Mobility Modelling

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Mob i l i t y Mode l ing in Th i r d Genera t ion Mob i le

Te lecom m un ica t ion Sys tem s

J.G.Mark ou l i dak is , G.L.Lyberop oulo s, D.F.Ts i rk as, E.D.Syk as

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]

Abs t rac t : In mobile communications, mobility modeling is involved in several aspects related tosignaling and traffic load analysis. I n t hird generation systems, the influence of mobility on t he network

performance (e.g., handover rate) will be strengthened, mainly due to the huge number of mobileusers 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. Inthis paper, we propose three basic types of mobility models, which are appropriate for the analysis ofthe full range of mobile communications' design issues. The models provide different levels of detailregarding 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 StreetUnit 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 modelingtool, which considers the basic mobility models as components is proposed, aiming at the developmentof 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 thecomponent models. To justify the applicability of the proposed integrated tool for both the analysis ofdesign 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 earlyyears of the next century [1-3]. Aiming at a mass market telecommunication system, the TGMTS willoffer a plethora of telecommunication services (e.g., voice, low and high bitrate data, video) to MobileUsers(MU) via a range of mobile terminals1, operating in both public and private environments (officeareas, residences, transportation media, etc.). Due to the mass market nature, TGMTS should bedesigned as a high capacity system, able to cope with the envisaged overwhelming traffic demands. Toachieve 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, theemployment 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 onthe number of database transactions, constituting thus the database a possible bottle-neck at the fixednetwork side. Consequently, and given the scarcity of radio resources, methods for signaling loadreduction are emerging for TGMTS [8-21]. It is obvious that optimization techniques and efficientnetwork planning algorithms are critical issues, concerning the overall TGMTS performance.

Mobility modeling is involved in the analysis of: (a) location management related aspects (location areaplanning [8,12,13,18], paging strategies [9,11,17], etc.), (b) radio resource management related

1 The terminals can range from basic low cost simple types, through hand portable devices and vehicle mountedspeech devices up to portable B-ISDN terminals.

2 The expected user penetration rate ranges from 50% to 70% of the total population.


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aspects (multiple access techniques, channel allocation schemes, etc.) [10,14,22] and (c) propagationrelated aspects (fading, handover decisions, etc.) [44,45]. Evaluation studies involve the considerationof 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 modelsinvolved 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 criticalnetwork 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]. Onthe other hand, computer simulation studies [8-10,31,32] consider more detailed and realistic mobilitymodels. Among the disadvantages of the above models are: (a) the amount of the required inputparameters, (b) the verification of results vs. real measurements and (c) the required computationaleffort.

In this paper, three basic types of mobility models which are appropriate for the full range of theTGMTS design issues (e.g., location and paging area planning, handover strategies, channelassignment schemes, etc.) are introduced. In particular:

The Ci ty Area Mode l . 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 crossingrate per area zone, the percentage of non-moving and moving users (car passengers, pedestrians)for each area zone vs. time, etc.

The Area Zone Mode l . The model consists of a street network and a set of building blocks. It maybe utilized for the estimation of: the pdf (probability distribution function) of a user residence time inan area zone, the pdf of a user crossing time in an area zone, etc.

The St ree t Un i t Mode l . This model considers three street types: (a) highways, (b) streets withtraffic light(s) controlled flow and (c) high/low priority streets. Candidate output parameters mayinclude: the pdf of car density and car speed in a street segment, the pdf of car residence time in astreet segment, etc.

Taking into account that each model concentrates on a specific range of design issues, we propose amethodological modeling approach, the so-called Integrated Mobility Modeling Tool ( I M M T), thatconsiders the basic models as components among which mobility-related parameters can beexchanged. 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 mobilitymodeling is given, identifying candidate input and output parameters. Section 3 stresses the necessityfor the development of various mobility model types for TGMTS. Section 4 provides an overview oftransportation theory approach in conjunction with the three basic mobility models. In section 5, theIMMT approach is described. Section 6 presents some indicative results, which are derived fromsimulation-based application examples of the three basic mobility models (Annexes A, B and C). AnnexD provides a brief analysis on the effect of mobility on the user calling behavior. Finally, conclusions aredrawn 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 ofI n p u t P ar a m e t e r s 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 populations mobility is modelled.

The set of O u tp u t Pa ra me te rs Sout, consisting of a set of functions. Each function provides thelocation of an individual pover the set Gfor each time instance of the set T:

{ }S x x g p P g t G t T out p p= = : , , ( ) ,


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where, gp(t) is the location of the individual pat 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 eithermeasure or derive the output parameters via a set of functions/methods. This is mainly due to the hugenumber of parameters that have to be considered, regarding the user mobility behavior, the vehiculartraffic conditions, etc. To alleviate these problems, the simplified modeling approach described belowmay be followed:

Pop u la t i o n ( P ) : The population is grouped into classes e.g., pedestrians, car passengers, workingpeople, students, etc., based on the mobility behavior characteristics. Another possible simplification

might be the consideration of a representative sample of the total population. Geograph ica l 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, andnot with an accuracy of a specific point. Example categorization of areas may be the city center,urban area, suburban area, rural area, etc.

Time Per iod (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 rushhours, 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 x x g p P g t G t T out p p= = : , , ( ) ,

Note that the development of the appropriate mobility model should be based on a set of criteriaregarding the accuracy required in terms ofpopulation, spaceand t ime. Another crucial parameter isthe required effort. The effort may refer either to the collection of real measurements or to thedemanded computational cost.

Real Phenomena

Output Parameters

Measurements

Generic Mobility ModelGeneric Mobility Model

Functions and Methods

Input Parameters

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 forthe continuity of ongoing calls.

The performance of the above procedures is influenced by the user mobility behavior. Their applicationdirectly 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, thehandover procedure affects the offered traffic volume per cell as well as the Quality of Service (Qo S)experienced by the MUs (e.g., call dropping). In TGMTS, the estimation of the above parameters, whichare critical for network planning and system design (e.g., location and paging area planning, handoverstrategies, channel assignment schemes, etc.) urge for the development of appropriate mobilitymodels. Due to diversification of the above issues, different mobility detail levels are required. Inparticular:


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Location Management Aspects: Location area planning, multiple step paging strategies, datalocating strategies, database query load, etc. [8,9,11-13,16-21,33-35]. Location managementrelated 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 resourcemanagement related aspects require medium-scale area accuracy (cell area).

Radio Propagat ion 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 followingsection.

4. Mobility Models for Mobile Communications

Within the context of the generic modeling approach presented in Section 2 and taking into account therequirements relevant to mobile communications, three types of mobility models are proposed. Theframework for the development of those models is based on transportation theory, an overview ofwhich 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, streetnetworks, 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 systemshould carry. The input framework which is utilized as a basis for the development of the relevantmodels is described by the following items:

Tr ip s: A trip (movement) is characterized by: (a) the purpose, (b) the end-points (origination-destination), (c) the transportation means utilized and (d) the route followed. Given a certaingeographical 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. Thedivision 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 ofan area zone.

Popu la t ion Groups: The population of the area under study is divided into groups according totheir mobility characteristics. Example groups are working people, residential users, students, etc.

Mo ve me n t A t t ra c t i o n Po in t s (MAP) : MAPs represent locations that attract the populationmovements 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 certaintypes of movements take place (e.g., movements towards work-places) and time periods wherecertain population groups reside to certain MAPs (e.g., working hours, shopping hours, etc.). Thesetime 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.Transpor ta t ion Sys tems Charac te r is t i cs: A transportation system (e.g., a street network, theurban buses network, the subway, etc.) is characterized by: (a) its capacity, (b) the trips it may

support and (c) the usage cost3.

The basic models used by the transportation theory are:

Trip Production and Attraction Models: The output parameters of these models are the number oftrips 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.


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Trip Distribution Models: The output of these models is the so-called origination-destination matrixOD(Ai,Aj). Each element of this matrix equals to the number of trips originated from area zone A iand 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 toperform 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 acertain route is selected, given the trip end-points and the street network [49]. The criteria utilizedhere 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. Theneed to analyze the user mobility behavior over large-scale geographical areas is raised by locationmanagement related aspects. Network planning purposes, impose the use of city area modelsrepresenting specific cities (i.e., based on geographical databases, demographic data and existingtransportation studies). On the other hand, typical city area models are required for the evaluation ofproposed 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 characteristicscan be observed in most contemporary cities. For example:

Cities are usually developed in such a way that densely populated areas (urban areas) surround acity center (high density of work places and shopping centers). While moving towards the cityedges 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 theedge 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 ageneric city area model is given below, while a typical application example model, adopted in variousstudies [8,9], is given in Annex A.

High Capacity Route

Figure 2 : The City Area Model

4.2.1. Input Parameters

Geograph ica l Area: The geographical area covers the whole city area, consisting of a set of areazones connected via high capacity routes (see Figure 2).

Area Zones: Combining transportation theory aspects and mobile telecommunication requirements, itseems reasonable to assume that an area zone equals to a network area (e.g., macro-cell, localexchange area, etc.).

High Capacity Routes: They represent the most frequently selected streets (routes) for the support ofmovements between different area zones.

Note that areas outside the city can also be modeled as area zones which attracts a relatively lownumber of trips.


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Popu la t ion : Mobile communication systems focus merely on the mobility behavior of MUs, andtherefore, only this relevant portion of the total population needs to be considered. However, takinginto account that third generation systems are expected to support high user penetration rates -similarto 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. Foreach 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 criteriaaccording 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 itsmembers, i.e., available services, call arrival rates, call duration, etc. A detailed analysis of the MUcalling patterns is presented in Annex D.

Time Per iod : 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 busyhour. However, there are problems, especially the ones related to the mobility related signaling, whichrequire 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 Loca t ion Upda tes for a given Location Area (LA ) planning scheme. Various, eitherstatic or dynamic LA planning schemes have been proposed in the literature [8,12,18]. The existinganalytical 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. Inshort term, their accuracy can be considered as higher compared to the city area model (whereonly the high capacity routes are considered). However, their assumptions are not valid for longtime 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 tothe individual MU mobility behavior [8].

Pag ing S igna l ing Load in Multiple Step Paging Strategies. Paging Strategies which aim at theminimization 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 areadimensioning.

Database Query Load. Taking into account the solutions proposed for the (distributed) databasein TGMTS [19-21], it is necessary to provide estimations regarding the relative location of thecalling 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 thequery 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 MUlocation 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 bedeveloped 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-networkgraph can be considered. The latter leads to the well-known Manhattan grid, according to which, anarea 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.


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Applying the methodology described in section 2, the basic set of input and output parameters of ageneric 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


Geograph ica l Area: The area consists of a set of building blocks and the corresponding streetnetwork.

Building Blocks: A building block is characterized by: (a) its type (residential, business, shoppingcenter, metro station, etc.) and (b) its capacity (number of people). The distribution of the buildingblock 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, numberof lanes), (b) the average car speed, and (c) its orientation. Note that pavements are (can be)regarded as part of the street network.

Popu la t ion : As justified in subsection 4.2.1, only a sample of the MUs population needs to bemodeled, without affecting the accuracy level of the output parameters. For example, the estimation ofthe offered traffic load in radio resource management related studies, require the consideration of (atleast) 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 onthe street network. The basic random variables that describe the mobility behavior of a moving MUare:

the time required to cross two crossroads, the probability of a user selecting a specific direction upon reaching a crossroad, the time an MU belongs to a certain group (not moving, pedestrian, car passenger, etc.), the probability that a user transits between different mobility states during a call [10,31] and the MU trip type (e.g., internal, external).

In general, an area zone is surrounded by other areas, the incoming and outgoing MUs should alsobe 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-stepapproach described in Annex B).

Traffic Behavior: Each MU group is assigned a set of parameters describing the traffic behavior of itsmembers (i.e., service profile, call arrival rates, call duration, etc.). A detailed analysis of the MUcalling patterns is presented in Annex D.

Time Per iod : Depending on the purpose of the study, either the rush hours or the busy hour should beconsidered.


An example set of output parameters is presented below.


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Signa l ing and Tra f f i c Re la ted Paramet e rs:offered traffic load, resource utilization factor, handoverrate, user residence time in a cell area, etc.

QoS Related Aspects: call and handover blocking probabilities, call-dropping probability, averagenumber 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 onsimplifying assumptions (e.g., exponential distributed user residence time in a cell) and may lead togeneric 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 (seestudies 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 thecar/pedestrian motion and the street type under any vehicular traffic conditions, is needed. Theanalysis concerning the car motion is presented in Annex C, while the basic set of input and outputparameters of a generic street unit model follows.


Geograph ica l Area: The geographical area under consideration consists of one or more streetsegments 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 trafficflow control, the following street unit types can be identified:

Highway: It is characterized by high average car speed, high capacity, non-interrupted vehiculartraffic flow and usually contains several lanes per direction. The length of a highway may range from afew up to hundreds of kilometers.

Traffic Light Controlled Flow:Vehicular traffic flow is controlled by traffic lights. The time interval thetraffic light remains in each state (red, orange and green) is assumed constant. The length of such astreet 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 controlledby 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).

Popu la t ion and Car Dr ive r Behav io r : The analysis of the mobility parameters imposes theconsideration 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 thefollowing 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 Per iod :From the description of the other mobility models, it is obvious that the street unit modelshould be analyzed under both rush hours and busy hour conditions.

Car Speed vs. Car Densi ty :According to transportation theory, there is strong relation between thecar density and the average car speed [46]. This is because safe driving requires a safety distancebetween cars, which increases with the car speed. In general, the average car speed on a street unit

may range from almost zero (traffic jam) up to a maximum value, which is the free flow speed6.

Note that an important issue here, is the assumed car arrival process. The application example ofAnnex C follows a realistic arrival process.


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 safetydistance but from the street characteristics (e.g. street width, driver visibility, etc.).


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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 offeredtraffic load in micro-cells (where the number of users is quite low and the large number theorems donot provide realistic estimations [30]).

Lane 1

Lane 2

Lane 3

Vmax=

v3

Vmax = v2

Vmax = v4

Vmax = v5

Vmax = v1

Lane 4

Low Priority Street

Traffic Light Controlled Flow

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 thederivation of a more realistic modeling approach, which combines the advantages of these models.Within this context, two approaches can be envisaged:

Ap p ro a ch 1 : The basic models are combined into a single mobility model, having the followingcharacteristics. The geographical area under study, covers a city area consisting of a set of area zonesconnected via high capacity routes. Each area zone is an area zone model, consisting of a set ofbuilding blocks and a street network. Each street segment of the area zone model is a street unitmodel. It is obvious that in order to sufficiently load the street network, the whole (city) populationshould 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 isprobably overwhelming7.

Ap p ro a ch 2 : The basic mobility models are regarded here as independent components of anIntegrated Mobility Modeling Tool (I M M T), shown in Figure 5a. This approach succeeds in improvingthe input parameters accuracy of each basic model, by exploiting mobility-related output parametersderived by the other models. This leads to the refinement of the basic mobility models making thus, theIMMT 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 theinvestigation of a limited set of design/research aspects, demand tolerable computational effort.


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aspects, at a reasonable computational effort (simulation approach) and tolerable complexity (analyticalapproach).

During the refinement process of a basic mobility model (see Figure 5b), three methods for theestimation of the model output parameter(s) are evaluated: (a) direct measurements, (b) simulationmodels and (c) analytical models. The aim of the refinement process is to increase the accuracy of theestimated 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 costof measuring the target parameter(s)). In this context, the IMMT can be exploited for the validation oftheoretical assumptions, the evaluation of analytical models and the investigation of the effect of themobility modeling accuracy on system design decisions.

Real Phenomena

Output Parameters

Input Parameters

StreetUnit

Integrated Mobility Modelling ToolIntegrated Mobility Modelling Tool

AreaZone

CityArea

Mobility Related Parameters

Basic Mobility Model Refinement ProcessBasic Mobility Model Refinement Process

Input Parameters

Analytical

Models

Other Basic

Mobility Models

Simulation

Models

Validation of Results

Selection of Appropriate

Approach

Measurements

(a) (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.

Ci ty Area Mode l

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 Mode l

The trip types, e.g., internal, external, etc. (measured by the city area model) that can be utilizedso 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 perstreet unit type and (c) the car speed vs. street unit type (measured by the street unit model).

St ree t Un i t Mode l

Statistics concerning more realistic (car) arrival rates (measured by the city area and/or the areazone model).

Statistics regarding the motion of pedestrians: continuous, interrupted (measured by the city areamodel).

6. Results

In this section, indicative results obtained by the application of the example simulation modelspresented in Annexes A, B and C, are presented. In our study the basic mobility models are detailed


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simulation ones, however, following the IMMT approach one simulation model can be replaced by ananalytical as soon as the analytical approach is proved to provide results of adequate accuracy.

Ci ty Area Mode l: 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 zonetypes 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 planninganalysis [8], can be compared to the crossing rates provided by the area zone model.

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 highcapacity 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 thestreet unit model has been exploited so as to measure the pdf of the time an MU spends in a highcapacity route. The street unit model receives as an input the street length (known from the city areageometry) as well as the arrival rate of cars as this is estimated from the initial city area modelsimulation (taking into account that the measurements of this model correspond to a sample of thetotal city population). As shown, the IMMT approach slightly alters the results. This is due to the factthat the city area model results refer to relatively long time-periods and mainly depend on aspects suchas geographical distribution of maps and number of performed trips rather than the specific pdf of theMU residence time in an area zone/high capacity route.

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PercentageofPopulationperAreaZone

Type

Initial

7:00-8:00

8:00-9:00

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11:00-12:00

Figure 6 : Percentage of Users per Area Zone Type vs. Day Time Period

0

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60

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Area type

Percentageofmov

ements Internal

Outgoing

IncomingExternal

Figure 7 : Percentage of User Movement s vs. Area Type


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rush hour

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Figure 8 : Outgoing Crossing Rate vs. Area Zon e for Rush Hours and Busy Hour

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Day Time Period

Not-Moving

Not-Moving (IMMT)

Pedestrians

Pedestrians (IMMT)

Passengers

Passengers (IMMT)

PercentageofMobileUsers

Figure 9 : Percentages of Moving ( passengers, pedestr ians) and Not-Moving Users vs. Day Time Period

Area Zone Mode l: Figure 10 depicts the pdf of a busy MU cell residence time 8, using: (a) the basicarea zone model (Annex B), (b) the model proposed by Hong and Rappaport [22], (c) the IMMT

approach and (d) the exponential distribution9. To compare the resulting pdfs, all cases refer to a

common average MU cell residence time equal to the one of case (a). The assumed cell characteristicsappear in Figure B.1 (cross shaped, L=185m), while the IMMT approach regards streets as traffic lightcontrolled flow street units with red/green states duration equal to 60/60 sec. The street unit model inthe 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, theexponential distribution is quite good approximation for (a) and (b) cases. However, the IMMT approachindicates that, in more realistic models, the exponential distribution approximation, although applicable,is not excellent.

Figure 11 depicts the pdf of a busy MU cell crossing time10 for the above mentioned cases (a-d). As itcan be observed, neither the Hong model nor the exponential distribution provide a good approximation

8 It represents the time period between the establishment of a call initiated inside a cell, and the instance the busy MUcrosses 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.


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for the cases (b) and (c). Case (b) (Annex B model), which obviously approximates a Gaussiandistribution, is closer to the realistic approach of IMMT (case (c)).

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pdf

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Basic Model

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Exp.Distr.

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

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Exp.Distr.

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 thesimulation model of Annex B, for the following cases:

i. Exponentially distributed MU cell residence time where the car density and average car speed arethe ones assumed in Annex B.

ii. The IMMT approach, where the streets of the area zone model of Annex B represent traffic lightcontrolled flow street units. The pdf of the time a moving MU spends inside a street of the areazone 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 thecar density (equal to the one assumed in Annex B as in case (i)). Note that in this case a differentaverage car speed resulted (equal to 11.035km/hr) because Eq. B.1 is not valid for the traffic lightcontrolled flow street unit.

iii.An alternative application of the IMMT approach. The MU cell residence time in the area zone modelof Annex B is assumed to be exponentially distributed (as in case (i)), however, since the streetsrepresent traffic light controlled flow street units, the average car speed is the one measured bythe street unit model in case (ii). The car density on the streets of the area zone model is the oneassumed 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 handoverattempt.


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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) showthat the speed-density relation affects the estimation of call blocking and call dropping probabilities. Onthe other hand, cases (ii) and (iii) indicate that the assumption of exponentially distributed MU cellresidence time is adequate, provided that the car density and average car speed have been accuratelyestimated.

This study provides an example of how the IMMT approach can be exploited so as to verify theoreticalassumptions (e.g., validity of the exponentially distributed MU cell residence time) and analyse theimportance 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 parameterscan be significantly affected in the case that the effect of mobility on the user calling behavior isencountered (see analysis in Annex D).

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BlockingProbability

Call Blocking (i) Call Blocking (ii) Call Blocking (iii)

Call Dropping (i) Call Dropping (ii) Call Dropping (iii)

Figure 1 2: Call Blocking and Call Dropping Probabilities vs. User Penetr ation Rate for cases (i), (ii) and

(ii i).

St ree t Un i t Mode l: The results presented in this section are based on the model of Annex C regardinga street unit model of length L=500m. The pdf of a car residence time

12in a street unit is illustrated in

Figures 13 (high and low priority street units) and 14 (highway and traffic light controlled flow streetunits). 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 atthe moment a new car enters the street), while Figure 16 depicts the pdf of the car speed in the samestreet 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 arrivalrate and the red/green state duration. As shown, the average speed decreases as the proportion ofred/green states increases. This is because cars stop more frequently as the duration of red stateincreases (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 turningprobabilities (TP)13) vs. the car density in a high priority street. As it can be observed, the average carspeed in low priority streets is rather invariant, as the car density in high priority street increases. Thisis due to the fact that, as the car density increases, the distance between cars decreases and thus it ismore difficult for a car coming from a low priority street to cross/enter the high priority street. As aconsequence, the average car speed decreases and therefore, the safety distance between a cross-road and the nearest car also decreases. On the other hand, the average speed is more stronglyinfluenced 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.


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Figures 17, 18 depict the critical parameters that affect the average car speed in the cases thatvehicular traffic flow is prioritized or controlled by traffic lights. Within this context, the resultspresented in these figures provide means to model the relevant street unit types in the area zonemodel.

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Figure 13: The pdf of a Car Residence Time in: (a) Low and (b) High Priority Street Unit

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Figure 14: The pdf of a Car Residence Time in: (a) Highway and (b) Traffic Light Controlled Flow Street

Unit


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Figure 1 6: The pdf of t he Car Speed in a Traffic Light Contr olled Flow Street Unit

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0,1 0,2 0,3 0,4

Car Arrival Rate (cars/sec)

Av

erageCarSpeed(km/hr)

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Figure 1 7: Average Car Speed in a Traffic Light Controlled Flow Street Unit vs. Car Arr ival Rate and the

Red/Green State Duration


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0

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6,49 12,61 21,97 26,57

Average Number of Cars in High Priority Street (cars)

AverageCarSpeed(Km/h)

High Prior. Str.

Low Prior. Str.(TP=0.2)Low Prior. Str.(TP=0.3)

Low Prior. Str.(TP=0.4)

Figure 18: Average Car Speed in High/Low Priority Street vs. Car Density in the High Priority Street

(expressed as the average num ber 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 pagingarea 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 detailconcerning the user location, three basic mobility models have been specified. In particular:

The c i t y a re a mo d e l considers a city area as a set of area zones and high capacity routes. Thismodel is valid for the analysis of location management related aspects, where the accuracy of theuser location is considered at the level of a location/paging area.

The a re a zo n e mo d e l considers an area zone as a set of street segments and building blocks. Themodel is valid for the analysis of radio resource management related aspects, where the userlocation is considered at the level of a cell area.

The s t re e t u n i t mo d e l considers a set of street network segments. The model is valid for theanalysis of radio propagation related aspects, where the user location is considered at the accuracyof a few wavelengths.

Taking into account that each model focuses on a specific set of design issues, we have proposed amethodological modeling approach, the so-called Integrated Mobility Modeling Tool (I M M T). The IMMTapproach considers the basic models as independent components among which mobility-relatedparameters can be exchanged. The results obtained, indicate its applicability for the validation of thetheoretical input assumptions and the results of existing analytical models. In this context, the IMMTapproach contributes in the investigation of the effect of the mobility model accuracy on designdecisions. Moreover, the ability of the IMMT to represent any specific geographical area, constitutes thetool appropriate for network planning and thus stresses the relation between mobility modeling andnetwork implementation cost.


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ANNEX ACity Area Model Application Example

The city area under consideration (see Figure A.1) has a radius of 20 Km. Four area types areidentified: city center, urban, suburban and rural area. The model consists of 32 area zones (8 per cityarea type), 4 peripheral (one per area type) and 4 radial high capacity routes. The population is 6millions inhabitants and the MU penetration rate is 50% (i.e., there are 3 millions of MUs roaming withinthe city area). In our simulation tool, a sample of 100000 MUs has been assumed.

Area Borders

Peripheral - Radial High Capacity Route

City Centre

Urban Area

Suburban Area

Rural Area

Figure A.1: The City Area Model Consisting of Area Zones Connected v ia High Capacity Routes

Mo ve me n t A t t ra c t i o n Po in t s (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 assumeddistribution of MAPs over the whole city area. Note that within a certain area type (e.g., urban,suburban area) the MAPs are uniformly distributed.

Other

Work

Places

Residen

ces

Rural

Suburban

Urban

Center

0

10

20

30

40

50

%

Figure A.2: The Distr ibution of MAPs over t he City Area

MU G ro u p in g b a se d o n t h e i r Mo b i l i t y Be h a v io r : As shown in Figure A.3, MUs are groupedaccording to: (a) the mobility behavior they exhibit (working people, residential users and high mobilityusers) and the (b) transportation means they use (private car, public transportation).


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WorkingPeople

Mobile Users

ResidentialHigh MobilityUsers

Private Car Taxi PublicTransport. Private Car

Taxi Private Car Taxi PublicTransport.

60% 25% 15%

35% 30% 70%5%60% 18% 16%

66%

Users

Figure A.3: Categor ization 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 rushhours (7:00-9:00 a.m.) and the busy hour (11:00 a.m.-12:00 p.m.).

I n i t i a l MU Dis t r i b u t i o n o ve r t h e Ci t y A re a : MUs are initially distributed over the city area byassuming 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 thehigh 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, isdiscriminated 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 theperipheral direction. When an MU moves towards an outer city ring, the reverse order is followed i.e.,first peripheral and then radial.

Mo ve me n t A lg o r i t h m fo r Wo rk in g Pe o p le (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 ofwalking/waiting -depending on the transportation mean that will be used- (uniformly distributedbetween 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 distancemovements around their work place may also be performed during the working hours e.g., lunchtime.

Mo ve me n t A lg o r i t h m fo r Re sid e n t i a l Use rs (see Figure A.4): We assume that every residentialuser initiates a movement, at a moment in time uniformly distributed between 7:30 a.m. and 9:30a.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 areregarded 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. Inthis case, MUs are regarded as pedestrians visiting banks, shops or other attraction points inside thisarea zone.

Mo ve me n t A lg o r i t h m fo r H ig h Mo b i l i t y Use rs (see Figure A.5):We assume that MUs belonging tothis category are already in motion, having a destination when the simulation starts. After havingcompleted their movement, they reside for a short period (0-15 min.) before they are assigned a newdestination. This procedure is repeated during the whole simulation process.

Origin Pedestrian

Car

Taxi

Public Trans. Pedestrian Public Trans.

Pedestrian Destination

Figure A.4. Movement Algorithm for Working People and Residential users

Origination Destination

Car

Taxi

Figure A.5. Movement Algorithm for High Mobility Users


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Mobi l i t y Cond i t ions : The average pedestrian speed is 5 km/hr (in [46] the average pedestrian speedis 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 densityand speed on a certain street (e.g., based on the model of Equation (b.1)).

Tra f f i c Cond i t ions

We consider the arrival of both incoming and outgoing calls. The call arrival process is assumed to bePoisson. 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 correspondingoutgoing, because incoming calls are for both private and business communications.

VEHICLE TYPE

AREA TYPE Public Transportation Media Car/TAXI

CENTRE 5 - 15 km/hr 10 - 20 km/hr

URBAN 10 - 30 km/hr 15 - 40 km/hr

SUBURBAN 30 - 70 km/hr 40 - 80 km/hr

RURAL 60 - 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 0.5 2.0 3.5 50 % - 50 %

Residential Users 0.5 1.5 2.0 50 % - 50 %

High Mobility Users 1.0 2.0 3.5 70 % - 30 %

Table A.2. Call Arrival Rate (calls/MU/h) for all MU Categories vs. Day Tim e


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ANNEX BArea Zone Model Application Example

Geograph ica l 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. Toachieve a realistic population distribution, various types of environments have been defined, eachcharacterized 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 30 % 150000

Business 41 % 75000

Domestic 10 % 9000

Streets 15 % (see Fig. B.1)

Other 4 % 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 ofpassengers per car is 1.5, (d) there are 2 buses per street segment, (e) the average number ofpassengers per bus is 45 and (f) pedestrians are uniformly distributed on the pavements (see FigureB.1). The resulting densities are 51000 passengers/km2and 66000 pedestrians/km2, where the km2

corresponds to the street area only and not to the whole geographical area.

Mobi l i t y Charac te r is t i cs : Three MU groups are considered (MUs are not allowed to alter categoryduring a call): (a) users located in buildings, (b) pedestrians with a speed following the Gaussiandistribution with mean value 5 km/hr and variance 30%, and (c) car passengers with a speed followingthe Gaussian distribution variance 30% and a mean value which is calculated by the formula (alsoutilized in [29]):

v vD

Ds f

jam

=

1 (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 probabilityof 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 outgoingones.

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 outgoingrate is still higher than the incoming.

3) Measure the percentage of incoming MUs that cross the area zone, and reduce the rate of incomingMUs accordingly.


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L = 185 m

L (m)

Pedestrian

Pavement Building BlockStreet segment

Pavement

Lstr = 15 m

9 m

9 m

4 m

3 m

Figure B.1: The Population Distr ibution on the Str eets of a Micro-Cell

Tra f f i c Charac te r is t i cs : 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 callarrival 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 callarrival rate could differ between business and residential users). We assume that 65% of the MUslocated inside buildings are served by private wireless networks.

Regarding the multiple access protocol, the one presented in [50] has been adopted. The protocol iscapable of supporting three service classes, namely, circuit-mode voice, burst-mode voice and data, byperforming statistical multiplexing of connections of the three classes at two different levels: (a) thecall-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 inevery micro-cell, 2 carriers with 96 full-duplex channels (96 slots/frame, FDD) are available [50]. Amicro-cell area equals to the area depicted in Figure B.1.

Service Type Call Arrival Rate(Calls/User/Hr)

Mean CallDuration (sec)

Voice 3,0 90

Data 2,78 50

Table B.2: Call Arrival and Call Duration per Service Type

Serv ice Pene t ra t ion Rate

En v i r on m en t Vo ice Dat a

Busy Spots 95 % 5 %

Business 99 % 70 %

Domestic 95 % 10 %Street 98 % 2 %

Other 95 % 5 %

Table B.3: Penetration Rate per Service and Environment


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ANNEX CStreet Unit Model Application Example

In this annex, we describe a simulation tool, which models all types of street units i.e., highways, trafficlight controlled traffic flow and prioritized flow control streets. For the sake of simplicity, our simulationtool considers a single lane street unit (see Figure C.1). As far as the behavior of a car driver isconcerned, 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).

L

(c) High-Low Priority Street

L

STOPSTOPHigh Priority Street

Low Priority Street

L

(b) Traffic Light Controlled Flow

S

L

(a) Highway

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 carspeed. This empirical law correlates: (a) the car acceleration with the distance between a car and theforegoing car, (b) the maximum car speed on the street unit and (c) the car acceleration-decelerationcharacteristics. The empirical law is expressed by the following formula:

v t

tg k

v t c

vc c

m

( )exp

( )=

+

1 1 (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 vd t

d v tv t cm f

safe pre

p

pre=

+

min ,

( )

( ( ))( ) (c.2)

where,

d(t): The current distance between this car and the preceding one (km).

vpre(t): The current speed of the preceding car (km/h).


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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 ofthe preceding car (assumed value 2).

Finally, the safe distance between two cars traveling at speed v, is given by the following formula:

d v a v d safe ( ) min= + (c.3)

where,

: a constant expressing the time it takes a driver to stop the car by the moment the preceding carstarts 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 isassumed equal to 5m.

The above mentioned empirical law describes the behavior of an individual driver in a street unit andcan be utilized for simulating the car motion. To adopt realistic values for the parameters appearing inthe above formulas, we have performed a series of experiments. In these experiments, the speed of asingle car just entering the street unit with an initial speed set to zero, is analyzed for the followingcases:

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.

0

10

20

30

40

50

60

70

80

0,08 2,08 4,08 6,08 8,08 10,08 12,08 14,08 16,08 18,08

Time (sec)

Ca

rVelocity(km/hr)

Stop at 100m

Free Flow

Prec.Car 60km/hr

Prec.Car 40km/hr

Prec.Car 10km/hr

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 modelconsiders 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 caseof the high/low priority streets, the probability of a car in a low priority street entering a high prioritystreet is 0.2. Cars in low priority streets, decide to enter/cross the high priority street when thedistance between the cross-road and the nearest arriving car on the high priority street is safe. Theminimum safe distances for entering/crossing the street are assumed to be a function of the speed Vcarof a car moving in high priority street: cross: 1.2*Vcar, enter: 2*Vcar.


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ANNEX DMobile Users Calling Behavior

An important issue influenced by user mobility concerns the MU calling behavior expressed by the theincoming/outgoing call arrival rate and the average call duration. From fixed networks it is well-knownthat different calling behavior characterizes business and residential users. In mobile communicationsystems, 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 Mov in g 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 ofa user to initiate calls. E.g., compared to a user situated in his office a pedestrian will normallyinitiate 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 generalignores 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 themobility 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 beaffected by the user mobility class, according to the hierarchy listed in table D.1. Note that the higherthe position in the hierarchy the higher the corresponding value is expected.

Cal l I n i t ia t ion Cal l Du r at ion

Not moving business Not moving residential

Not moving residential Not moving business

Car passenger Car passenger

Public transportation passenger Pedestrians

Pedestrians Public transportation passenger

Table D.1: The Hierarchy of User Mobility Classes

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