Mobility Modeling in Third Generation Mobile Telecommunication Systems J.G.Markoulidakis, G.L.Lyberopoulos, D.F.Tsirkas, E.D.Sykas National Technical University of Athens (NTUA) Department of Electrical and Computer Eng. 9, Heroon Polytechniou Str. 157 73, Zographou, Athens, GREECE Tel.: + 30 1 772 2278, Fax: + 30 1 772 2530 e-mail:
[email protected]
Abstract: In mobile communications, mobility modeling is involved in several aspects related to signaling and traffic load analysis. In third generation systems, the influence of mobility on the network performance (e.g., handover rate) will be strengthened, mainly due to the huge number of mobile users in conjunction with the small cell size. In particular, the accuracy of mobility models becomes essential for the evaluation of system design alternatives and network implementation cost issues. In this paper, we propose three basic types of mobility models, which are appropriate for the analysis of the full range of mobile communications' design issues. The models provide different levels of detail regarding the user mobility behavior. In particular: (a) the City Area Model traces user motion at an area zone level, (b) the Area Zone Model considers users moving on a street network and (c) the Street Unit Model tracks user motion with an accuracy of a few meters. The validity of the basic models for mobile communications’ design aspects is highlighted. Moreover, an "integrated mobility modeling tool”, which considers the basic mobility models as components is proposed, aiming at the development of a refined modeling approach. This is achieved by improving the accuracy of the input parameters of each basic model, via the exchange of some specific (mobility related) parameters among the component models. To justify the applicability of the proposed integrated tool for both the analysis of design aspects and network planning, indicative results are presented, derived from simulation-based application examples of the three basic mobility models.
1. Introduction Third Generation Mobile Telecommunication Systems (TGMTS), will be brought into service the early years of the next century [1-3]. Aiming at a mass market telecommunication system, the TGMTS will offer a plethora of telecommunication services (e.g., voice, low and high bitrate data, video) to Mobile Users (MU) via a range of mobile terminals1, operating in both public and private environments (office areas, residences, transportation media, etc.). Due to the ‘mass market nature’, TGMTS should be designed as a high capacity system, able to cope with the envisaged overwhelming traffic demands. To achieve this, a layered cell architecture consisting of macro-, micro- and pico- cells, has been adopted [4]. Compared to second generation systems [5-7] and apart from the increased traffic demands, the employment of location management and handover procedures in a micro-cellular environment, in conjunction with the huge number of MUs2, will generate a considerable ‘mobility related signaling’ load. The increase of the ‘mobility related signaling’ -apart from the radio link- will have a major impact on the number of database transactions, constituting thus the database a possible bottle-neck at the fixed network side. Consequently, and given the scarcity of radio resources, methods for signaling load reduction are emerging for TGMTS [8-21]. It is obvious that optimization techniques and efficient network planning algorithms are critical issues, concerning the overall TGMTS performance. Mobility modeling is involved in the analysis of: (a) location management related aspects (location area planning [8,12,13,18], paging strategies [9,11,17], etc.), (b) radio resource management related
1
2
The terminals can range from basic low cost simple types, through hand portable devices and vehicle mounted speech devices up to portable B-ISDN terminals. The expected user penetration rate ranges from 50% to 70% of the total population.
Mobility Modeling in Third Generation Mobile Telecommunication Systems
aspects (multiple access techniques, channel allocation schemes, etc.) [10,14,22] and (c) propagation related aspects (fading, handover decisions, etc.) [44,45]. Evaluation studies involve the consideration of user mobility behavior and therefore, the accuracy of the results (and consequently the conclusions) heavily depends on the assumed mobility models. Note that the accuracy of the mobility models involved in network planning is highly desirable, since it may affect the ratio of system capacity vs. network implementation cost. Several mobility modeling approaches (simulation and analytical) can be found in the literature. Analytical models, based on simplifying assumptions, may provide useful conclusions regarding critical network dimensioning parameters [11,17,22-30]. Studies on more realistic analytical models, indicate that closed form solutions can be derived for simple cases only (e.g., highways at free flow) [29,30]. On the other hand, computer simulation studies [8-10,31,32] consider more detailed and realistic mobility models. Among the disadvantages of the above models are: (a) the amount of the required input parameters, (b) the verification of results vs. real measurements and (c) the required computational effort. In this paper, three basic types of mobility models which are appropriate for the full range of the TGMTS design issues (e.g., location and paging area planning, handover strategies, channel assignment schemes, etc.) are introduced. In particular: •
The City Area Model. It consists of a set of area zones connected via high capacity routes. Candidate output parameters may include: the user distribution per area zone vs. time, the crossing rate per area zone, the percentage of non-moving and moving users (car passengers, pedestrians) for each area zone vs. time, etc.
•
The Area Zone Model. The model consists of a street network and a set of building blocks. It may be utilized for the estimation of: the pdf (probability distribution function) of a user residence time in an area zone, the pdf of a user crossing time in an area zone, etc.
•
The Street Unit Model. This model considers three street types: (a) highways, (b) streets with traffic light(s) controlled flow and (c) high/low priority streets. Candidate output parameters may include: the pdf of car density and car speed in a street segment, the pdf of car residence time in a street segment, etc.
Taking into account that each model concentrates on a specific range of design issues, we propose a methodological modeling approach, the so-called ‘Integrated Mobility Modeling Tool’ (IMMT), that considers the basic models as components among which mobility-related parameters can be exchanged. The IMMT aims at: •
the improvement of the accuracy of the results obtained by each basic model,
•
the validation of the theoretical input assumptions and analytical models and
•
the investigation of the effect of the mobility model accuracy on design decisions.
The material included in this paper is organized as follows. In section 2, a general discussion on mobility modeling is given, identifying candidate input and output parameters. Section 3 stresses the necessity for the development of various mobility model types for TGMTS. Section 4 provides an overview of transportation theory approach in conjunction with the three basic mobility models. In section 5, the IMMT approach is described. Section 6 presents some indicative results, which are derived from simulation-based application examples of the three basic mobility models (Annexes A, B and C). Annex D provides a brief analysis on the effect of mobility on the user calling behavior. Finally, conclusions are drawn in Section 7.
2. Mobility Modeling in General Mobility modeling attempts to describe the mobility behavior of an individual or a set of individuals. Thus, a generic mobility model (see Figure 1) can be described by defining: •
The set of Input Parameters Sin. This includes: -
•
A set of points G, which represents all possible locations. A set of individuals P, which constitutes the population of the model. A set of time instances T, i.e., the time period the population’s mobility is modelled.
The set of Output Parameters Sout, consisting of a set of functions. Each function provides the location of an individual p over the set G for each time instance of the set T:
{
S out = x : x = g p , ∀p ∈ P , g p ( t ) ∈ G , ∀t ∈ T
} Page 2
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where, gp(t) is the location of the individual p at time t over the set of possible locations G. Taking into account the nature of mobility, it is obvious that it is quite difficult (if not possible) to either measure or derive the output parameters via a set of functions/methods. This is mainly due to the huge number of parameters that have to be considered, regarding the user mobility behavior, the vehicular traffic conditions, etc. To alleviate these problems, the simplified modeling approach described below may be followed: •
Population (P’): The population is grouped into classes e.g., pedestrians, car passengers, working people, students, etc., based on the mobility behavior characteristics. Another possible simplification might be the consideration of a representative sample of the total population.
•
Geographical Area (G’): The geographical area is organized into regions with specific mobility characteristics. If so, the location of an individual is known with an accuracy of an area region, and not with an accuracy of a specific point. Example categorization of areas may be the city center, urban area, suburban area, rural area, etc.
•
Time Period (T’): The time period is divided into time zones with specific mobility characteristics. Example time zones might be the rush hours, the busy hour, the night hours, the weekends’ rush hours, etc. Thus, depending on the output parameters, a specific time zone may be considered, instead of long time periods (e.g., a week).
Within this context, the set of output parameters of the simplified modeling approach is:
{
}
S out = x : x = g p , ∀p ∈ P ′, g p ( t ) ∈ G ′, ∀t ∈ T ′
Note that the development of the appropriate mobility model should be based on a set of criteria regarding the ‘accuracy’ required in terms of population, space and time. Another crucial parameter is the required effort. The “effort” may refer either to the collection of real measurements or to the demanded computational cost.
Generic Mobility Model Output Parameters
Functions and Methods
Input Parameters
Measurements
Real Phenomena Figure 1: Representation of a Generic Mobility Model
3. The Necessity of Mobility Models in Mobile Communications In mobile telecommunications, service provision to MUs is accomplished by the employment of: (a) the location management procedures (location update, domain update, user registration, user locating, etc.) used to keep track of the user/terminal location and (b) the handover procedure which allows for the continuity of ongoing calls. The performance of the above procedures is influenced by the user mobility behavior. Their application directly affects (a) the signaling load generated on both the radio link and the fixed network (e.g., location updating rate, paging signaling load, etc.) and (b) the database queries load. Additionally, the handover procedure affects the offered traffic volume per cell as well as the Quality of Service (QoS) experienced by the MUs (e.g., call dropping). In TGMTS, the estimation of the above parameters, which are critical for network planning and system design (e.g., location and paging area planning, handover strategies, channel assignment schemes, etc.) urge for the development of ‘appropriate’ mobility models. Due to diversification of the above issues, different mobility detail levels are required. In particular: Page 3
Mobility Modeling in Third Generation Mobile Telecommunication Systems
•
Location Management Aspects: Location area planning, multiple step paging strategies, data locating strategies, database query load, etc. [8,9,11-13,16-21,33-35]. Location management related issues require the knowledge of the user location with an accuracy of a ‘large scale’ area (e.g., location or paging area).
•
Radio Resource Management Aspects: Cell layout, channel allocation schemes (FCA, DCA), multiple access techniques (TDMA, CDMA), system capacity estimation, QoS related aspects, signaling and traffic load estimations, user calling patterns, etc. [10,14,22,36-43]. Radio resource management related aspects require ‘medium-scale’ area accuracy (cell area).
•
Radio Propagation Aspects: Fading, signal strength variation, handover decision algorithms, etc. [44,45]. The analysis of radio propagation aspects needs accuracy of a ‘small-scale’ area (comparable to the wavelength level).
In order to tackle with the above mentioned issues, three mobility model types are proposed, namely, the city area, the area zone and the street unit model, which are described in detail in the following section.
4. Mobility Models for Mobile Communications Within the context of the generic modeling approach presented in Section 2 and taking into account the requirements relevant to mobile communications, three types of mobility models are proposed. The framework for the development of those models is based on transportation theory, an overview of which is provided in the following section.
4.1. Overview of Transportation Theory Approach [46] Transportation theory aims at the analysis and design of transportation systems (e.g., railways, street networks, etc.). The basic issue that the transportation theory attempts to resolve, is the following: “Given a transportation system serving a certain geographical area, determine the load this system should carry”. The input framework which is utilized as a basis for the development of the relevant models is described by the following items: Trips: A trip (movement) is characterized by: (a) the purpose, (b) the end-points (originationdestination), (c) the transportation means utilized and (d) the route followed. Given a certain geographical area, a trip can be characterized according to its end-points’ locations as: (a) internal (both end-points inside the area), (b) outgoing (origination inside the area and destination outside), (c) incoming (the opposite of outgoing) and (d) external (both end-points outside the area). Area Zones: Transportation theory divides the geographical area under study into area zones. The division is based on criteria related to: (a) the population density and (b) natural limits (e.g., rivers, parks, highways, railway tracks, etc.). Note that, the trip end-points are considered with accuracy of an area zone. Population Groups: The population of the area under study is divided into groups according to their mobility characteristics. Example groups are working people, residential users, students, etc. Movement Attraction Points (MAP): MAPs represent locations that attract the population movements and at which people spend considerable time periods. Examples are work places, residences, the shopping centers, etc. Each MAP characterizes the population group type it attracts. Time Zones: During a day time, it can be observed that there are time periods during which certain types of movements take place (e.g., movements towards work-places) and time periods where certain population groups reside to certain MAPs (e.g., working hours, shopping hours, etc.). These time periods are called time zones. Transportation theory concentrates on the so-called ‘rush hours’, where the peak load occurs on the transportation system under study. Transportation Systems Characteristics: A transportation system (e.g., a street network, the urban buses network, the subway, etc.) is characterized by: (a) its capacity, (b) the trips it may 3 support and (c) the usage cost . The basic models used by the transportation theory are: Trip Production and Attraction Models: The output parameters of these models are the number of trips produced and attracted by each area zone. Example model is the ‘regression model’ [47].
3
Cost is measured in terms of time cost and money cost. Page 4
Mobility Modeling in Third Generation Mobile Telecommunication Systems
Trip Distribution Models: The output of these models is the so-called origination-destination matrix OD(Ai,Aj). Each element of this matrix equals to the number of trips originated from area zone Ai and destined to area zone Aj. Example model is the ‘gravity model’ [48]. Modal Split Models: The output of these models is the transportation mean an individual selects to perform a trip with given end-points. The major factors considered here are the user annual income, the transportation mean usage cost [46]. (Vehicular) Traffic Assignment Models: These models are used for the estimation of the probability a certain route is selected, given the trip end-points and the street network [49]. The criteria utilized here are the route length and the usage cost.
4.2. City Area Model A city area model describes the user mobility and traffic behavior within a city area environment. The need to analyze the user mobility behavior over large-scale geographical areas is raised by location management related aspects. Network planning purposes, impose the use of city area models representing ‘specific’ cities (i.e., based on geographical databases, demographic data and existing transportation studies). On the other hand, ‘typical’ city area models are required for the evaluation of proposed system design alternatives [8,9]. According to transportation theory, although each individual city area exhibits specific characteristics (e.g., population distribution, distribution of MAPs, street network, etc.), some generic characteristics can be observed in most contemporary cities. For example: •
Cities are usually developed in such a way that densely populated areas (urban areas) surround a city center (high density of work places and shopping centers). While moving towards the city edges the population density gradually decreases (suburban and rural areas).
•
The street network supports two movement types: (a) radial (i.e., from the city center towards the edge of the city and vice versa) and (b) peripheral.
Applying the methodology described in section 2, the basic set of input and output parameters of a ‘generic’ city area model is given below, while a ‘typical’ application example model, adopted in various studies [8,9], is given in Annex A.
High Capacity Route
Figure 2: The City Area Model
4.2.1. Input Parameters Geographical Area: The geographical area covers the whole city area, consisting of a set of area zones connected via high capacity routes (see Figure 2). Area Zones: Combining transportation theory aspects and mobile telecommunication requirements, it seems reasonable to assume that an area zone equals to a network area (e.g., macro-cell, local exchange area, etc.). High Capacity Routes: They represent the most frequently selected streets (routes) for the support of movements between different area zones. Note that areas outside the city can also be modeled as area zones which attracts a relatively low number of trips. Page 5
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Population: Mobile communication systems focus merely on the mobility behavior of MUs, and therefore, only this relevant portion of the total population needs to be considered. However, taking into account that third generation systems are expected to support high user penetration rates -similar to contemporary fixed networks (i.e., in the range of 70%)- it seems absolutely inefficient to simulate the total number of MUs4. Instead, a representative sample of MUs seems sufficient. The population is divided into MU groups, according to the mobility characteristics of the individuals. For each MU group, certain mobility and traffic characteristics are assigned: Mobility Behavior: The mobility behavior of an MU group is determined by the type of movements, the distribution of MAPs, the movement initiation time, the utilized transportation means, the criteria according to which a user selects the route and the time the user spends at certain MAPs. Traffic Behavior: Each MU group is assigned a set of parameters describing the traffic behavior of its members, i.e., available services, call arrival rates, call duration, etc. A detailed analysis of the MU calling patterns is presented in Annex D. Time Period: As mentioned above, transportation theory concentrates on the so-called ‘rush hours’. On the contrary, telecommunication systems design and dimensioning focus on the well-known ‘busy hour’. However, there are problems, especially the ones related to the mobility related signaling, which require the analysis of both the high mobility hours (rush hours) and the busy hour.
4.2.2. Output Parameters The output parameters may include: •
Amount of Location Updates for a given Location Area (LA) planning scheme. Various, either static or dynamic LA planning schemes have been proposed in the literature [8,12,18]. The existing analytical models [24-27], for the estimation of an area (LA in this case) border-crossing rate, assume uniform user distribution, constant average speed and fixed percentage of moving users. In short term, their accuracy can be considered as higher compared to the city area model (where only the high capacity routes are considered). However, their assumptions are not valid for long time periods, since mobility conditions in a city area are quite dynamic. Moreover, in certain cases, more complex mobility models are required e.g., overlapping LAs [12] or LAs defined according to the individual MU mobility behavior [8].
•
Paging Signaling Load in Multiple Step Paging Strategies. Paging Strategies which aim at the minimization of the paging signaling load have been studied [9,11,17]. The critical parameter here, is the probability that a user is located within the paging area (a portion of an LA) that the paging related information5 indicates [9]. Existing analytical models [11,17], based on simplifying assumptions and detailed simulation models [9], provide useful results for paging area dimensioning.
•
Database Query Load. Taking into account the solutions proposed for the (distributed) database in TGMTS [19-21], it is necessary to provide estimations regarding the relative location of the calling and called users, as well as the relative location of the called user to a certain database node (e.g., Home Location Register - HLR [5]). The city area model provides means to estimate the query load of a (distributed) database, which covers the whole city area.
4.3. Area Zone Model The evaluation of the various radio resource management schemes requires the knowledge of the MU location with an accuracy of a micro-cell area. The model described in this section considers an area zone (see subsection 4.2.1), consisting of a set of building blocks and a street network (see Figure 3), covered by several micro-cells. Similarly to the city area model, a ‘specific’ area zone model can be developed for network planning purposes, while a ‘typical’ area zone can be used for research reasons. To derive a ‘typical’ area zone model, regular-shaped building blocks and a regular street-network graph can be considered. The latter leads to the well-known Manhattan grid, according to which, an area zone is represented by square shaped building blocks and orthogonal grid street network [10,31].
4
Assuming a large city of 10 millions inhabitants, the number of mobile users will be in the range of 7 millions (70% penetration).
5
E.g., the paging area in which the user was roaming during his most recent interaction with the network. Page 6
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Applying the methodology described in section 2, the basic set of input and output parameters of a ‘generic’ area zone model is given below, while a ‘typical’ application example model, adopted in [10], is given in Annex B.
Figure 3: The Area Zone Model
4.3.1. Input Parameters Geographical Area: The area consists of a set of building blocks and the corresponding street network. Building Blocks: A building block is characterized by: (a) its type (residential, business, shopping center, metro station, etc.) and (b) its capacity (number of people). The distribution of the building block types within a certain area zone depends mainly on the area zone type (city center, urban, etc.). Street Network: The street network surrounds the building blocks, forming in general a random graph. The nodes of the graph are the crossroads. A street is characterized by: (a) its size (length, number of lanes), (b) the average car speed, and (c) its orientation. Note that pavements are (can be) regarded as part of the street network. Population: As justified in subsection 4.2.1, only a sample of the MUs population needs to be modeled, without affecting the accuracy level of the output parameters. For example, the estimation of the offered traffic load in radio resource management related studies, require the consideration of (at least) the busy MUs. Users may be categorized according to their current mobility state as: not moving, pedestrians, passengers, etc. For each MU group certain mobility and traffic characteristics are assigned: Mobility Behavior: The mobility behavior of an MU group is determined by the mobility conditions on the street network. The basic random variables that describe the mobility behavior of a moving MU are: • • • • •
the the the the the
time required to cross two crossroads, probability of a user selecting a specific direction upon reaching a crossroad, time an MU belongs to a certain group (not moving, pedestrian, car passenger, etc.), probability that a user transits between different mobility states during a call [10,31] and MU trip type (e.g., internal, external).
In general, an area zone is surrounded by other areas, the incoming and outgoing MUs should also be encountered. To achieve a constant average MU density within an area zone (an important assumption for traffic analysis), the incoming and outgoing rates should be equal (see three-step approach described in Annex B). Traffic Behavior: Each MU group is assigned a set of parameters describing the traffic behavior of its members (i.e., service profile, call arrival rates, call duration, etc.). A detailed analysis of the MU calling patterns is presented in Annex D. Time Period: Depending on the purpose of the study, either the rush hours or the busy hour should be considered.
4.3.2. Output Parameters An example set of output parameters is presented below.
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Signaling and Traffic Related Parameters: offered traffic load, resource utilization factor, handover rate, user residence time in a cell area, etc. QoS Related Aspects: call and handover blocking probabilities, call-dropping probability, average number of handovers per call (and per user category), etc. A set of analytical models has been proposed in the literature for the estimation of the handover rate, as well as the average number of handovers per call [22-26, 30]. These models are based on simplifying assumptions (e.g., exponential distributed user residence time in a cell) and may lead to generic conclusions (e.g., in [23]). In layered cell architectures, the development of accurate analytical models is rather complex, mainly due to the involvement of radio resource management aspects (see studies in [30]). Moreover, such models do not provide estimations for indoor-outdoor handover cases.
4.4. Street Unit Model The street unit model describes the mobility behavior of (moving) MUs (pedestrians, passengers, etc.) with an accuracy of a few meters. To develop such a model, a very detailed analysis, regarding the car/pedestrian motion and the street type under any vehicular traffic conditions, is needed. The analysis concerning the car motion is presented in Annex C, while the basic set of input and output parameters of a ‘generic’ street unit model follows.
4.4.1. Input Parameters Geographical Area: The geographical area under consideration consists of one or more street segments connected at crossroads (see Figure 4). A single segment (street unit) is characterized by: (a) its length, (b) the number of lanes and (c) its capacity (cars/hr). Concerning the vehicular traffic flow control, the following street unit types can be identified: Highway: It is characterized by high average car speed, high capacity, non-interrupted vehicular traffic flow and usually contains several lanes per direction. The length of a highway may range from a few up to hundreds of kilometers. Traffic Light Controlled Flow: Vehicular traffic flow is controlled by traffic lights. The time interval the traffic light remains in each state (red, orange and green) is assumed constant. The length of such a street unit may be in the range of a building block side (e.g., 50-200 m). Prioritized Traffic Flow: In this street unit type, the vehicular traffic flow (on crossroads) is controlled by a set of driving rules, defined by the use of specific signs (e.g., STOP, GIVE WAY, etc.) The length of this street type may be in the range of a building block side (e.g., 50-200 m). Population and Car Driver Behavior: The analysis of the mobility parameters imposes the consideration of the mobility behavior of any passenger/pedestrian located at the street unit. Pedestrians move at slow speeds (2-5 km/hr), while their motion can be characterized as continuous (walking) or interrupted (e.g., shopping). The behavior of a car driver can mainly be guided by the following rules: - Minimization of the travelling time (i.e., based on route and speed optimization ). - Safe driving (i.e., the car speed is limited by the car density and the street characteristics). Time Period: From the description of the other mobility models, it is obvious that the street unit model should be analyzed under both rush hours and busy hour conditions. Car Speed vs. Car Density: According to transportation theory, there is strong relation between the car density and the average car speed [46]. This is because ‘safe driving’ requires a safety distance between cars, which increases with the car speed. In general, the average car speed on a street unit 6 may range from almost zero (traffic jam) up to a maximum value, which is the “free flow speed” . Note that an important issue here, is the assumed car arrival process. The application example of Annex C follows a realistic arrival process.
4.4.2. Output Parameters Example output parameters include the pdf of the following random variables:
6
The free flow speed corresponds to very low car density conditions, where the car speed is not limited by the safety distance but from the street characteristics (e.g. street width, driver visibility, etc.). Page 8
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•
The time an MU spends inside the street segment (residence time).
•
The MU speed.
•
The number of MUs (passengers, pedestrians) inside a certain street segment.
The street unit model can directly be used for propagation related aspects (e.g., slow fading analysis). Moreover, it is appropriate for handover related studies [44,45], as well as for the analysis of offered traffic load in micro-cells (where the number of users is quite low and the large number theorems do not provide realistic estimations [30]). Vmax = v1 Vmax = v2
Lane 1 Lane 2 Lane 3 Lane 4
Low Priority Street
Traffic Light Controlled Flow
Vm ax =v 3 Vmax = v4 Vmax = v5
Figure 4: The Generic Street Unit Model
5. Mobility Models Integration In this section, we investigate the integration of the presented basic mobility models, aiming at the derivation of a more realistic modeling approach, which combines the advantages of these models. Within this context, two approaches can be envisaged: Approach 1: The basic models are combined into a single mobility model, having the following characteristics. The geographical area under study, covers a city area consisting of a set of area zones connected via high capacity routes. Each area zone is an area zone model, consisting of a set of building blocks and a street network. Each street segment of the area zone model is a street unit model. It is obvious that in order to sufficiently load the street network, the whole (city) population should be taken into account. Although this approach provides a high level of accuracy, the computational effort (simulation approach) and the complexity (analytical approach) it introduces is 7 probably overwhelming . Approach 2: The basic mobility models are regarded here as independent components of an ‘Integrated Mobility Modeling Tool’ (IMMT), shown in Figure 5a. This approach succeeds in improving the input parameters’ accuracy of each basic model, by exploiting mobility-related output parameters derived by the other models. This leads to the refinement of the basic mobility models making thus, the IMMT approach a powerful framework for the analysis of mobile communication systems related
7
This was the original reason for the development of basic models, which although individually aim at the investigation of a limited set of design/research aspects, demand tolerable computational effort. Page 9
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aspects, at a reasonable computational effort (simulation approach) and tolerable complexity (analytical approach). During the refinement process of a basic mobility model (see Figure 5b), three methods for the estimation of the model output parameter(s) are evaluated: (a) direct measurements, (b) simulation models and (c) analytical models. The aim of the refinement process is to increase the accuracy of the estimated output parameter(s) at minimum cost. Cost in this case may refer to computational cost (e.g., computation time required by a simulation model) or to real cost (e.g., corresponding to the cost of measuring the target parameter(s)). In this context, the IMMT can be exploited for the validation of theoretical assumptions, the evaluation of analytical models and the investigation of the effect of the mobility modeling accuracy on system design decisions.
Integrated Mobility Modelling Tool Output Parameters
Basic Mobility Model Refinement Process Selection of Appropriate Approach
City Area Area Zone
Validation of Results
Street Unit
Analytical Models
Simulation Models
Input Parameters
Input Parameters Real Phenomena
Mobility Related Parameters
Other Basic Mobility Models
(a)
Measurements (b)
Figure 5: (a) The Integrated Mobility Modeling Tool (IMMT) and (b) the Refinement Process of a Basic Mobility Model Within the IMMT An example list of parameters that could be exchanged among the basic models is given below. City Area Model • • •
The pdf of the residence time within an area zone (measured by the area zone model). The pdf of the residence time in high capacity routes (measured by the street unit model). The duration of an internal trip (measured by the area zone model).
Area Zone Model • • •
The trip types, e.g., internal, external, etc. (measured by the city area model) that can be utilized so as to enhance the movement algorithm of the area zone model. The MU moving states probabilities: (a) not moving, (b) pedestrians and (c) car passengers (measured by the city area model). The pdf of: (a) the residence time in a street unit vs. street unit type, (b) the number of cars per street unit type and (c) the car speed vs. street unit type (measured by the street unit model).
Street Unit Model • •
Statistics concerning more realistic (car) arrival rates (measured by the city area and/or the area zone model). Statistics regarding the motion of pedestrians: continuous, interrupted (measured by the city area model).
6. Results In this section, indicative results obtained by the application of the example simulation models presented in Annexes A, B and C, are presented. In our study the basic mobility models are detailed Page 10
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simulation ones, however, following the IMMT approach one simulation model can be replaced by an analytical as soon as the analytical approach is proved to provide results of adequate accuracy. City Area Model: Figure 6 presents the percentage of MUs per area zone type (city center, urban, suburban and rural) vs. time. The results indicate that, apart from location management studies [8,9], the city area model can provide a clear view of the traffic demand distribution over certain area zone types and its (time) variance. The latter results can be utilized in DCA related studies [38-40]. Figure 7 depicts the distribution of user movements with respect to an area zone of a certain type (e.g., city center). Figure 8 illustrates the amount of area zone border crossings for outgoing users vs. the area zone for the busy and the rush hours. This type of results, which are the basis for LA planning analysis [8], can be compared to the crossing rates provided by the area zone model.
Percentage of Population per Area Zone Type
Figure 9 depicts the percentages of moving (passengers, pedestrians) and not-moving users vs. time. This figure also provides an example of how the IMMT approach can be applied to the city area model. IMMT columns refer to results obtained by the city area model, regarding city center and urban high capacity routes as traffic light controlled flow street units (red/green states duration equal to 60/60) while suburban and rural high capacity routes are regarded as highway street units. In this case the street unit model has been exploited so as to measure the pdf of the time an MU spends in a high capacity route. The street unit model receives as an input the street length (known from the city area geometry) as well as the arrival rate of cars as this is estimated from the initial city area model simulation (taking into account that the measurements of this model correspond to a sample of the total city population). As shown, the IMMT approach slightly alters the results. This is due to the fact that the city area model results refer to relatively long time-periods and mainly depend on aspects such as geographical distribution of maps and number of performed trips rather than the specific pdf of the MU residence time in an area zone/high capacity route. 60 Initial 50
7:00-8:00 8:00-9:00
40
9:00-10:00 10:00-11:00
30
11:00-12:00
20 10 0 City Centre
Urban
Suburban
Rural
Area Zone Type
Figure 6: Percentage of Users per Area Zone Type vs. Day Time Period
Percentage of movements
60 Internal
50
Outgoing 40
Incoming External
30 20 10 0 City centre
Urban
Suburban
Rural
Area type
Figure 7: Percentage of User Movements vs. Area Type Page 11
Mobility Modeling in Third Generation Mobile Telecommunication Systems
rush hour
300000
busy hour 250000 200000 150000 100000
31
29
27
25
23
21
19
17
15
13
11
9
7
5
0
3
50000
1
Outgoing Crossing Rate for rush and busy hours (crossings/hr)
350000
Area Zone
Figure 8: Outgoing Crossing Rate vs. Area Zone for Rush Hours and Busy Hour
Percentage of Mobile Users
90 80 70 60 50
Not-Moving
40
Not-Moving (IMMT)
30
Pedestrians
20
Pedestrians (IMMT)
10
Passengers Passengers (IMMT)
0 Initial
7:008:00
8:009:00
9:0010:00
10:0011:00
11:0012:00
Day Tim e Period
Figure 9: Percentages of Moving (passengers, pedestrians) and Not-Moving Users vs. Day Time Period Area Zone Model: Figure 10 depicts the pdf of a busy MU cell residence time , using: (a) the basic area zone model (Annex B), (b) the model proposed by Hong and Rappaport [22], (c) the IMMT 9 approach and (d) the exponential distribution . To compare the resulting pdf’s, all cases refer to a common average MU cell residence time equal to the one of case (a). The assumed cell characteristics appear in Figure B.1 (cross shaped, L=185m), while the IMMT approach regards streets as traffic light controlled flow street units with red/green states duration equal to 60/60 sec. The street unit model in the IMMT approach, receives as an input the street length (185 m) while the car arrival rate is adjusted so as to achieve the same average MU cell residence time as in case (a). As it can be observed, the exponential distribution is quite good approximation for (a) and (b) cases. However, the IMMT approach indicates that, in more realistic models, the exponential distribution approximation, although applicable, is not excellent. 8
Figure 11 depicts the pdf of a busy MU cell crossing time for the above mentioned cases (a-d). As it can be observed, neither the Hong model nor the exponential distribution provide a good approximation 10
8
It represents the time period between the establishment of a call initiated inside a cell, and the instance the busy MU crosses the cell boundary.
9
A common assumption in the literature.
10
It represents the time period between two successive crossings of a cell area borders by a busy MU. Page 12
Mobility Modeling in Third Generation Mobile Telecommunication Systems
for the cases (b) and (c). Case (b) (Annex B model), which obviously approximates a Gaussian distribution, is closer to the realistic approach of IMMT (case (c)). 0,12 Hong Basic Model IMMT Exp.Distr.
0,1
pdf
0,08 0,06 0,04 0,02
142,5
132,5
122,5
112,5
102,5
92,5
82,5
72,5
62,5
52,5
42,5
32,5
22,5
12,5
2,5
0
Busy MU Residence Time (sec)
Figure 10: The pdf of the Busy User Cell Residence Time for the: (a) Hong Model, (b) Basic Area Zone Model, (c) IMMT Approach and (d) Exponential Distribution
0,14 Hong Basic Model
0,12
pdf
0,1
IMMT Exp.Distr.
0,08 0,06 0,04 0,02
142,5
132,5
122,5
112,5
102,5
92,5
82,5
72,5
62,5
52,5
42,5
32,5
22,5
12,5
2,5
0
Busy MU Crossing Time (sec)
Figure 11: The pdf of the Busy User Cell Crossing Time for the: (a) Hong Model, (b) Basic Area Zone Model, (c) IMMT Approach and (d) Exponential Distribution Figure 12 depicts the variation of the call blocking and call dropping probability11 which derive from the simulation model of Annex B, for the following cases: i. Exponentially distributed MU cell residence time where the car density and average car speed are the ones assumed in Annex B. ii. The IMMT approach, where the streets of the area zone model of Annex B represent “traffic light controlled flow” street units. The pdf of the time a moving MU spends inside a street of the area zone model, is the one measured by the street unit model. The street unit model in this case receives as an input the street length (185 m), the red/green states duration (60/60 sec) and the car density (equal to the one assumed in Annex B as in case (i)). Note that in this case a different average car speed resulted (equal to 11.035km/hr) because Eq. B.1 is not valid for the traffic light controlled flow street unit. iii. An alternative application of the IMMT approach. The MU cell residence time in the area zone model of Annex B is assumed to be exponentially distributed (as in case (i)), however, since the streets represent “traffic light controlled flow” street units, the average car speed is the one measured by the street unit model in case (ii). The car density on the streets of the area zone model is the one assumed in Annex B (like in cases (i) and (ii)). 11
The call dropping probability is the probability that a call is blocked either during call setup or during a handover attempt. Page 13
Mobility Modeling in Third Generation Mobile Telecommunication Systems
As it can be observed, compared to the results of cases (ii) and (iii) which are very close, case (i) provides an overestimation of call blocking and call dropping probabilities. The results of case (i) show that the speed-density relation affects the estimation of call blocking and call dropping probabilities. On the other hand, cases (ii) and (iii) indicate that the assumption of exponentially distributed MU cell residence time is adequate, provided that the car density and average car speed have been accurately estimated. This study provides an example of how the IMMT approach can be exploited so as to verify theoretical assumptions (e.g., validity of the exponentially distributed MU cell residence time) and analyse the importance of mobility related input parameters (e.g., the speed-density relation) for the estimation of certain QoS parameters that judge the system capacity. Note that, the estimation of QoS parameters can be significantly affected in the case that the effect of mobility on the user calling behavior is encountered (see analysis in Annex D). 0,045 0,04
Call Blocking (i)
Call Blocking (ii)
Call Blocking (iii)
Call Dropping (i)
Call Dropping (ii)
Call Dropping (iii)
Blocking Probability
0,035 0,03 0,025 0,02 0,015 0,01 0,005
0,52
0,516
0,513
0,509
0,506
0,502
0,499
0,495
0,492
0,488
0,485
0,481
0,478
0,474
0,471
0,467
0,464
0,46
0,457
0,453
0
User Penetration Rate
Figure 12: Call Blocking and Call Dropping Probabilities vs. User Penetration Rate for cases (i), (ii) and (iii). Street Unit Model: The results presented in this section are based on the model of Annex C regarding a street unit model of length L=500m. The pdf of a car residence time12 in a street unit is illustrated in Figures 13 (high and low priority street units) and 14 (highway and traffic light controlled flow street units). As it can be observed, the pdf(s) are quite different and do not seem to fit to some known pdf. However, the results obtained by the street unit model provide means to define approximating pdf(s). Figure 15 depicts the pdf of the number of cars in a traffic light controlled flow street unit (measured at the moment a new car enters the street), while Figure 16 depicts the pdf of the car speed in the same street unit type. As it can be observed, the pdf(s) approximate the Gaussian. Figure 17 illustrates the average car speed in a traffic light controlled flow street unit vs. the car arrival rate and the red/green state duration. As shown, the average speed decreases as the proportion of red/green states increases. This is because cars stop more frequently as the duration of red state increases (against the green state duration) and therefore, their average speed is reduced. Finally, Figure 18 depicts the average car speed in high/low priority streets (for various turning probabilities (TP)13) vs. the car density in a high priority street. As it can be observed, the average car speed in low priority streets is rather invariant, as the car density in high priority street increases. This is due to the fact that, as the car density increases, the distance between cars decreases and thus it is more difficult for a car coming from a low priority street to cross/enter the high priority street. As a consequence, the average car speed decreases and therefore, the safety distance between a crossroad and the nearest car also decreases. On the other hand, the average speed is more strongly influenced by the turning probability.
12
It represents the time, during which a car moves along this street unit type.
13
It represents the probability that a car enters a high priority street from a low priority one. Page 14
Mobility Modeling in Third Generation Mobile Telecommunication Systems
Figures 17, 18 depict the critical parameters that affect the average car speed in the cases that vehicular traffic flow is prioritized or controlled by traffic lights. Within this context, the results presented in these figures provide means to model the relevant street unit types in the area zone model. 0,25 High Priority Str. 0,2
Low Priority Str.
pdf
0,15 0,1
133.5
127.5
121.5
115.5
109.5
103.5
97.5
91.5
85.5
79.5
73.5
67.5
61.5
0
55.5
0,05
Time (sec)
Figure 13: The pdf of a Car Residence Time in: (a) Low and (b) High Priority Street Unit
0,45 0,4
Traffic Light Controlled Flow
0,35
Highw ay
pdf
0,3 0,25 0,2 0,15 0,1
111
105
99
93
87
81
75
69
63
57
51
45
39
33
27
21
15
9
0
3
0,05
Time (sec)
Figure 14: The pdf of a Car Residence Time in: (a) Highway and (b) Traffic Light Controlled Flow Street Unit
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Mobility Modeling in Third Generation Mobile Telecommunication Systems
0,06 0,05
pdf
0,04 0,03 0,02 0,01
40
37
34
31
28
25
22
19
16
13
10
7
4
1
0 Number of Cars
Figure 15: The pdf of the Number of Cars in a Traffic Light Controlled Flow Street Unit
0,25 0,2
pdf
0,15 0,1
43,2
39,6
36
32,4
28,8
25,2
21,6
18
14,4
10,8
7,2
0
3,6
0,05
Car Speed (Km/hr)
Figure 16: The pdf of the Car Speed in a Traffic Light Controlled Flow Street Unit
30/60
Red/Green (sec) 60/60
60/30
Average Car Speed (km/hr)
29 27 25 23 21 19 17 15 0,1
0,2 0,3 Car Arrival Rate (cars/sec)
0,4
Figure 17: Average Car Speed in a Traffic Light Controlled Flow Street Unit vs. Car Arrival Rate and the Red/Green State Duration
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Mobility Modeling in Third Generation Mobile Telecommunication Systems
Average Car Speed (Km/h)
35 30 25 20 15 High Prior. Str. Low Prior. Str.(TP=0.2) Low Prior. Str.(TP=0.3) Low Prior. Str.(TP=0.4)
10 5 0 6,49
12,61
21,97
26,57
Average Number of Cars in High Priority Street (cars)
Figure 18: Average Car Speed in High/Low Priority Street vs. Car Density in the High Priority Street (expressed as the average number of cars on the street)
7. Conclusions In this paper, we have proposed a mobility modeling approach which caters for the whole range of design aspects met in third generation mobile telecommunication systems (e.g., location and paging area planning, handover strategies, cell layout, channel assignment schemes, etc.). At a first step, based on the observation that the analysis of various design aspects requires different level of detail concerning the user location, three basic mobility models have been specified. In particular: •
The city area model considers a city area as a set of area zones and high capacity routes. This model is valid for the analysis of location management related aspects, where the accuracy of the user location is considered at the level of a location/paging area.
•
The area zone model considers an area zone as a set of street segments and building blocks. The model is valid for the analysis of radio resource management related aspects, where the user location is considered at the level of a cell area.
•
The street unit model considers a set of street network segments. The model is valid for the analysis of radio propagation related aspects, where the user location is considered at the accuracy of a few wavelengths.
Taking into account that each model focuses on a specific set of design issues, we have proposed a methodological modeling approach, the so-called ‘Integrated Mobility Modeling Tool’ (IMMT). The IMMT approach considers the basic models as independent components among which mobility-related parameters can be exchanged. The results obtained, indicate its applicability for the validation of the theoretical input assumptions and the results of existing analytical models. In this context, the IMMT approach contributes in the investigation of the effect of the mobility model accuracy on design decisions. Moreover, the ability of the IMMT to represent any specific geographical area, constitutes the tool appropriate for network planning and thus stresses the relation between mobility modeling and network implementation cost.
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Mobility Modeling in Third Generation Mobile Telecommunication Systems
ANNEX A City Area Model Application Example The city area under consideration (see Figure A.1) has a radius of 20 Km. Four area types are identified: city center, urban, suburban and rural area. The model consists of 32 area zones (8 per city area type), 4 peripheral (one per area type) and 4 radial high capacity routes. The population is 6 millions inhabitants and the MU penetration rate is 50% (i.e., there are 3 millions of MUs roaming within the city area). In our simulation tool, a sample of 100000 MUs has been assumed.
City Centre Urban Area Suburban Area Rural Area
Area Borders Peripheral - Radial High Capacity Route
Figure A.1: The City Area Model Consisting of Area Zones Connected via High Capacity Routes Movement Attraction Points (MAPs): The following types of MAPs are considered: (a) residences, (b) work places and (c) other e.g., shopping centers, parks, etc. Figure A.2 presents the assumed distribution of MAPs over the whole city area. Note that within a certain area type (e.g., urban, suburban area) the MAPs are uniformly distributed.
50 40 30
% 20 10 0
er s Oth lace ces rk P o iden W Res
Cen ter Urb an Sub urba n Rur al
Figure A.2: The Distribution of MAPs over the City Area MU Grouping based on their Mobility Behavior: As shown in Figure A.3, MUs are grouped according to: (a) the mobility behavior they exhibit (working people, residential users and high mobility users) and the (b) transportation means they use (private car, public transportation).
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Mobility Modeling in Third Generation Mobile Telecommunication Systems
Mobile Users
Working People 35%
Private Car
High Mobility Users 60%
5%
Taxi
15%
25%
60%
18%
70%
30%
Public Transport.
Residential Users
Private Car
Taxi
66%
16%
Private Car
Taxi
Public Transport.
Figure A.3: Categorization of MUs According to Their Mobility Behavior Time Zones: The simulation time ranges from 7:00 a.m. to 12:00 p.m., including thus both the rush hours (7:00-9:00 a.m.) and the busy hour (11:00 a.m.-12:00 p.m.). Initial MU Distribution over the City Area: MUs are initially distributed over the city area by assuming that the majority (95%) is situated at their residences. MU Movements: The way MUs move depends on the MU group, the MAPs distribution, as well as the high capacity routes topology. Upon entering to a MAP, a residence time is assigned. When this expires, the movement destination is selected based on the gravity model [46,48], and a route is determined. In general, the route from one area zone to another, due to the high capacity routes topology, is discriminated into two parts: (a) radial and (b) peripheral. In our model, the shortest path approach is applied: when an MU moves towards an inner city area zone, firstly selects the radial and then the peripheral direction. When an MU moves towards an outer city ring, the reverse order is followed i.e., first peripheral and then radial. Movement Algorithm for Working People (see Figure A.4): Working people initiate a movement, at a moment in time uniformly distributed between 7:00 a.m. and 7:30 a.m. After a short period of walking/waiting -depending on the transportation mean that will be used- (uniformly distributed between 5-15 min.) the MU rides on a vehicle (private car, taxi or a set public transportation means). After another short period of walking, the MU reaches his/her work place. Some short distance movements around their work place may also be performed during the working hours e.g., lunch time. Movement Algorithm for Residential Users (see Figure A.4): We assume that every residential user initiates a movement, at a moment in time uniformly distributed between 7:30 a.m. and 9:30 a.m. We distinguish two movement types: (a) those performed inside the area zone where the MU residence locates and (b) those destined to a different area zone. For movements of type (a), MUs are regarded as pedestrians for a time interval uniformly distributed between 0.5 and 2 hours. For type (b) movements, MUs may use either their private car, a taxi or some public transportation mean. The "residence time" within the destination area zone is uniformly distributed between 0.5 and 3 hours. In this case, MUs are regarded as pedestrians visiting banks, shops or other attraction points inside this area zone. Movement Algorithm for High Mobility Users (see Figure A.5): We assume that MUs belonging to this category are already in motion, having a destination when the simulation starts. After having completed their movement, they reside for a short period (0-15 min.) before they are assigned a new destination. This procedure is repeated during the whole simulation process. Car
Origin
Pedestrian
Public Trans.
Taxi
Pedestrian
Pedestrian
Destination
Public Trans.
Figure A.4. Movement Algorithm for Working People and Residential users Taxi Destination
Origination Car
Figure A.5. Movement Algorithm for High Mobility Users Page 19
Mobility Modeling in Third Generation Mobile Telecommunication Systems
Mobility Conditions: The average pedestrian speed is 5 km/hr (in [46] the average pedestrian speed is in the range of 3km/hr to 5km/hr). The vehicle (private car, taxi, bus) speed is based on Table A.1. Note that, the model could be further enhanced by taking into account the relation between car density and speed on a certain street (e.g., based on the model of Equation (b.1)). Traffic Conditions We consider the arrival of both incoming and outgoing calls. The call arrival process is assumed to be Poisson. Table A.2 presents the call arrival rate (both incoming and outgoing) for each MU category during three day time periods: (a) 7:00a.m.-9:00a.m., (b) 9:00a.m.-11:00a.m. and (c) 11:00a.m.12:00p.m. In addition, we present the percentage of incoming and outgoing calls for each MU category. For high mobility users, the rate of incoming calls is assumed to be higher than the corresponding outgoing, because incoming calls are for both private and business communications. VEHICLE TYPE AREA TYPE
Public Transportation Media
Car/TAXI
CENTRE URBAN
5 - 15 km/hr 10 - 30 km/hr
10 - 20 km/hr 15 - 40 km/hr
SUBURBAN RURAL
30 - 70 km/hr 60 - 80 km/hr
40 - 80 km/hr 60 - 100 km/hr
Table A.1: The Range of Vehicle Velocities in Conjunction with the Area Type CALL ARRIVAL RATE (calls/MU/h) MU Category
7:00-9:00
9:00-11:00
11:00-12:00
Incoming- Outgoing
Working People Residential Users High Mobility Users
0.5 0.5 1.0
2.0 1.5 2.0
3.5 2.0 3.5
50 % - 50 % 50 % - 50 % 70 % - 30 %
Table A.2. Call Arrival Rate (calls/MU/h) for all MU Categories vs. Day Time
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Mobility Modeling in Third Generation Mobile Telecommunication Systems
ANNEX B Area Zone Model Application Example Geographical Area: The geographical area is square shaped and represents a typical city center area (4 km2) modeled as a Manhattan grid i.e., buildings are squares and streets form a regular grid. To achieve a realistic population distribution, various types of environments have been defined, each characterized by: (a) the percentage of the total area it covers and (b) the corresponding population density (see Table B.1). Environment
Coverage Percentage
Population Density (people/km2)
Busy Spots Business Domestic Streets Other
30 % 41 % 10 % 15 % 4%
150000 75000 9000 (see Fig. B.1) 6500
Table B.1: Area Characteristics The number of pedestrians and car passengers is calculated by the following assumptions: (a) 66.67% of the street area is covered by cars, (b) streets are bi-directional, (c) the average number of passengers per car is 1.5, (d) there are 2 buses per street segment, (e) the average number of passengers per bus is 45 and (f) pedestrians are uniformly distributed on the pavements (see Figure B.1). The resulting densities are 51000 passengers/km2 and 66000 pedestrians/km2, where the km2 corresponds to the street area only and not to the whole geographical area. Mobility Characteristics: Three MU groups are considered (MUs are not allowed to alter category during a call): (a) users located in buildings, (b) pedestrians with a speed following the Gaussian distribution with mean value 5 km/hr and variance 30%, and (c) car passengers with a speed following the Gaussian distribution variance 30% and a mean value which is calculated by the formula (also utilized in [29]):
D v s = v f ⋅ 1 − D jam
(b.1)
where, vs:
The average car speed on the street (km/hr).
vf:
The free flow speed (60 km/hr).
D:
The linear car density per lane (cars/km).
Djam: The linear car density per lane at traffic jam (cars/km). In our case it is obvious that D/Djam=0.667 (since the cars are assumed to cover 66,67% of the street). Thus, the resulting average car speed is vs=20 Km/hr. The MU movement direction may alter only at crossroads. The same direction is kept with a probability of 0.5, while the user turns left or right with a probability of 0.25 (backward movement is not allowed). To model the fact that MUs leave/enter the area zone, we consider a Poisson process of incoming MUs at a rate equal to the rate of outgoing which is estimated by a three-step approach: 1) Run the simulation without considering incoming users, and measure the arrival rate of outgoing ones. 2) Run the simulation with a generator of incoming MUs at a rate equal to the one measured in step (1). In this case, a portion of the incoming MUs crosses the area zone and as a result the outgoing rate is still higher than the incoming. 3) Measure the percentage of incoming MUs that cross the area zone, and reduce the rate of incoming MUs accordingly.
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Mobility Modeling in Third Generation Mobile Telecommunication Systems
9m
9m
Lstr = 15 m
Pavement L (m)
3m
4m
Pedestrian L = 185 m
Pavement
Street segment
Building Block
Figure B.1: The Population Distribution on the Streets of a Micro-Cell Traffic Characteristics: Traffic related parameters are shown in Tables B.2, B.3 [10]. We assume a Poisson call arrival process, and an exponentially distributed call duration (see Table B.3). The call arrival rate refers to the total number of incoming and outgoing calls during busy hour conditions. Further improvements of the MU calling patterns can be based on the analysis of Annex D (e.g., the call arrival rate could differ between business and residential users). We assume that 65% of the MUs located inside buildings are served by private wireless networks. Regarding the multiple access protocol, the one presented in [50] has been adopted. The protocol is capable of supporting three service classes, namely, circuit-mode voice, burst-mode voice and data, by performing statistical multiplexing of connections of the three classes at two different levels: (a) the call-level (for circuit-mode voice) and (b) the talkspurt/message-level (for burst-mode voice and data). In our simulation, we assume that 70% of the voice calls are of the packet-mode type. Regarding the radio resource allocation, a Fixed Channel Allocation (FCA) scheme is considered, while in every micro-cell, 2 carriers with 96 full-duplex channels (96 slots/frame, FDD) are available [50]. A micro-cell area equals to the area depicted in Figure B.1. Service Type
Call Arrival Rate (Calls/User/Hr)
Mean Call Duration (sec)
Voice Data
3,0 2,78
90 50
Table B.2: Call Arrival and Call Duration per Service Type Service Penetration Rate Environment
Voice
Data
Busy Spots Business Domestic Street Other
95 % 99 % 95 % 98 % 95 %
5% 70 % 10 % 2% 5%
Table B.3: Penetration Rate per Service and Environment
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Mobility Modeling in Third Generation Mobile Telecommunication Systems
ANNEX C Street Unit Model Application Example In this annex, we describe a simulation tool, which models all types of street units i.e., highways, traffic light controlled traffic flow and prioritized flow control streets. For the sake of simplicity, our simulation tool considers a single lane street unit (see Figure C.1). As far as the behavior of a car driver is concerned, this is mainly guided by the following rules: - Minimization of the traveling time (i.e., based on route and speed optimization). - Safe driving (i.e., the car speed is limited by the car density and the street characteristics). S
L
L
(a) Highway
(b) Traffic Light Controlled Flow
Low Priority Street
High Priority Street
STOP
L
L
(c) High-Low Priority Street
Figure C.1: Street Unit Models: (a) Traffic Light Controlled Flow and (b) High-Low Priority Street Based on those two rules, we built up an empirical law regarding the way the driver controls the car speed. This empirical law correlates: (a) the car acceleration with the distance between a car and the foregoing car, (b) the maximum car speed on the street unit and (c) the car acceleration-deceleration characteristics. The empirical law is expressed by the following formula:
∂v (t ) = gc ∂t
v (t ) + c ⋅ 1 − exp k c ⋅ − 1 vm
(c.1)
where, v(t): The car speed at time t (km/h) gc:
A constant expressing the car accelerating capabilities (20 m/sec2).
kc:
A constant expressing the car decelerating capabilities (assumed value 0.6).
c:
An arbitrary constant (assumed value 0.5 km/hr).
vm:
The maximum safety speed based on the distance from and the speed of the preceding car (km/h).
The vm is given by the following empirical formula:
v m = min v f
p
d (t ) ⋅ v pre (t ) + c , d safe (v pre (t ))
(
)
(c.2)
where, d(t): vpre(t):
The current distance between this car and the preceding one (km). The current speed of the preceding car (km/h).
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Mobility Modeling in Third Generation Mobile Telecommunication Systems
dsafe(v):
The safety distance between two cars traveling at speed v (km).
p:
An empirical constant expressing the sensitivity of the driver to the speed changes of the preceding car (assumed value 2).
Finally, the ‘safe distance’ between two cars traveling at speed v, is given by the following formula:
d safe ( v ) = a ⋅ v + d min
(c.3)
where,
α : a constant expressing the time it takes a driver to stop the car by the moment the preceding car starts decelerating (the assumed value is 0.7 sec).
dmin: the minimum distance between not-moving cars (0.5 m). Note that the average car length is assumed equal to 5m. The above mentioned empirical law describes the behavior of an individual driver in a street unit and can be utilized for simulating the car motion. To adopt realistic values for the parameters appearing in the above formulas, we have performed a series of experiments. In these experiments, the speed of a single car just entering the street unit with an initial speed set to zero, is analyzed for the following cases: • • •
No other car on the street (free flow). One car at a distance of 30m traveling with 10, 40 or 60 km/hr. One not moving car at a distance of 100m.
The experiment results for this set of representative cases are presented in Figure C.2. Stop at 100m Free Flow Prec.Car 60km/hr Prec.Car 40km/hr Prec.Car 10km/hr
80
Car Velocity (km/hr)
70 60 50 40 30 20 10 0 0,08
2,08
4,08
6,08
8,08
10,08
12,08
14,08
16,08
18,08
Time (sec) Figure C.2: The Behavior of the Empirical Model of the Street Unit Model. It depicts the car speed vs. time for the following cases: (a) free flow (no preceding car exists), (b) preceding car at 30m with speed 60km/hr, (c) preceding car at 30m with speed 40km/hr, (d) preceding car at 30m with speed 10km/hr, (e) preceding car stopped at 100m. The street unit model has been utilized so as to analyze all types of street types: (a) highway, (b) traffic light and (c) high/low priority streets. To achieve a more realistic car arrival process, our model considers three street units is series, where the arrival process of cars in the first street is Poisson (default rate: 0.2 cars/sec) while measurements are performed in the third street unit. In the case of traffic light, the greed/orange/red states duration is 60/3/60sec, respectively. In the case of the high/low priority streets, the probability of a car in a low priority street entering a high priority street is 0.2. Cars in low priority streets, decide to enter/cross the high priority street when the distance between the cross-road and the nearest arriving car on the high priority street is ‘safe’. The minimum safe distances for entering/crossing the street are assumed to be a function of the speed Vcar of a car moving in high priority street: cross: 1.2*Vcar, enter: 2*Vcar.
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Mobility Modeling in Third Generation Mobile Telecommunication Systems
ANNEX D Mobile Users Calling Behavior An important issue influenced by user mobility concerns the MU calling behavior expressed by the the incoming/outgoing call arrival rate and the average call duration. From fixed networks it is well-known that different calling behavior characterizes business and residential users. In mobile communication systems, different calling patterns can be identified for moving and not moving users. For example, shorter call duration is expected for car drivers compared to not moving users. The estimation of the traffic-related parameters is subject to the following assumptions: Not Moving Users: Estimations can be based on relevant estimations from fixed networks. Moving Users: Estimations can be based on the following assumptions: •
The rate of outgoing calls of a specific service type depends on the user mobility class (e.g. pedestrian, car passenger, etc.). This is due to the fact that the MU class affects the convenience of a user to initiate calls. E.g., compared to a user situated in his office a pedestrian will normally initiate a lower number of voice calls and an even lower number of (if not any) fax calls.
•
The rate of incoming calls does not depend on the user mobility class, since the calling MU in general ignores the current moving state of the called MU.
•
The call duration is strongly affected by the user mobility class. This is due to the fact that the mobility class determines the user convenience for making longer calls (e.g., shorter call duration are expected for metro passenger compared to a private car passenger).
The convenience to communicate (by means of call initiation and call duration) is assumed to be affected by the user mobility class, according to the hierarchy listed in table D.1. Note that the higher the position in the hierarchy the higher the corresponding value is expected. Call Initiation Not moving business Not moving residential Car passenger Public transportation passenger Pedestrians
Call Duration Not moving residential Not moving business Car passenger Pedestrians Public transportation passenger
Table D.1: The Hierarchy of User Mobility Classes
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