Simulation-based Local Train Mobility Model Aftab Ahmad Norfolk State University, 700 Park Avenue, Norfolk VA 23504
[email protected]; +1(757)823-8311 Keywords: Mobility, Train, Wireless Networking ABSTRACT1 Mobility models are essential part of wireless network design. Simulation of user mobility scenarios is a tricky business due to the boundary behavior of simulated objects (people, vehicles, trains, etc.). In this paper we present the initial results of a user mobility simulation scenario for applications to broadband Internet access. We simulated a local train in a square area with straight tracks of random length. The train accelerates uniformly to a maximum velocity and decelerating uniformly to a stop at the end of the track. The track lengths, stop times and speeds are all uniformly distributed. The mobility at the boundaries is simulated simply by discarding a track that falls outside of the simulated area. By comparing this simple model to a mean-values model, we see that this method yields pretty accurate results. More complex models with reallife track shapes and acceleration/deceleration ramps can thus be derived from simple boundary models like proposed here. We used 3D OpenGL for visual simulation and uniform random sampling for model derivation. 1. INTRODUCTION Wireless networks present a variety of scenarios with respect to mobility of the users. These scenarios range from localized user mobility within the area covered by a single base station to high speed highway traffic in which the user frequently changes the base station. In every instance of mobility, the network is expected to provide a constant level of service, transparent to the location changes. In order for this to happen, the network provider must allocate resources to mobile devices keeping the potential hiccups in view. Such resources consist of network capacity and call 1
The work in this paper was supported by Title III funding from the Office of Education.
© 2010 SCS. All rights reserved. Reprinted here with permission.
processing and signaling overheads. Analytical or simulation studies of user mobility are required to evaluate the resource allocation. Mobility models are also needed in simulation and analysis of mobile networks. Mobility has mainly been studied for cellular networks [2]. Typical mobility models assume that the user is either a pedestrian or in a vehicle, even though office environment models are not uncommon [3]. Ad hoc networks offer slightly different set of conditions from other networks. In an ad hoc network, users have a peer-to-peer connection through other users whose devices act as routers or forwarders. As such the coverage area of user devices is much smaller than a base station of a cellular network, an access point in an infrastructure WLAN, or even a base station in a cordless phone. Due to this reason, mobility models for ad hoc networks are studied as a special case for such networks. Mobility in ad hoc networks does not have a typical form, there are various possibilities, such as group mobility [4]. Among the relatively late arrivals in wireless networking is the wireless broadband access via the WMANs, such as based on IEEE 802.16 [5] and IEEE 802.20 standards [6]. While both networks are supposed to be used by mobile users, the IEEE 802.20 is expected to provide seamless connection to users on high-speed vehicles, such as trains (higher than highway speed limits). In other words, the mobility models applicable to cellular phone environment are also applicable to IEEE 802.16 user mobility, but not to the IEEE 802.20 users. The effect of a coarse mobility model would be in allocating inappropriate network resources to calls. If the allocated resources are too much, the operator loses revenue or the service is unnecessarily expensive. Contrarily, if sufficient resources are not allocated, the call quality may suffer. This is undesirable in two respects: first, there is an increasing number of users with multimedia devices demanding strict quality of service (QoS) and not meeting QoS is equal to losing customers, secondly, the Internet Protocol (IP) does not provide a deterministic QoS, meaning inefficient resource allocation at other protocol layers (e.g., medium access control or MAC layer in this case) will result in a pronounced
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degradation of quality when compounded with IP layer QoS uncertainty. Thus, a reasonably accurate mobility model is needed for the engineering of any network with mobile users. The objective of this paper is to present a mobility model for IEEE 802.20 based access while the user is on a high-speed local train. This is different from many existing user and network scenarios.
Special Case II: For hybrid group mobility (with some nodes having infrastructure as well as ad hoc connections and others with just the ad hoc connection), the model can be divided into two levels, level I same as Special Case I above with the center of the group defining the position and level II defining a model for relative positioning of the devices within the group.
2. MOBILITY MODELING
2.2. Mobility Parameters A mobile user has a known initial position, which in the crudest form can be determined from the received signal power by a group of Base Stations, or by an onboard Global Positioning System (GPS) for more sophisticated devices. Instantaneous velocity and acceleration values can be used to determine the position after a short period of time δt during which acceleration remains constant. If vi (t) is the velocity at time t and a is the acceleration then the new position at time t+ δt is given by( a. δt) δt with respect to the position at time t. The problem is that the change in velocity also includes direction. Therefore, in order to incorporate the new position in any meaningful engineering system, the velocity has to be split into speed and direction. The most commonly used direction parameter is the angle (relative or absolute). With that in mind, now if we define a position vector Pi (t)={s(t), θ(t), a(t)}, then the final position after δt is given by Pi (t+δt)={ a(t) δt+s(t), θ(t)+ δ θ(t), a(t+ δt)}. The acceleration a(t+ δt) is important only for the next position and is useful only for the interval in which it remains constant. It is noteworthy that a(t) δt+s(t) = s(t+ δt) and θ(t)+ δ θ(t) = θ(t+δt). In order to model mobility of a user, we need rules to determine the changes in speed, direction and acceleration. In view of the above discussion, we will briefly mention some popular mobility models available and how they can be incorporated in computer simulation.
The user behavior with respect to mobility is mostly studied for cellular networks. Generally, the mobility is modeled for three scenarios, (i) vehicular users, (ii) pedestrians and (iii) office building [3] and short distances for direction change for (ii) and reflection, diffraction, refractions and hallways for (iii). For each case, in cellular systems, mobility model would help Base Station (BS) adjust the resources assigned to the user and in prediction of handoff. In IEEE 802.20, a soft handoff is employed which requires multiple simultaneous connections during the handoff process in order to pick up the most suitable one. Ad hoc networks resulted in mobility models investigation for network without a base station (BS) or access point (AP). Once ad hoc network technology is fully understood, we will have hybrid networks in which some devices will be connected to a BS/AP and others will form ad hoc network cluster with these devices. In that case, there will be two types of users from mobility point of view; ones that are connected to the Internet and their mobility being modeled with respect to the access point through which they have Internet connection, and the others completely ad hoc devices whose mobility is significant only within the group of other ad hoc devices. In other words, for the later case, it is the relative velocity and acceleration that need to be modeled instead of absolute ones. 2.1. Defining Mobility Modeling Problem A general modeling problem can be defined as follows. Let ni and nj be two network devices whose positions pi (t) and pj(t) are functions of time with respect to some general coordinate system . Let the vector Pij(t) = pj(t) – pi (t) be the position vector of node nj with respect to ni . Then a mobility model should give a way of predicting Pij(t+δt) = pj(t+δt) – pi (t+δt) at time t+δt. Special Case I: For cellular networks, node ni can be the BS and the position vector Pij(t) = pj(t) – pi (t) = pj(t) and thus the subscript can be dropped.
2.3. Example Mobility Models The work reported in [8] divides all mobility models into three categories; (i) random speed, random direction at all times, (ii) random speeds, random directions at specified points, (iii) random speed in a direction to a known destination. Type (i) models apply to situations in which no assumption can be made about the user, type (ii) apply to situations in which users can move according to a map and type (iii) applies to situations in which user changes speed more often than direction. Here, we will describe one model from each
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type cited in the same paper. There are a number of papers reporting surveys of mobility models, such as the research report [9].
not speed, as in RWP. The strengths and weaknesses along with extensions of RD model are described in [11].
2.3.1. Random Waypoint (RWP) Model This is the most general mobility model and does not make any assumption about the knowledge of either the direction, or the velocity or the sojourn times of the moving user. In other words, a user (a) picks a random destination point and (b) moves towards it in a straight line with a random but constant speed until the destination is reached, then (c) makes a stop of random duration. Usually, the speed is chosen from a uniform distribution vmin to vmax, with an amplitude of 1/(vmaxvmin). The strengths, weaknesses and extensions of RWP model are superbly explained in [10].
2.3.3. Obstacles Mobility (OM) Model Obstacle based model s depict a more realistic picture of the user mobility than RWP and RD. There is a variety of such models as well. In [12] such a model has been proposed with obstacle corners modeled by Voronoi diagrams, together with movement graphs and a rule to pick up the shortest paths. In a way it’s a more realistic version of RWP with the difference that a straight path is not assumed automatically. Instead the path is calculated for every destination point. Random sojourn times are assumed just like RWP and RD.
2.3.2. Random Direction (RD) Model In this model the user selects a direction and a duration to travel in that direction with a random speed. The sojourn times are also random, as in RWP. The direction in this case can be integrated with the speed by defining the velocity as the random variable with values varying from a negative maximum to a positive maximum. In other words, if we set vmin = - vmax in RWP, we essentially get RD model with the difference that the interpretation of vx is that it is the velocity and relative position and repositioning of individual nodes. 2.3.5. Train/Local Train Models The mobility models for subway and local trains are limited in scope and variety. One of the models derived as a result of a research sponsored by New York CAT, among others, [14] proposes a Subway Model (SM). In this model, assumptions are made about passenger arrival process, train size and frequency of operation, speed (constant), number of stops, stop time (45 secs), even the time it takes a passenger to leave the platform. In this paper, our objective is to derive a general but realistic model for a local train. We base the simulation on real-life model of local train and then take samples of speed, direction and acceleration to derive a model. 3. LOCAL TRAIN MODEL As against Papdopouli and Schulzrinne’s Subway Model [14], we assume that the users are active only when they are aboard the train. Therefore, this model is applicable for handoff for the MBWA network as the train moves from one cell/sector to another. The train moves on a track and stops at the train stations for a random time, and moves on. There is an acceleration ramp on which the train gains maximum speed. After
2.3.4. Group Mobility Models For ad hoc networks, group mobility is more realistic than individual user mobility. In [13], a group mobility model has been described, called Reference Point Group Mobility (RPGM). In this model, each node in a group (with a logical center) is assigned a reference point. The node itself is located at a random point in the neighborhood of the reference point. The trajectory of the group center defines the group mobility, while the reference point defines the gaining the maximum speed, the train keeps moving with this speed until it hits the deceleration ramp near the next stop. It starts slowing down until it comes to a complete stop. After stopping for a specified time (different from other stations), the same process repeats. The overall track consists of many segments, each segment at an angle from the previous track segment. The track is designed to avoid sharp turns except at the borders where the train either comes back or takes a sharp turn or two to get on the track in a different direction. 3.1. Simulation Model We have designed two-fold simulation. First, we have discrete event simulation in which the train moves from the current position towards the endpoint of track segment in events of duration of a fixed amount of time (DELTA_T). A graphical depiction is designed to visually show the track and movement. The current version of the simulation model has the assumptions, such as listed in Table 1. All quantities of distances are given in pixels to facilitate the graphical drawing. We use C++ with OpenGL API for the display.
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Since track segment length and angle are random, they are assumed to be independent and identically distributed (i.i.d.). The accuracy of this assumption depends on the random number generator. We assume such is the case for this simulation. This helps resolve the border crossing issue. We simply use a test to see if the next segment will cross border or not, and if does cross border, the segment is discarded and a new one is generated and tested until we find one that does not cross border. This has the potential of creating sharp turns near area boundaries. We believe this is not unrealistic in real-life. We do not use a deterministic border testing method so that the samples taken retain randomness from modeling point of view. Even though we do uniform sampling, we use a very small probability that the train values will be sampled at a given instance. The values sampled are; speed, direction and acceleration.
begin Set the train center at the starting point; Generate a new track segment; if the segment is within simulation
Following text-box shows the algorithm for sampling as well as display. Samples are taken with a probability that can be adjusted to increase or reduce the sample size for a given run of simulation. OpenGL’s GLUT library provides a function GLUT_TIMERFUNC() that can be used to redraw a scene after a given amount of time (DELTA_T in this case). Animation is created due to the changed position of the train in every new drawing. For every run of the simulation, the seed of random number generator is changed to the current system time but the initial position of the track is kept at (0,0) due to the fact that it will have no effect on the results for a sufficiently long run. Fig. 1 shows examples of tracks. There is no ‘bias’ obvious from Fig. 1, even though it is expected that in a very long run of the simulation, the track will be mostly between circles of radii MIN_TRACK_LENGTH and MAX_TRACK_LENGTH. A MIN_TRACK_LENGTH of zero will completely randomize the tracks, but will result in rather unrealistic model. We have modeled turning points as the stations in this version, which may not sound realistic. But the fact the samples are taken randomly will compensate for this. However, we will consider stops at random locations in future.
space;{ reached segment)
while (the train has not end of
4. SIMULATION-BASED MOBILITY MODEL FOR LOCAL TRAIN
Calculate the new velocity after DELTA_T; Move the train for DELTA_T;
In this section, we will describe some of the results of simulation samples. For simplicity, let’s assume values given in Table 2 to be used. Average time spent on the Ramp = TR = 2R/Vm+2R/Vm = 4R/Vm TR is derived from the fact that the average velocity on the ramp is Vm/2 and there is an acceleration ramp and a deceleration ramp. Average time at maximum speed = Tm = (L – 2R)/Vm
end 4.1. Mean Value Model With the above parameters given, we can derive an approximate model from the mean values. For this purpose, let’s use the following notations for convenience. Minimum Stop time: Tso Maximum Stop time: Tsm Maximum track length: Lx Minimum track length: Li Maximum Speed: Vm Ramp length: R Acceleration = ±a From the above, we can easily get the following: Average track length = L = (Lx + Li )/2 Average stop time: Ts = (Tso+Tsm)/2
From the above calculations, it’s obvious that: The probability that the velocity is zero = P(V = 0) = Ts/( Ts+ TR+ Tm) = (Tso+Tsm) Vm / (VmTso+ VmTsm+2L+4R) The probability that the velocity is maximum = P(V = Vm) = Tm/( Ts+ TR+ Tm ) =2 (L – 2R)/ (VmTso+ VmTsm+8R) For the ramp, the probability mass of velocity is zero, as it varies on a continuum (0, Vm). However, we can derive an expression for P{ v(t) ≤ v(t)} easily for
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constant acceleration; v(t) is the random variable denoting the velocity. Let’s denote this quantity by Fv(v). This is the cumulative distribution function (CDF) of the velocity, the main modeling quantity. P(V ≤ a.t) = Fv(v=a.t) = 2t/( Ts+ TR+ Tm) = 2t/(Vm.Tso+Vm.Tsm+2R+L) Fig. 2 shows a plot of Eq (1). Fig. 3 shows the distribution function of the velocity derived from the simulation model. With appropriate mapping between simulation and realworld scenarios, the two distributions can be regarded as equivalent. The direction plot from simulation is given in Fig. 4. The trend line shows that the distribution is uniform, and there is no real bias at any point. This is a welcome result in wake of the border crossing problem. 5. APPLICATIONS OF THE MODEL The model derived in Eq(1), Eq(2) conforms well to the simulation models of Figs. 3 and 4. It is for the simple case. It is hard to derive models from analytical reasoning for situations with more details, such as nonsharp turns, non-linear acceleration. A simulation model could be used for this purpose to derive theoretical curves that can be employed in design and analysis of networks. With the help of local train mobility model, a network provider can determine the frequency of handoffs by users traveling via such a train. In case of local train, there is a risk that a large number of users will need simultaneous handoff as soon as the train crosses a cell/sector boundary into the next. This will put sudden load on the system resources. With the help of appropriate analytical models, the network designer can do cell planning to avoid such sudden overloads. As an example, systems with overlapping sectors/cells could solve this problem by distributing the connection population among non-co-centric cells so that the handoffs are not needed at the same time when the train crosses boundary of one cell/sector. 6. CONCLUSION AND FUTURE COURSE With the help of a simple model for local train moving on a random track with stops, acceleration/deceleration and constant speed, we show that simulation can be used to derive a local train mobility model. Most
For ramp up and ramp down and 2t ≤ TR Fv(v) = 4tVm /[(Tso+Tsm)Vm+2R+L] for t ≤ TR/2 secs The probabilities are plotted in Fig. 2, and calculated for the values of parameters in Table 3. studies in mobility modeling have been done for cell phone networks. Handoffs are more critical in wireless broadband access networks, such as MBWA or IEEE 802.20. In such networks, a large amount of data can be lost during a very short duration. In our model, we find the cumulative distribution function (CDF) of the train velocity. Our finding is that there are jumps at the zero velocity and maximum velocity and the in-between values depend on acceleration. For constant acceleration/deceleration, our results show that the CDF is linear, as expected. Analytical CDF based on mean values follows the same shape. This is a continuing work. In the next phase, we plan to introduce more rigorous sampling mechanisms to minimize the error of sampling. Also, more complex models for acceleration/deceleration will be incorporated. REFERENCES [1] Walter H. W. Tuttlebee, “Cordless Personal Communications”, IEEE Communications Magazine , December 1992, pp.42-53. [2] Jun Luo and Jean-Pierre Hubaux, “A Survey of Inter-Vehicle Communication, Technical report IC/2004/24, School of Computer and Communications Sciences, EPFL, CH-1015, Laussane, Switzerland. [3] ETSI. Universal Mobile Telecommunications System (UMTS); selection procedures for the choice of radio transmission technologies of the UMTS (UMTS 30.03, version 3.2.0). Technical report, European Telecommunication Standards Institute, Apr. 1998. [4] Qunwei Zheng, Xiaoyan Hong, and Sibabrata Ray, “Recent Advances in Mobility Modeling for Mobile Ad Hoc Network Research”, ACMSE’04 April 23, 2004, Huntsville, Alabama, USA, pp. 70-75. [5] Roger Marks, “IEEE Standard 802.16: A Technical Overview of the WirelessMAN™ Air Interface for Broadband Wireless Access” , IEEE, June 2004, available online at http://wirelessman.org/docs/02/C80216-02_05.pdf. [6] Arnorld Greenspan, Mark Klerer, Jim Tomcik, Radhakrishna Canchi and Joanne Wilson, “IEEE 802.20: Mobile Broadband Wireless Access for the
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Twenty-First Century”, IEEE Communications Magazine, July 2008, pp. 56-63. [7] Mark Klerer, “Introduction to IEEE 802.20: Technical and Procedural Orientation”, IEEE802.20 – PD-04, March 2003, available online at http://ieee802.org/20/P_Docs/IEEE%20802.20%20PD04.pdf. [8] Christian Bettstetter, “Smooth is Better than Sharp: A Random Mobility Model for Simulation of Wireless Networks” Proceedings of the 4th ACM international workshop on Modeling, analysis and simulation of wireless and mobile systems, Rome, Italy, Pages: 19 – 27, 2001. [9] J´erˆome H¨arri, Fethi Filali and Christian Bonnet, “Mobility Models for Vehicular Ad Hoc Networks: A Survey and Taxonomy, March 5th, 2006, Last update March 26th, 2007, available online at http://www.cs.odu.edu/~mweigle/courses/cs795s08/papers/harri-mar07.pdf. [10] E. Hyytia, H. Koskinen, P. Lassila, A. Penttinen and J. Virtamo, “Random Waypoint Model in Wireless Networks, available online at http://mathstat.helsinki.fi/mathphys/EVERGROW/virta mo.pdf. [11] Philippe Nain∗, Don Towsley, Benyuan Liu, Zhen Liu, “Properties of Random Direction Models”, Proceedings of the IEEE Infocom, 2005.
[12] Amit Jardosh, Elizabeth M. BeldingRoyer, Kevin C. Almeroth, Subhash Suri, “Towards Realistic Mobility Models For Mobile Ad hoc Networks”, Proceedings of the ACM Mobicom 2003, Sep. 2003. [13] Xiaoyan Hong, Mario Gerla, Guangyu Pei and Ching-Chuan Chiang, “A Group Mobility Model for Ad Hoc Wireless Networks, Proceedings of the 2nd ACM international workshop on Modeling, analysis and simulation of wireless and mobile systems, Seatle, WA, 1999, pp. 53-60. [14] Maria Papadopouli Henning Schulzrinne, “Seven Degrees of Separation in Mobile Ad Hoc Networks”, IEEE Globecom 2000. BIOGRAPHY Aftab Ahmad (SMIEEE’05/MACM) is currently an Associate Professor in the Computer Science Department at Norfolk State University, Norfolk VA, USA. He teaches courses in Wireless Networking, Computer Graphics and Computer Organization. Dr. Ahmad has published two books and several journal and conference papers in refereed journals and conferences. His research is on resource management and network security. His current funded research includes wireless sensor networks for implantable sensors for healthcare and wireless network security.
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TABLES Table 1. Simulation assumptions 2 (X-Y) Mobility Dimensions Area shape Rectangular/Square (MIN_WINX, MIN_WINY) to (MAX_WINX, MAX_WINY) Speed Varies between VELOCITY_MIN and VELOCITY_MAX (VELOCITY_MIN = 0) Acceleration Could have positive or negative values (ACCEL > 0, and DECEL < 0) Discrete time value DELTA_T in msec (can be mapped to any value in real-life) Stop time
Random time between MIN_STOP and MAX_STOP times
Track segment length
Random for each track between (MIN_TRACK_LENGTH, MAX_TRACK_LENGTH) Random for each track between (MIN_TRACK_ANGLE, MAX_TRACK_ANGLE)
Turning angle
Table 2. List of parameter values for simulation (units are in pixels) MAX_TRACK_LENGTH 500 MIN_TRACK_LENGTH 200 MIN_TRACK_ANGLE -60o MAX_TRACK_ANGLE MIN_WIN_X MAX_WIN_X MIN_VELOCITY MIN_STOP_TIME ACCEL RAMP
1
-350 350 0 20 DECEL 100
MIN_WIN_Y MAX_WIN_Y MAX_VELOCITY MAX_STOP_TIME -1 //acceleration, deceleration ramp to achieve max_velocity or stop
60o // relative to the previous track -350 //700 x 700 350 100 40 //msecs
Table 3. Train Mobility Parameters Maximum velocity Stop time Ramp length acceleration Minimum track length Maximum track length
100 mi/h = 146.667 ft/s 20-40 secs ½ mi = 2640 ft either side (accel/decel) ±4.074 ft/s2 (100 mph in 36 secs) 1 mi = 5280 ft 10 mi = 52800 ft
Ts = 30, L = 5.5 = 29040 ft a = 4.074, ,R = 100, Vm = 100, TR = 72 secs (36 each side of track) Tm = (29040-5280)/146.667 = 162 secs Ts+ TR+ Tm =30 + 72 +162 = 264 P(V = 0) = 30/264 = 15/132 P(V = Vm) = 162/264 = 81/132 P(V ≤ a.t) = t/132 for 0 < t ≤ 36
Eq(2)
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FIGURES
Fig. 2. Distribution function of velocity using mean values. Fig. 1. Four instances of track generation to collect 10 random samples.
1 1
0.8 0.6 0.4 0.2
1 8 15 22 29 36 43 50 57 64 71 78 85 92 99
0
0 1 31 61 91 121151181211241 271301331
Fig. 3. Distribution function of velocity derived from simulation. Fig. 4. Distribution function of the angle of direction of mobility.
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