.0 - http://sumo.dlr.de/) was used as the simulation environment and the simulations were run on a PC with 24G of RAM.

In the first scenario, illustrated in Figures 6 and 7, the dominant flow patterns (vehicles following the same path for a period of time) were extracted based on historical and real time traffic data from the aggregation service in addition to the road layout during a specific window of time in Shenzen city, from locations a-h. These flows can be used to optimize traffic lights and adjust their offsets to reduce jams and create green waves, and to build analytical dashboards. The traffic model for Shenzhen was provided by Shenzhen Police department. In this small-scale scenario, eight traffic lights systems were studied controlling: a highway intersection (4 directions, 5-6 lanes per direction), a T-type intersection (3 directions 3-4 lanes per direction), and a regular intersection (4 directions, 3-4 lanes per direction). This allows for 30 different routes, on which vehicles travels with a certain probability. Other modelling details, such as the fact that right turns are always green and that the simulation can run indefinitely, were included in the simulation. Figures 6 and 7 show the dominant flow patterns that were extracted at two different instants, tl and t2.

In the second scenario, illustrated in Figure 8, the online multi-metric traffic light optimization system was applied on data from seven intersections of Tianjin city. The simulation was run during the morning rush hours using an offline optimized reinforcement learning model and a real time adjusted model of the offline optimized plans. In this small-scale scenario, seven traffic lights systems were considered controlling: a highway intersection (4 directions, 2-4 lanes per direction), a T-type intersection (3 directions 2-3 lanes per direction), and a regular intersection (4 directions, 2-4 lanes per direction). Use of the online multi-metric adjusted model provided a reduction of 13.82 % in the average delay time.

The present disclosure enables a city-level smart traffic management system for online traffic light model optimization for multiple intersections, which may improve traffic flow in a spatial region. Based on the aggregated data, the traffic reasoner enables the evaluation of traffic quality and traffic diagnostics across regions of a city or at the city level. It also enables the real-time computation of traffic flow patterns that represent vehicles following the same path for a certain distance. The created flow patterns are useful for real-time adjustment of offline optimized traffic light plans at a city-level by creating green light waves, such that vehicles can drive through several intersections without having to stop at a red light. The real-time and historical traffic aggregated data also enables the deployment of a range of intelligent traffic services, which allows traffic insights, patterns, cross-location or cross-intersection correlations and knowledge to be extracted, such as dominant traffic flows, traffic quality, anomaly detection (such as accidents), AI analytics, traffic prediction and delay computation. The system can therefore enable the evaluation of traffic quality and traffic diagnostics across regions or at the city level.

The system also enables online adaptability of the scheduling control based on a real-time up- to-date view of the environment and a single or multi-metric optimization algorithm. The traffic reasoner provides the necessary analytics data for building real-time traffic visualization tools and dashboards, which may allow for the efficient monitoring, management and optimisation of road traffic at the city-level.

The traffic reasoner solution described herein can provide a detailed insight about a current traffic situation and can predict traffic flow using online statistical and machine learning techniques. The real-time collected data and traffic flow predictions can advantageously be used by traffic intelligence agents and online multi-metric traffic optimization techniques to adjust traffic light timings to reduce traffic jams and increase the flow at a particular location or intersection.

Multiple flow patterns of vehicles following different trajectories might overlap at some point or constrain each other on an intersection, creating a jam. Detecting major flow patterns and adjusting traffic light parameters based on these detections can help to increase the throughput and may reduce delays. Coordinating plan offsets across adjacent intersections to create green waves may reduce the duration of trips and delays and may help to decrease the number of stops of vehicles at traffic lights to a minimum.

Non-recurrent events such as accidents are a major cause of traffic jams. The system described herein allows for the continuous monitoring of flows across intersections that is necessary to detect these incidents in real-time and can adapt the traffic light sequences to decrease jam in the area of the event, trigger the re-routing process, and start a back-pressure mechanism to avoid spreading of the congestion.

Most prior art systems are deployed on governmental workstations and computers that manage the traffic lights. The services and components of the system described herein may advantageously be deployed and split between more than one cloud-based entity, such as between a public cloud and a governmental cloud, allowing for the benefit of cloud computing advantages and processing power.

The system is applicable to smart cities’ infrastructures, as well as to traffic light management, scaling from a small sector of the city with a small number of intersections to the level of a whole city.

The applicant hereby discloses in isolation each individual feature described herein and any combination of two or more such features, to the extent that such features or combinations are capable of being carried out based on the present specification as a whole in the light of the common general knowledge of a person skilled in the art, irrespective of whether such features or combinations of features solve any problems disclosed herein, and without limitation to the scope of the claims. The applicant indicates that aspects of the present disclosure may consist of any such individual feature or combination of features. In view of the foregoing description, it will be evident to a person skilled in the art that various modifications may be made within the scope of the disclosure.