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Journal on Vehicle Routing Algorithms

, Volume 1, Issue 1, pp 33–46 | Cite as

Commuters’ traffic pattern and prediction analysis in a metropolitan area

  • Suresh Chavhan
  • Pallapa Venkataram
Regular Paper

Abstract

A metropolitan area is an area with dynamic demands and is one of the main indicators of economic growth of nation. It involves the complexity of efficient analysis and prediction of patterns of growth or decline of traffic volume and patterns of resource utilization with respect to time and place. To solve these complexities, we propose agent-based commuters’ traffic pattern and prediction analysis model in a metropolitan area. The proposed system model is capable of analyzing and predicting the patterns of commuters’ traffic flow volume and resource utilization in each zone and region, using the population density, availability of resources, type of place, time period, and commuters’ and vehicles’ arrival rates. The proposed model provides qualitative form of traffic; increases the probability of measure of unpredictable information; and aids in emergency traffic planning and route-finding services. The result shows the effectiveness of the model at different time periods in a day for forecasting of the resource utilization and changes in traffic volumes in zones and regions in the metropolitan area.

Keywords

Agents Commuters Traffic Prediction Resource utilization Metropolitan area 

1 Introduction

In recent years, rapid development and urbanization of metropolitan areas resulted in the increase in traffic density, uncertain commuter arrivals, resource scarcity, etc. Metropolitan areas are complex and dynamic with respect to their demands, time and place. The traffic in metropolitan areas varies across location, time, infrastructure facilities, type and conditions of resources available. The growth of traffic is directly linked with growth of accidents and fatalities [1]. The deficit resources and accidents account for significant share of recurring delays. As the traffic increases, commuters feel less safe to use the streets [2, 3]. Resources (for example fuel) get wasted during traffic congestion and lane blockage in a metropolitan area. Therefore, commuters road safety, resource utilization, resource allocation, and traffic volume pattern predictions are much important in many intelligent transportation systems (ITSs) applications such as traffic control, traffic management, and route guidance [2, 4, 5, 7, 8, 9, 13]. Hence, traffic and resource utilization prediction has garnered considerable attention in the field of transportation studies.

The greatest challenges in the metropolitan areas are: traffic and resource prediction, and management of traffic and scarcity of resources, especially during the disaster situations. These challenges can be met by developing the mathematical model of metropolitan area using spatio-temporal data, resource information and commuters’ arrival rates. The model analyzes and predicts accurate patterns of traffic, resource requirements and traffic conditions over time and space at every zones and regions in a metropolitan area. The mathematical model provides complete behavior of metropolitan area, which makes use of real-time traffic data at specific location and constant intervals of time [10, 11, 18], for analysis and prediction of pattern of traffic growth or decline and resource utilization.

In the literature, most of the mathematical models are of the comparative static type, although quasi-dynamic. The objective of this paper is to develop a mathematical model, which is capable of analyzing and predicting patterns of commuters’ traffic flow volume and resource utilization in zones and regions, using population density, place, time period and commuters’ arrival rates as inputs. The developed analysis and prediction model is adaptable to any kind of situation, place and time period for providing more reliable prediction accuracy for predicting patterns of resource utilization and commuters traffic flow volume in the metropolitan areas. The proposed model provides the qualitative form of traffic rather than the quantitative form; increases the measure of unpredictable information; and it also provides emergency traffic planning and route-finding services in metropolitan areas. Depending upon predicted value the commuters’ choice model will choose an optimal path from the source to destination in a metropolitan area.

The organization of the rest of the paper is as follows: Sect. 2 presents some of the existing works; definitions and concepts are given in Sect. 3; Sect. 4 presents the proposed mathematical modeling of the metropolitan public transportation system; simulation and analysis results are given in Sect. 5; and conclusions are drawn in Sect. 6.

2 Existing works

In the literature, many traffic analysis and prediction models have been developed. The existing traffic prediction methods are classified as parametric methods [e.g., time series analysis (TSA) and support vector regression (SVR)], non-parametric methods [e.g., k nearest neighbor (KNN) model] and artificial intelligence methods [e.g., artificial neural network (ANN) method].

The authors in [12] extensively reviewed many statistical and machine learning methods to predict short-term traffic flow, and they have proposed 2-new SVR models for accurate prediction and efficient computation.

The TSA model, called seasonal autoregressive moving average model presented in [12], is used for performing highly competitive for forecasting during highly congested periods. The authors in [13], presented an application of a supervised statistical learning technique called on-line-support vector regression (OL-SVR) for short-term freeway traffic flow prediction under both typical and atypical conditions. These parametric methods are more time consuming and costly for choosing and setting up appropriate parameters. Hence, these methods are difficult to manage immediate change in the road conditions and new road structure compared to proposed model in this paper.

Authors in [14, 15] proposed short-term traffic prediction method using the KNN algorithm. The multivariate non-parametric regression traffic congestion estimation model makes future prediction based on speed, traffic flow and occupancy measured at loop detector on a per minute basis. If we consider large amount of historical data with the currently available data the KNN method becomes inefficient, because low computing speed and parameters adjustment method are not flexible enough to process.

Work in [16] described a fuzzy neural network known as the POPFNN-TUR for traffic flow analysis and prediction. They have demonstrated the comparative analysis of POPFNN-TVR and conventional feed forward neural network using back propagation learning.

The authors in [17] proposed an urban traffic flow prediction system using a multifactor pattern recognition model, which combines the Gaussian mixture model clustering with an artificial neural network. This system forecasts traffic flow by combining road geographical factors and environmental factors with traffic flow properties from ITS detectors. ANN is not flexible in the case of huge information (e.g., unanticipated road conditions and history information) and is popular as a good prediction method when the available information is less because ANNs are simulated on sequential machines, giving rise to a very rapid increase in processing time requirements as size of the processing information expands.

Work in [18] developed the method for real-time traffic prediction at a fine granularity over different time periods of a day by making use of advanced and smart transportation technologies. The method provides real-time route guidance and short-term traffic prediction from the point of view of network operators and commuters.

Zhang and Chang [19] demonstrated the use of entropy maximizing models in analyzing impacts of government policies and metropolitan planning. Models are simplified version of reality, and they constitute mechanisms for understanding city systems and for designing the future city.

Work in [20] developed an optimization model formulated as an integer linear program. This model consists of two modules and they run sequentially, first determines the pickup locations of commuters and second determines route and schedule of each transit vehicle based on vehicle availability and patterns of commuters’ demand.

The authors in [21] analyzed the change of commuters’ pattern in railway networks at different time periods in weekdays and weekends. The objective is achieved using the proposed two data mining techniques, namely common orthogonal basis extraction (COBE) and joint and individual variation explained (JIVE).

Authors in [22] proposed the model of day to day traffic evolution based on strategic thinking and marginal decision rule. The proposed framework enables to capture both benefit and cost associated with route changes.

The driver seeks to maximize their perceived route costs. They analyzed theoretical properties, such as invariance, asymptotic stability, and relationship with rational behavioral adjustment process.

Work in [23] collected the traffic data through various sensors such as loop detectors, cell phones, probe vehicles, video cameras, Bluetooth, remote sensing and public transport smart cards. Using these data they have built a real-time traffic prediction model for arterial corridors.

As the metropolitan area’s traffic is very complex and dynamic in nature with respect to time and place, analyzing, processing and predicting the traffic-related information are also complex. The size of this complex problem expands and the existing methods, such as KNN, ANN, TSA and SVR, take more time for processing; do not adapt to dynamic change in the road conditions; and are of low computing speed. Hence, the existing methods are inefficient in analyzing and predicting the traffic pattern and resource utilization pattern in a metropolitan area. Therefore, we have developed analysis and prediction model, which is adaptable to any kind of situation, place and time period for providing more reliable prediction accuracy in predicting patterns of resource utilization and commuters traffic flow volume in metropolitan areas. The above-mentioned issues of the existing methods are resolved using proposed model with agent technology, because the static agent and mobile agents provide parallel processing of any kind of problem.

3 Definitions and concepts used

In this section, some of the relevant definitions and concepts used in the work are discussed.

Metropolitan area It is a densely populated urban core with more than one urban area. The territories share industry, infrastructure, and housing. It comprises multiple jurisdictions and municipalities: neighborhoods, townships, cities, exurbs, counties, districts, and even states. Metropolitan areas include one or more urban areas, as well as satellite cities, towns and intervening rural areas that are socio-economically tied to the urban core, typically measured by commuting patterns. The metropolitan area consists of many numbers of regions and zones, and these are geographically distributed in nature. The resource- and traffic-related information of each zone and region is also distributed in nature, and collecting and sharing of this distributed information in a metropolitan area is a very difficult task because this information is dynamic in nature, i.e., always changes with respect to time and place. In this paper, we use agents (both static and mobile) for collecting and sharing of these distributed information of zones and regions in a metropolitan area.

Agents The agents are self-contained and identifiable computer programs, bundled with three main components, i.e., data, code and execution state, and they perform actions on behalf of humans or others [6, 24]. The behaviors of agents are defined using the topology. The agents have interesting properties such as autonomy, communication skills, reactivity, mental notions, persistence, vitality, mobility, social ability and truthfulness [24]. The agents are categorized based on the nature of the task they would fulfill (user and service agent); nature of intelligence (user programmable, AI engineering and learning agent); and mobility of the agents (static and mobile agents). In the metropolitan area, the resource- and traffic-related information of each zone and region is distributed nature, and their values change continuously with respect to time and place. Hence, in this paper, we have used static and mobile agents for collection, analysis and allocation of these distributed information and decision-making in a metropolitan area.
  • Static agent (SA): the static agent’s mobility is static and hence it does not move in a heterogeneous network, which is deployed at the depot at each region in a metropolitan area. The SA creates mobile agents and dispatches to each zone in the region for collecting the resource- and traffic-related information. The SA analyzes these collected information and predicts the situation of the zones and region in a metropolitan area.

  • Mobile agent (MA): the mobile agents can move within a heterogeneous network. They can suspend their execution on an arbitrary point and transport themselves to another computer system. During migration the agent is transmitted completely, i.e., as a set of code, data, and execution state. At the migrated computer the agent resumes the execution at exactly the point where it was suspended before. The advantages of mobile agents in the distributed systems are [24] (1) reduce communication costs, (2) asynchronous execution, (3) direct manipulation, (4) dynamic deployment of software, and (5) easy development of distributed applications. The agent technology fulfills their desired goal by decomposing the tasks into subtasks and distributes and interacts among them. In this paper, the MAs migrate to each and every zone in regions of metropolitan area to collect resource information and traffic-related information and provides to the SA.

Static depot It is a place where vehicles are parked, maintained, scheduled, pick up and drop off commuters. The static depots may contain the internal and external parking, fueling point and fuel storage tanks, vehicle maintenance instruments and staffs, staff canteen, rest room, etc.
Dynamic depot It is a place where vehicles are parked for only a few minutes, and pick up and drop off commuters.
Fig. 1

Hierarchical analysis of metropolitan area

Fig. 2

System architecture at a depot

4 Proposed mathematical modeling of a metropolitan area

In this section, we discuss the proposed hierarchical analysis of the metropolitan area, system architecture, and mathematical model with respect to time, place, resource, commuters’ arrival rate, etc.

4.1 Hierarchical analysis of metropolitan area

The metropolitan area is divided into r regions and each region contains a depot (called static depot). Again, each region is subdivided into m zones, and they contain a depot (called dynamic depot). The hierarchical analysis of the metropolitan area is shown in Fig. 1.

The RoadSide units (RSUs), for example base stations and access points, are deployed along the roads at every zone in the region to provide seamless connectivity coverage for sending and receiving information. It greatly enhances timeliness of data collection and stores updated information of zone’s surrounding during communication with vehicles. A static agent (SA) deployed at every depot of region creates and dispatches mobile agents (MAs) to zones. The MAs migrate to the zones and communicate with RSUs, and during the communication they collect resource information and traffic-related information of zones, and provide this information to the SA. The SA receives all zones information of a region, which analyzes and predicts the situation, requirements, future problems and solutions, patterns of growth or decline of traffic flow volume and resource utilizations. The MAs’ local activities and interactions with RSUs in the zone, and SAs’ local activities and interactions in the region give rise to the global structure and network information of the zones and regions in the metropolitan area [6, 24].

4.2 Proposed system architecture

In this subsection, we describe the proposed system architecture as shown in Fig. 2, which is available at SAs in regions (i.e., at static depot). The proposed system architecture consists of ‘Spatio-Temporal Module’ and ‘Analysis–Prediction–Commuters’ Choice Module’ and are explained as follows:
  1. 1.

    Spatio-temporal module (STM): it consists of a finite set of points with location information, relationships between pairs of points, time-dependent attributes attached to points and relationships. This module attempts to capture dynamic behavior and complex statistical dependencies that can arise from the evolution of phenomena at many spatial and temporal scales. This module provides traffic data to the APCM in the form of spatial-time series and is collected at specific locations and at constant intervals of time for predicting the actual behavior and conditions of the regions.

     
  2. 2.
    Analysis–prediction–commuters’ choice module (APCM): it consists of three sub-modules and are explained as follows:
    • Analysis module: it uses information given by the STM and also history, resource information, and commuters’ arrival rate to analyze each and every zone and region in the metropolitan area.

    • Prediction module: it makes use of information given by the analysis module and it predicts the situation of each zone and region, such as patterns of expected resource utilization; patterns of growth or decline of traffic volumes; uncertain commuters’ arrival pattern; breakdown of vehicles; and so on.

    • Commuters’ choice module: it finds an optimal route based on the predicted patterns of traffic flow volume and resource utilization and travel time. It is explained in subsection 4.6.

     

4.2.1 Analysis of zones and regions in a metropolitan area

All zones and regions are analyzed for predicting the patterns of resource utilization, patterns of growth of commuters’ traffic volume, status and transit segment depending upon the following information:
  1. 1.

    Dynamic factors: it contains the information about uncertain commuters’ arrival rates, sudden breakdown of vehicles, resource availabilities at different time periods, population, etc., in zones and regions.

     
  2. 2.

    Static factors: it contains information about traffic at static workplaces, commercial activities, educational institutes (schools, colleges, etc.), etc., in zones and regions.

     
  3. 3.

    History of depot: it contains the past behavior of dynamic and static depots. The history of the depot in zones and regions help agents to know the requirements during the emergency conditions.

     
  4. 4.

    History of resources: it contains the information about the resources assigned to the commuters in the past.

     
Analysis in zone i at place x and time t is denoted as \(Z_i ( {x,t})\) and is the sum of current observations, which include static and dynamic factors, and the past observations, which include the history of the place and the pattern of resource utilized in past at time \(t-1\). It is given by
$$\begin{aligned} Z_i \left( {x,t} \right) =\alpha \left( {w_{x,t} .O_{x,t} } \right) +\beta \left( {w_{x,t-1} .O_{x,t-1} } \right) \end{aligned}$$
(1)
where \(\alpha ( {w_{x,t} .O_{x,t} } )\) is the current observation and \(\beta (w_{x,t-1} .O_{x,t-1})\) is the past observation in zone i, where \(w,\alpha \ \mathrm{and}\ \beta \) are weights, and \(w_{x,t} \) is weight assignment to the place x at time t. Typically, these weights are chosen priorly by the researcher to reflect geographical characteristic of the regions and zones under consideration (e.g., shopping malls, workplaces, commercial activities, educational institutes, hospitals, etc.). The value of \(\alpha >\beta \)for giving more importance to the current situation than the past. The following properties satisfy for the weight assignment: (1) \(w_{x,t} ,\alpha \ \mathrm{and}\ \beta \ge 0\), and (2) \(\sum _{x\in X} w_{x,t} =1\) and \(\alpha +\beta =1\).
The observation at place x and time t is denoted by \(O_{x,t} \) and is given as
$$\begin{aligned} O_{x,t} =f\left( {O_{x,t}^d ,O_{x,t}^s ,H_{x,t} } \right) \end{aligned}$$
where \(O_{x,t}^d ,O_{x,t}^s ,\ \mathrm{and}\ H_{x,t} \) are the dynamic observation, static observation and history at place x and time t, respectively. The \(O_{x,t} \) gives the pattern of resource, traffic flow, and also pattern of resource and traffic in the history.

4.2.2 Estimation of dynamic observation

The dynamic observation is the function of commuters’ arrival, vehicles breakdown and resource availability at place x and time t. It gives the resource pattern in the zone and is given by
$$\begin{aligned} O_{x,t}^d =f\left( {N_\mathrm{a} \left( t \right) ,N_\mathrm{v} \left( t \right) ,R_\mathrm{a} \left( t \right) } \right) \end{aligned}$$
where \(N_\mathrm{a} ( t ),N_\mathrm{v} ( t),\ \mathrm{and}\ R_\mathrm{a} ( t)\) represents the total number of commuters, total number of breakdowns of vehicles and average number of resources available at time t in zone i, respectively. In each zone, RoadSide units (RSUs) are deployed to provide seamless network connectivity for sending and receiving information. The commuter arrivals to the zones are shown in Fig. 3 along with their arrival rates.
Fig. 3

Commuters’ arrival model

\(N_\mathrm{a} (t)\) represents the total number of commuters at t in zone i given by
$$\begin{aligned} N_\mathrm{a} \left( t \right) =\frac{\lambda _i \left( t \right) R}{ \bar{v}_i} \end{aligned}$$
(2)
where \(\lambda _i (t),\bar{v} ,\ \mathrm{and}\ R\) represent the arriving rate of commuters, the average speed of commuters’ and the coverage area of zone i at time t.
Similarly, the vehicles’ arrivals to zones are shown in Fig. 4 along with their arrival rates.
Fig. 4

Vehicles’ arrival model

The total number of vehicles in zone i is given by
$$\begin{aligned} N^{Z_i }=\frac{\mu _i \left( t \right) R}{\bar{s_i}} \end{aligned}$$
(3)
where \({\mu }_i ({t}),\bar{{s}_{{i}}} ,{\mathrm{and}}\ {R}\) represent the arriving rate of vehicles, the average speed of vehicles and the coverage area of zone i at time t.
\(N_\mathrm{v} (t)\) represents the average number of vehicle breakdowns in time period t and is given by
$$\begin{aligned} N_v \left( t \right) =\mathop \sum \limits _{j=1}^{N^{Z_i }} V_j P\left( {V_j } \right) \end{aligned}$$
(4)
where
$$\begin{aligned} P\left( {V_j}\right) =\left\{ {{\begin{array}{l} 0;\quad \mathrm{if}\ \mathrm{TB}_i \left( {\mathrm{Total\ Breakdowns}} \right) \quad \mathrm{and}\\ \quad \qquad \mathrm{PB}_i \left( {\mathrm{Partial\ Breakdowns}} \right) \\ {1;\quad \mathrm{if}\ \mathrm{NB}_i \left( {\mathrm{No\ Breakdowns}} \right) } \\ \end{array} }} \right. \end{aligned}$$
is the probability of breakdowns of jth vehicle, and \(R_\mathrm{a} (t)\) represents the average number of resources available in zone i at place x and time t and is given by
$$\begin{aligned} R_\mathrm{a} \left( t \right) =R_{j,x,t}^{Z_{i\mathrm{avail}} } =\mathop \sum \limits _j r_{j,x,t}^{Z_{i\mathrm{avail}} } P(r_{j,x,t}^{Z_{i\mathrm{avail}} }) \end{aligned}$$
(5)
where \(r_{j,x,t}^{Z_{i\mathrm{avail}} } \) is the percentage of jth’ resource available in zone i at place x and time t and is given by
$$\begin{aligned} r_{j,x,t}^{Z_{i\mathrm{avail}}} =\frac{\mathrm{Avail.number\ of}\ j{\mathrm{th}}\ \mathrm{resource\ in}\ i\ \mathrm{at\ place}\ x\ \mathrm{at\ time}\ t}{\mathrm{Max.capacity\ of}\ j{\mathrm{th}}\, \mathrm{resource\ in}\ i\ \mathrm{at\ place}\ x\ \mathrm{at\ time}\ t}\nonumber \\ \end{aligned}$$
(6)
The dynamic observation is given by
$$\begin{aligned} O_{x,t}^d =N_\mathrm{a} \left( t \right) \left( {\frac{R_\mathrm{a} \left( t \right) -N_\mathrm{v} \left( t \right) }{R\left( t \right) }} \right) \end{aligned}$$
(7)
where R(t) is the total amount of resources available in zone i. Equation 7 gives the resource pattern in zone i of metropolitan area.

4.2.3 Estimation of static observation

The static observation is the function of the average traffic volume at static place x at time t in the metropolitan area and is denoted as \(O_{x,t}^s \) and is given by
$$\begin{aligned} O_{x,t}^s =\frac{\mathrm{Hourly\ volume\ in\ zone}\ i}{6\cdot V_{10}^i }=\frac{V^{i}}{6 \cdot V_{10}^i } \end{aligned}$$
(8)
where V is the average traffic volume at peak hour and \(V_{10} \) is the average volume during the peak 10 min of flow (vehicles per 10 min), \(V_{10} \) is multiplied by 6 because \(6 \cdot 10 = 60\) min. Equation 8 gives the traffic volume pattern in zone i of metropolitan area.

4.2.4 Estimation of resource and traffic volume history

The estimation of resource and traffic volume history is the analysis of past average traffic volume and resources utilized pattern in the metropolitan area. The percentage of average traffic volume and resources allocated in history is denoted by \(H_{x,t} \) of place x at time t and is given as follows:
$$\begin{aligned} H_{x,t} =\left( {\frac{R_{j,x,t-1}^{Z_{i\mathrm{max}} } -R_{j,x,t-1}^{Z_{i\mathrm{allocated}} } }{R_{j,x,t-1}^{Z_{i\mathrm{max}} } -R_{j,x,t-1}^{Z_{i\mathrm{min}} } }} \right) .O_{x,t-1}^s \end{aligned}$$
(9)
where \(R_{j,x,t-1}^{Z_{i\mathrm{max}} } \,\mathrm{and}\ R_{j,x,t-1}^{Z_{i\mathrm{min}}}\) denote the percentage of maximum and minimum of \(j{\mathrm{th}}\) resource requirements at place x and time \(t-1\) in zone i, respectively, and \(R_{j,x,t-1}^{Z_{i\mathrm{allocated}}}\) denotes the percentage of \(j{\mathrm{th}}\) resource allocated to the commuters at place x and time \(t-1\) in zone i in past and are given as follows:
$$\begin{aligned}&R_{j,x,t-1}^{Z_{i\mathrm{max}} } =N_{\mathrm{a}\left( {t-1} \right) } \cdot R_{j,x}^{Z_{i\mathrm{avail}} } , \end{aligned}$$
(10)
$$\begin{aligned}&R_{j,x,t-1}^{Z_{i\mathrm{min}} } =N_\mathrm{a} \left( {t-1} \right) \cdot \left( {\frac{R_{j,x,t-1}^{Z_{i\mathrm{avail}} } +R_{j,x,t-1}^{Z_{i\mathrm{max}} } }{2}} \right) \quad \mathrm{and} \end{aligned}$$
(11)
$$\begin{aligned}&R_{j,x,t-1}^{Z_{i\mathrm{allocated}} } =\left( {\frac{R_{j,x,t-1}^{Z_{i\mathrm{max}} } +R_{j,x,t-1}^{Z_{i\mathrm{min}} } }{2}}. \right) \end{aligned}$$
(12)
Equation 9 gives the pattern of resource utilized and traffic pattern in the history.
The complete analysis of zone i at time t is denoted as \(Z_i \left( {x,t} \right) \) and is given by:
$$\begin{aligned} Z_i \left( {x,t} \right) =\frac{1}{\left| {Z_i } \right| }\mathop \int \limits _{k=1}^m Z_k \left( {x,t} \right) \end{aligned}$$
(13)
where \({k}=1, 2, \ldots ,\ {m}\) and m be the total number of areas in zone i. Similarly, the complete analysis of region l at time t is denoted as \(R_l (x,t)\) and is given by:
$$\begin{aligned} R_l \left( {x,t} \right) =\frac{1}{\left| {R_l } \right| }\mathop \int \limits _{i=1}^n Z_i \left( {x,t} \right) \end{aligned}$$
(14)
where \({l} = 1, 2, \ldots ,\ {r}\) and r be the total number of regions in the metropolitan area and n be the total number of zones in region l. The complete analysis of zones and regions in a metropolitan area is explained in Algorithm 1.

4.3 Resource utilization patterns in zones and regions

The zone analysis given by Eq. 13 predicts the status of the zones such as patterns of resource utilization, patterns of growth or decline of traffic volume and unpredictable information (like sudden breakdown of vehicles and uncertain arrivals of commuters) at different time periods of a day in the metropolitan area.

The percentage of \(j{\mathrm{th}}\) resource utility in zone i at time t is the ratio of actual resources allocated to the resources available, and is given as
$$\begin{aligned} U_{j,k}^{Z_i } \left( {x,t} \right) =\frac{R_{j,x,t}^{Z_{i\mathrm{allocated}} } }{R_{j,x,t}^{Z_{i\mathrm{avail}} } } \end{aligned}$$
(15)
The prediction of \(j{\mathrm{th}}\) resource is given by
$$\begin{aligned} U_{j,k}^P \left( {x,t} \right) =U_{j,k}^{Z_i } \left( {x,t} \right) +\max \left( {H_{j,t}^{Z_i } -U_{j,k}^{Z_i } \left( {x,t} \right) ,0} \right) \end{aligned}$$
(16)
where \(H_{j,t}^{Z_i } \) is the historical utilization of the j th resource at the same time in the same day.
The prediction of \(j{\mathrm{th}}\) resource utilization in the complete zone i is given by
$$\begin{aligned} U_{i,j} \left( {x,t} \right) =\frac{1}{\left| {Z_i } \right| }\mathop \int \limits _{k=1}^m U_{j,k}^P \left( {x,t} \right) \mathrm{d}x \end{aligned}$$
(17)
Similarly, the prediction of \(j{\mathrm{th}}\) resource utilization in the region l at time t is given as
$$\begin{aligned} U_{l,j} \left( {x,t} \right) =\frac{1}{\left| {R_l } \right| }\mathop \int \limits _{i=1}^n U_{i,j} \left( {x,t} \right) \mathrm{d}x \end{aligned}$$
(18)
Algorithm 2 shows the complete patterns of resource utilization in zones and regions in a metropolitan area.

4.4 Traffic volume patterns in zones and regions

The predicted patterns of growth or decline of traffic volume in zone i at time t is denoted as \(\Delta \mathrm{TV}_{x,t,i} \). The total number of commuters’ in zone i at time t is given by
$$\begin{aligned} N_{a,x,t}^{Z_i } =\frac{\lambda _i \left( t \right) R}{\bar{v}} \end{aligned}$$
(19)
The traffic arrival is a Poisson point process with density \(\beta \). The probability of finding n number of commuters’ in zone i is given by
$$\begin{aligned} p^{z_i }\left( {n,R} \right) =\frac{\left( {\beta R} \right) ^{n}e^{-\beta R}}{n!} \end{aligned}$$
(20)
The predicted patterns of traffic flow density in zone i is given by
$$\begin{aligned} {\Delta }\mathrm{TV}_{x,t,i}= & {} N_{a,x,t}^{Z_i } +p^{z_i }\left( {n,R} \right) \nonumber \\&+\,\mathrm{max}\left( {H_{x,t} -\left( {N^{Z_i }+P^{Z_i }\left( {n,R} \right) } \right) ,0} \right) \end{aligned}$$
(21)
$$\begin{aligned} {\Delta }\mathrm{TV}_{x,t,i}= & {} \frac{\lambda _i \left( t \right) R}{ \bar{v}}+\frac{\left( {\beta R} \right) ^{n}e^{-\beta R}}{n!}\nonumber \\&+\,\mathrm{max}\left( {H_{x,t} -\left( {N^{Z_i }+P^{Z_i }\left( {n,R} \right) } \right) ,0} \right) \end{aligned}$$
(22)
The predicted patterns of growth of traffic volume in complete \(i{\mathrm{th}}\) zone at time t is denoted as \({\Delta }C_{x,t,i}\) and is given as follows:
$$\begin{aligned} {\Delta }C_{x,t,i} =\frac{1}{\left| {Z_i } \right| }\mathop \int \limits _{x=1}^m {\Delta }\mathrm{TV}_{x,t,i} \mathrm{d}x \end{aligned}$$
(23)
Similarly, the predicted patterns of growth of traffic volume in the \(l{\mathrm{th}}\) region is given by
$$\begin{aligned} {\Delta }C_{x,t,l} =\frac{1}{\left| {R_l } \right| }\mathop \int \limits _{x=1}^m {\Delta }C_{x,t,i} \mathrm{d}x \end{aligned}$$
(24)
Algorithm 3 shows the complete traffic volume patterns in zones and regions in a metropolitan area.

4.5 Commuters’ choice of a route

The commuters’ choice of a route is based on the predicted patterns of traffic volume, travel time and patterns of resource utilization. Let \(C_{t,d}^r \) denote commuters’ choice of a route r to the destination d at time t and \(S_{t,d}^r\) is the reliability of commuters’ choice of route r to destination d at time t. The static agent chooses route r, which is having less resource consumption, minimum travel time and congestion free among the set of routes \(\mathfrak {R}\). Hence, static agent forms the following objective function, which maximizes the reliability of choosing a route r to the commuters’ desired destination d.
$$\begin{aligned} C_{t,d}^r =\mathop {\max }\limits _{{\mathrm{r}}\in \mathfrak {R}} \left( {S_{t,d}^r } \right) \end{aligned}$$
(25)
where
$$\begin{aligned} S_{t,d}^r =P\left( {R_{t,d}^R\ \cdot R_{j,d}^U \left( t \right) \ \cdot R_{t,d}^{Tr} \left( {T_1 ,T_2 |t} \right) } \right) \end{aligned}$$
(26)
where \(R_{t,d}^R \) is the reliability of traffic flow volume on route r and is given as
$$\begin{aligned} R_{t,d}^R =P\left( {{\Delta }C_{x,t,d}^r \le {\Delta }C_{x,t,d}^{rT} } \right) \end{aligned}$$
(27)
where \({\Delta }C_{x,t,d}^{rT} \) is the threshold value of traffic flow volume on route r to the destination d at time t.
The \(R_{t,d}^U \) is the reliability of resource utilization on route r to the destination d at time t and is given as
$$\begin{aligned} R_{j,d}^U \left( t \right) =P\left( {U_{j,d}^r \left( t \right) \le U_{j,d}^{rT} \left( t \right) } \right) \end{aligned}$$
(28)
where \(U_{j,d}^{\mathrm{rT}} (t)\) is the threshold value of resource utilization on route r to the destination d at time t.
Fig. 5

Integration of Matlab and Mobile-C

The \(R_{t,d}^{\mathrm{Tr}} (T_1 ,T_2 |t)\) is the travel time reliability of route r and is defined as the probability that commuters’ choose a route within a time threshold value \(( {T_1 ,T_2 } )\). Travel time reliability depends upon the factors, such as \(D_r \), the distance between the source and destination on route r; \(S_r \), the speed of vehicles on route r; T, the travel time to reach the destination; t’, the departure time interval from the source; and \(E[ {T_r } ]\), the expected or mean travel time on route \(r=E[ {\frac{D_r }{S_r }} ]\cdot R_{t,d}^{\mathrm{Tr}} (T_1 ,T_2 |t)\) is the travel time reliability of vehicle arriving within a specified time threshold \(( {T_1 ,T_2} )\) on route r at t and is given by
$$\begin{aligned} R_{t,d}^{\mathrm{Tr}}\left( {{T_1},~{T_2}{|}t} \right)= & {} P~\left( {{T_1}< {t_1} - {{\Delta }}~t1 - t' - T < {T_2}~} \right) \nonumber \\= & {} {{\Phi }}\left( {\frac{{{t_1} - {{\Delta }}t1 - t' - {T_1} - E\left[ {\frac{{{D_r}}}{{{S_r}}}} \right] }}{{{\sigma _r}\left( T \right) }}} \right) \nonumber \\&- {{\Phi }}\left( {\frac{{{t_1} - {{\Delta }}t1 - t' - {T_2} - E\left[ {\frac{{{D_r}}}{{{S_r}}}} \right] }}{{{\sigma _r}\left( T \right) }}} \right) \nonumber \\ \end{aligned}$$
(29)
where \({\Phi }(.)\) is the distribution function of the standard normal distribution, \(\sigma _r (T)=\rho _r E[ {T_r } ]\) is the standard deviation of the travel time on path r during interval T. \(\rho _r \) is a constant related to path r, which reflects the degree of network variability or uncertainty. The smaller the value of \(\rho _r \), the more reliable the network, and vice versa. The specified time threshold \(( {T_1 ,T_2 } )\) value is exogenously determined by considering the travel time in different situations at different time periods of a day and that should be maintained even in the deteriorated situations in the metropolitan area.

Therefore, the proposed commuters’ choice of route model finds an optimal route, which is having highest reliability among the routes available to reach the destination.

5 Simulation and analysis results

In this section, we discuss performance evaluation of the proposed system by varying time, space and resources. The performance measures considered here are patterns of traffic volume and patterns of resource utilization in zones and regions of the metropolitan area.

The realistic traffic scenario and density generation, analysis, and prediction in each zone and region of metropolitan area are scripted and implemented in MATLAB interfaced with Mobile-C agent platform as shown in Fig. 5. Wireless communication aspects required in a metropolitan area also coded in MATLAB.

We have used real-time traffic data sets (traffic flow density and travel time), which are extracted from the Caltrans performance measurement system (PeMS) database [25] and are collected only in weekdays for performance analysis of proposed system. The MATLAB code produces statistical (traffic) information, spatio-temporal data, historical and resource (required and available) information of each zone and region in a metropolitan area, and gives it to Mobile-C agent platform. The Mobile-C is an IEEE FIPA (Foundation for Intelligent Physical Agents) standard complaint multi-agent platform, which supports C/C++ mobile agents in networked intelligent systems. It is installed in every depot of metropolitan area which deploys static agent (SA). The SA creates and dispatches mobile agents (MAs) to each zone in a region as shown in Fig. 6.

These MAs communicate with neighbor RSUs, MAs and vehicles and during communication they collect and share traffic flow density, travel time, commuters’ arrival time, historical and spatio-temporal data, etc. The SA gets these collected and shared information of each zone and region periodically. The SA analyzes and predicts exact behavior (of traffic flow density, resource utilization and travel time) in each zone and region in a metropolitan area.
Fig. 6

Mobile agent migration in a zone 1

Table 1

Simulation parameters and their values

Parameters

Values

Simulation area

\(2400\times 2400\)

Simulation time

100 s

Network simulation and traffic generation tool

MATLAB

Agent platform

Mobile-C

Number of regions

6

Number of zones

36

Number of static agents

6

Number of mobile agents

36

Static agent size

1000 KB

Mobile agent size

500 KB

Number of depots

6

Number of RSUs

12

Number of vehicles

250

Transmission range of RSU

300 m

Transmission range of OBU

200 m

Communication technology

IEEE 802.11p

Frequency band used

5.9 GHz

Resources

Vehicle, man power and fuel

The performance evaluation of the proposed system were carried out using the simulation parameters as shown in Table 1 on a dual-CPU Intel Core i5-2400 at 3.10 GHz Desktop computer with 12-GB RAM running Fedora version 25.

The scenario of metropolitan area consists of regions A–E as shown in Fig. 7. Region A is the residential area, region B is the industrial area, region C is the wholesale market area for agriculture produce in the city, region D has more temples, hotels and educational institutes, and region E consists of many educational institutes, shopping mall, companies and market area.

For simplicity and clarity we have considered region E as shown in Fig. 8 for analyzing and predicting at each and every zone in it. The following results show the patterns of resource utilization and patterns of traffic volume at different time periods in a day.

Figure 9 shows the pattern of resource utilization at different time periods in a day in the metropolitan area. Zone 1 has many educational institutes and hence the resource utilization in the morning (8–10 AM) is 30–50% and after that declines and again starts increasing in the afternoon period (12–2 PM) from 20 to 30%. In the evening period (4–6 PM) the patterns of resource utilization are between 40 and 50%. But there are no resource utilizations in the night time as shown in Fig. 9.

Zone 2 is a commercial activity area such as shopping mall and companies. The patterns of resource utilization are more between 10 AM and 8 PM and decline gradually after 8 PM as shown in Fig. 9. Similarly, zone 3 is a marketing area and its pattern of resource utilization is shown in Fig. 9 at different time periods in a day in the metropolitan area.
Fig. 7

Regions of metropolitan area

Fig. 8

Region E’s zones

Fig. 9

Pattern of resource utilization at different time periods of a day in zones

Fig. 10

Pattern of growth or decline of traffic volume at different time periods of a day

Figure 10 shows the pattern of growth or decline of traffic volume at different time periods in a day. Due to shopping malls, companies, etc., in zone 1, the traffic volumes in the morning (8–10 AM) and evening (4–6 PM) are more, i.e., between 60 and 80%. Similarly, in the afternoon period (12–2 PM) is moderate i.e., between 55 and 65%. During night time, there are no growths of traffic volume in a metropolitan area.

In zone 2, the pattern of growth of traffic volumes are more between time 10 AM and 8 PM. The traffic volumes are almost 90% in between 1 and 5 PM time periods as shown in Fig. 10. But in the night time the pattern of traffic volumes is approximately 5–10%. Similarly, the patterns of growth or decline of traffic volume in zone 3 are shown in Fig. 10 at different time periods in a day in the metropolitan area.
Fig. 11

Pattern of resource utilization in a metropolitan area

Fig. 12

Pattern of growth or decline of traffic volume in a metropolitan area

Figures 11 and 12 show the pattern of resource utilization and pattern of growth or decline of traffic volume at different time periods in a day in the metropolitan area. Region A is a residential area, the patterns of resource utilization and growth of traffic volume are more in the morning time (7.30–10.30) and evening time (4–9.30 PM) than in the afternoon and night time. Similarly, for regions B–D the pattern of resource utilization and traffic volumes are shown clearly in Figs. 11 and 12.

The metropolitan area scenario as shown in Fig. 7 in which we have considered two different routes to reach destination e from source a are: route \(1 = \hbox {region}\) A (residential area) \(\rightarrow \) C (wholesale market area) \(\rightarrow \) E (educational institutes, shopping malls, etc.) and route \(2 = \hbox {region}\) A \(\rightarrow \) B (industrial area) \(\rightarrow \) D (temples, hotels, educational institutes) \(\rightarrow \) E.
Fig. 13

Commuters’ choice of route 1 and 2 in the morning time

Fig. 14

Commuters’ choice of route 1 and 2 in the afternoon time

Fig. 15

Commuters’ choice of route 1 and 2 in the evening and night time

Figures 13, 14 and 15 are the simulation and analytical results of probability of commuters’ choice of a route with varying time periods in a day.

Route 1 goes from region A \(\rightarrow \) C \(\rightarrow \) E to reach a destination e from a, and hence the traffic flow densities in the morning time (6 AM–8.30 AM) are less and probability of choosing route 1 is more as shown in Fig. 13. But as time progresses (after 8.30 AM) the traffic flow densities start growing and hence the probability of choosing route 1 becomes less. Similarly, route 2 has less traffic congestion in the morning (6 AM–8.30 AM) and it gradually increases as time progresses, and the probability of choosing route 2 is less after the time 9 AM.

In Fig. 14, in route 1 in the afternoon 12 PM–13.30 PM there will be very less traffic density and hence the probability of choosing a route 1 is more compared to route 2. The probability of choosing routes exponentially decreases after 13.30 PM.

Similarly, in the evening and afternoon, the traffic density and choosing a route with respect to time in a day are shown clearly in Fig. 15. In this figure, there is a more probability of choosing route 2 in the period 17 PM–19 PM and after 19 PM–23 PM the probability of choosing route 1 is more preferable compared to route 2 because of the traffic density in the respective regions.
Fig. 16

Computational time of agents in zones

We have analyzed the computational time required in zones 1, 2 and 3 of region E. In each zone we have considered 1, 2, 4, and 8 number of mobile agents in a group, and computational time required in these zones are computed by the static agent of region E. We have ran the simulation 20 times for each group size and taken the mean value of them. Figure 16 shows that as the population of mobile agents increases in the zones, the computational time required for analyzing, processing and predicting the traffic-related information decreases.

Overall we have modeled the metropolitan area and tested its behavior with different performance measures at different time periods, conditions, and places in MATLAB interfaced with Mobile-C agent platform. Also the computational time complexity with respect to the agents is shown.

6 Conclusions

The importance of the proposed work is to develop a mathematical model of metropolitan area. The static and mobile agents are used to analyze and predict the patterns of traffic flow and resource utilization, and also find an optimal route to the destination. The proposed model provides highly accurate and realistic performance measures at every spatial and over multiple time periods in a day in zones and regions in the metropolitan area. The agent technology reduces the computational time overhead faced during the analyzing, processing and predicting the traffic flow and resource utilization information. In future, the analyzed and predicted information is used for traffic management, which improves efficiency of traffic and reduces the fuel consumption in metropolitan area.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Protocol Engineering and Technology Unit, Department of Electrical Communication EngineeringIndian Institute of ScienceBangaloreIndia

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