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Comparison of User Mobility Pattern Prediction Algorithms to increase Handover Trigger Accuracy
Stefan Michaelis Christian Wietfeld christian. wietfeld@ uni-dortmund. de stefan. michaelis @ uni-dortmund. de Communication Networks Institute University of Dortmund, Germany
Abstract- The estimation of correct triggers for handover in cellular networks belongs to the critical tasks for accurate network operation. The importance of seamless handover even rises according to the increasing number of available radio access technologies, demanding for a reliable vertical handover. To aid the handover process, mobility prediction technologies gain interest and provide the possibility to prepare for handover in advance. The approaches presented here feature prediction of macro-mobility as an additional measure to aid handover decisions. The prediction is based on statistical data gained from the observation of movement across multiple cells. One of the main features lies in a generic user centric calculation of the most likely next hop during user movement, compared to network specific technological methods.

traces is the key driver for successful training of mobility detection and position prediction algorithms. Historical and simulation data about user movements provide the input for prediction algorithms trying to detect regularities. In case of simulation, the scenario parameters are of major importance, defining the degree of regularity inside the generated traces, as the users are bound to streets and areas

A. Movement Models One of the most widely spread and general mobility models is the so called Random Walk model. In this model the users follow no certain rules, but their movement is completely Mobility of users with seamless accessibility and without independent of position, other users or movement history. This the need to care about the underlying topology is the most model is easily to implement and easily to parameterise, but popular feature in wireless networks. Otherwise, to guarantee obviously contains no detectable patterns inside the generated a seamless service the correct estimation of when to trigger a movement traces. Nevertheless this model still holds some handover is critical. benefits in producing Noise to test the robustness of applied Different research approaches try to use movement pre- pattern detection methods. dictions as an addition to classical handover triggers. They The Gravity Model (i.a. in [5]) assigns values indicating a vary from statistical analysis ([9], [3]) up to complex pattern given level of attractiveness to certain areas. The higher the detection algorithms ([7]). In the majority of cases these attractiveness of an area is, the higher is the probability that a methods target at specific networks and input parameters and user will try to reach this area. This model provides a balanced the methodology behind is not generalizable to heterogeneous mixture between deterministic and random parts. The first few networks. In this paper we compare different generic pattern users of a large bunch of users, all heading to an attractive area, detection algorithms regarding their performance and propose can generate detectable movement patterns, which are then methods to further enhance their quality, enabling predictions used to predict location updates for the later users. In contrast, to be a reasonable addition to handover triggering. the stochastic nature of area attractiveness leads to travelling To evaluate the prediction approaches presented in this pa- only a subset of all users residing inside the simulation system per, we explore the overall success rate for the predictions on to these areas. The remaining users can be considered as noise simulation generated trace data. This analysis is accompanied to the pattern detection algorithms, performing stability tests by a detailed per base station analysis ofprediction accuracy regarding the prognosis accuracy. Finally the last mobility model outlined in this context is and an analytical investigation of the underlying simulation setup. The question has to be examined, how accurate the the Path Following Model([5]). This model gives a sequence of predictions of future user's base stations can be and how areas to reach or cross during mobile movement. Depending on intense the impact of input data is. To let prediction be an the selection of the waypoints, certain degrees of determinism addition to classical handover measures, the algorithms have can be achieved. Additionally, this model complements the gravity model, when assigning the target area to a user by the to deliver stable results for varying conditions. gravity model and afterwards switching to the path follower model leading to this area. When the area is reached, the I. GENERATION OF MOBILITY PATTERNS gravity model can select a new target again. Beside the capturing of short term (micro) movements, longer and repeating trends (macro inter-cell movement) in B. Available Data for Prediction user movement enable management of the networks on a During tracking of the user movements, different granularregular basis. Generation of a sufficient amount of movement ities of available information are expected: connectivity to
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base stations, estimated exact location (GPS, triangulation, timing advance etc.) or signal quality measurements. Main problem here rises for heterogeneous networks, where vertical handovers may occur and not all types of data may be available. This leads to the precondition that a stable prediction algorithm is either insensitive to missing data in each trace or capable to perform good results even on minimal available data like pure entered/exited base station events. For the research carried out here we concentrate on the smallest common denominator: Entered/Exit traces of base stations. This keeps the examinations independent of a specific serving mobile network (comparing differences of GSM to WLAN) and capabilities needed in the end user equipment (GPS hardware). These sequences are kept, in contrast to most other approaches targeting at mobility prediction, independently of the generating user. This generally complicates the prediction process, as users can not be treated individually, but greatly reduces amount of stored data and allows topology driven pattern detection. The length of sequences depends on the usage of applications, e.g. if the user shuts down mobile equipment before completing the whole path to his target, this will result in shorter sequences and less unique path patterns. The next section presents how the mobility models used for pattern generation are used in a specific scenario.
II. EVALUATION ENVIRONMENT AND REFERENCE SCENARIO

Start Area Random
A
TL

TL2

TR2

c

D BL Start Area Path

BM

BR

BL2

BR2

F

Start Area Gravity

Fig. 1. Asymmetric double T-shaped scenario

This section presents and explains a reference scenario, which is used as the evaluation environment for testing pattern detection algorithms.
A. Network and Geographical Topology Setup Figure 1 illustrates a simple example topology scenario for user mobility. Six user areas are connected with streets, generating a topology of a shape similar to typical exhibition centers. While moving, the users are bound to the streets connecting the areas (pavilions). The base stations are labeled in the notation XY, e.g. TL=T(op)L(eft), for later reference. This scenario has its main challenge for prediction at the crossing sections in the middle areas. Input data for location prediction algorithms is generated by tracking the sequences of traversed base stations while the users move. The areas and streets forming the geographical model are covered by a series of base stations. We normally assume circles as approximations for the range of the stations in contrast to the widespread hexagons, because actual mobile networks favour soft handovers or macrodiversity in contrast to hard handovers without overlapping regions.
B. Topology population For the specific simulation setup used in the following section to analyze the prediction algorithms and results, three different user models populate the scenario. The mobile starting at the bottom left area D uses a semi-deterministic path

following model. Target area for the mobile is the upper right area. After reaching the target area, the mobile stays in this area and is allowed to move randomly inside its bounds. This generates a slight amount of noise to the pure deterministic behaviour through varyingly getting into and leaving the coverage of the last base stations. After the maximum duration for staying at this area has elapsed, the mobile user moves back to the starting area, simulating typical commuter behavior. This user would for example generate a traces like BL, BL2, BM, M2... The second user starts at the lower right area F, following a gravity based model. The upper left and right areas have associated weights to set an attractiveness value for these areas. The current target is chosen randomly and uniformly distributed between these two areas. Again, this model leads the user back to the starting area after the maximum stay time has expired. Asymmetry is achieved by assigning different levels of attractiveness (weights) to the pavilions. While these two users are rather easily to track because of their high level of determinism, the third user starting in area A introduces noise by following a random movement model. While this model is of no use for any prediction algorithm, it is an admirable choice for testing stability and performance of the algorithms.
III. ANALYSIS OF MOBILITY PATTERN PREDICTIONS

Pattern recognition algorithms from the field of computational intelligence offer one possibility to detect repeating behavior in user movement. In this section we present a selection of different pattern detections and discuss their benefits for prediction of the user's next base station.

A. Pattern detection algorithms Several algorithms for pattern recognition are compared: Decision trees (DT), instance based (IB) nearest-neighbour algorithms (similar to the dictionary approach used in [2]) and

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0.91

BR

0 0 0 0.09 0 0 0 0 0 0 0

0.94 0 0.06 0 0 0 0 0 0 0 0

TR 0

M2 0 0 0.92 0.03 0 0 0 0 0 0 0.02 0.03

0.05 0.83 0.08 0 0 0.04 0 0 0 0

TM 0 0

Predicted class BL M TL 0 0 0 0 0 0 0 0.02 0 0 0 0 0.82 0 0.02 0 0 1.00 0 0 0.07 0 0.85 0 0 0 0 1.00 0 0 0.06 0 0 0 0.05 0 0 0 0 0 0 0 0 0
BM 0 0 0.11 0

TR2 0 0 0 0 0 0 0.11 0 0.60 0.29 0 0

TL2 0 0 0 0 0 0 0 0 0 1.00 0 0

BR2 0 0 0 0 0 0 0 0 0 0 0.73 0.27

BL2 0 0 0 0 0 0 0 0 0 0 0 1.00

t Real class BR TR M2 TM BM BL M TL TR2 TL2 BR2 BL2

TABLE I EXAMPLE CONFUSION MATRIX RUNNING DECISION TREE PREDICTION ALGORITHM

support vector machines (SVM) ([11], comparable to neural networks in [7]). Decision trees (e.g. C4.5 or ID3, [8]) are generated using the so called training set, which is a set of movement sequences as described in the former sections. The trees define a set of rules, where based on the values at the different positions inside the movement sequence, a path down to the last node (leaf) in the tree is followed. The associated value will be the predicted class, in this context the next target base station of the user. To the class of the so-called lazy algorithms belongs IBk, a k-nearest neighbour algorithm. Lazy algorithms usually keep the input sequences unprocessed and try to find the best matching sequence and resulting target base station by calculating the distance to up to k stored sequences. While this algorithm is incredibly fast for data collection, the amount of time needed to find best matching sequences grows with the amount of collected data. This approach can be found in a modified form in [2] for paging of mobile equipment. The third algorithm used for prediction, SMO, is a variant of the class of support vector machines (SVM). Support vector machines try to classify the data by finding hyperplanes separating the trace data into subsets for target prediction. The choice of so-called kernel functions allows the transformation of the original data into another space, enabling data classification through many freeform surfaces instead of only hyperplanes. This class of algorithms is additionally interesting as the choice of an appropriate kernel function provides the SVM with the same capability as the popular neural networks (compare [7]). Main disadvantage of the SVM is the computationally very intensive generation of the prediction classifier.
B. Identification of Prediction Accuracy per Base Station Table I presents the so-called Confusion Matrix as the result of running a standard ten-fold stratified cross validation test for the base station predictions. Predictions have been performed using a decision tree algorithm ([11]). Amount of random walk users for pattern generation has been set to 33%, rest of users either used gravity or path following models, heading for a

certain user area and back, as described in section II. Each row is associated with the real class (base station) the user moved into from the current base station area, each colunm with the predicted class. The absolute number of predictions has been normalized along each colunm to [0,1], showing the prediction accuracy as ratio of wrong versus correct predictions. The main diagonal of the table therefore contains the percentage of correct predictions. The results in the matrix are based on historical data where the next base station is known for and which has not been used for decision tree generation and hence is new to the predictor. For the specific confusion matrix in table I a historical sequence length of 3 has been used, leading to an overall accuracy of about 85%. The confusion matrix enables a detailed view on problematic spots in the prediction scenario where an algorithm acts unstable and standard handover triggers should be applied. The most interesting regions occur where the predictions performed either very well (e.g. BL) or very poor (e.g. TR2). Manual investigation of the raw trace data reveals the reasons for this: because of the asymmetry chosen for the scenario parameters (33% randomness, different user speeds) different amounts of traces have been generated for each part of the topology. The worst predictions appear where the number of traces generated by random users outweigh the others.
C. Analytical Benchmarking of Predictions The transition rate A for handovers to cell x can be estimated following a Markovian model on the basis of the last known cell n. Focusing as an example on the base station TM, which allows handover to three neighbouring cells (TL2, TR2, M), leads to three values per user: For the random user of course ATM(X) = to each neighboring cell, as well for the gravity model user and ATM (X) = for the lower and right cell, 0 for the left cell, for the path following user. Remembering that we wanted to keep any prognosis independent of the specific user, the aggregated probabilities transform to ATM (X) = ~~~~~~~18 4 = 7 0.22 for the left and ATM(X) = 18 = 0.39 each for the right and the lower cell. This approximation enables to calculate transition and cell residence probabilities for TM and each

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neighboring cell. The analytical transition rates calculated using knowledge about the movement models allow comparison with the success rate of the pattern detection algorithms as discussed through the Confusion Matrix. Complementing this, calculating state probabilities allows identification of most important parts of the network for prediction. The higher the state probability for a certain base station is, the more important is the accuracy of the predictions done for this cell. The probabilities can be easily calculated by solving the equations for statistical balance:
PTL2 * 0.5 PTR2 * 0.5

95 90 85

-0
01 0-

80 75
70 65 60
55

PM 0.5 (PTL2 + PTR2 + PM) * 0.5
PTL2 + PTM + PTR2 + PM

PTM PTM PTM PTM 1

0.22 0.39 0.39 (0.22 + 2 0.39)

50

2

3

4

5

6

7

8

Sequence length [# transitions]
Fig. 3. Prediction accuracy dependent on length of historical data

Please notice, that for sake of simplicity this is only a subset of the equations needed to describe the whole scenario. Only the direct neighborhood of the T-crossing at base station TM is observed.
0.5
0.5

0.22
0.5

0.39 0.39

Fig. 2. Partial Markovian Model of base station transitions

The calculated state probabilities show as to expect that the center of the T-crossing TM has the highest probability for active users being served by this cell. As the predictions of user mobility could be used for reservation techniques, most interesting cells are with high loads of users. Therefore, the poor result of prediction accuracy for TR2 of 60% is less relevant than the results for TM (83%). For successful handovers it is much more important to gain good prediction results for users moving into high load cells than leaving from these cells.
D. Summarized prediction results As to expect the overall quality raises the longer the historical sequences are (see figure 3), allowing to differentiate the random from recurring movements. This trend in accuracy can be divided into three phases: For a sequence length of 1, i.e. only the actual base station as input for the algorithms, all algorithms perform poorly with a rate just marginally above

50%. A boost in accuracy can be seen for sequence lengths of two or greater, allowing the algorithms to at least detect the direction the users are heading for and raising performance for all three algorithms to about 80%. For sequence lengths up to six base stations the accuracy keeps roughly the same, with the exception of falling below 80% for the SVM at a length of four. The third interesting phase in the figure can be seen for lengths of seven and eight base stations traversed, raising the accuracy for all algorithms above 90%. Important is that the overall effect showing these three phases in pattern detection quality can be observed for all of the three completely different algorithms. This effect could lead to the conclusion that there is no relevant difference for the selection of the algorithm to prefer. But as figure 3 only illustrates the general accuracy for all predictions made, outliers for certain predictions are not visible, but exist for some base stations as can be observed in the confusion matrix. Remembering the poor results for base station TR2 in matrix I, investigating this cell in detail for longer sequences showed also a positive effect, e.g. resulting in 71% accuracy for lengths of 5 and 79% for lengths of 8.
E. Selective Prediction Validations and Enhancements Post-prediction filters using a-priori topology knowledge can further enhance overall prediction quality. For this scenario post-filtering could be explained looking at the matrix where BM was predicted. Evaluation on the test data showed an accuracy of 82% for BM, while in 11% of the predictions M2 and in 7% M was the correct base station. Comparing this to the topology in figure 1 indicates that in cases where M2 was the correct next target base station, the prediction BM can obviously not be correct, letting the prediction instantly be rejected. This kind of validation of predictions can be used to either only use standard triggers for handover or execute alternative prediction algorithms to get alternative estimations and reduce the overall rate of mispredictions. To overcome limitations through outliers of single algorithms we propose a hybrid approach of multiple algorithms

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in parallel, where the fittest (i.e. currently best performing) algorithm is weighted over others to achieve optimal results even with a high degree of randomness. A decision process, letting each algorithm vote for its prediction, helps eliminating the number of wrong predictions performed by a single algorithm. In [6] we show how sensitive the overall prediction accuracy depends on configuration of pattern detection algorithms. The task finding the correct parameterization for the pattern detectors is non-trivial, even training on data with low degrees of random walk users may result in poor prediction results.
45 40 35
0

to scheme 2. Performance of error reduction is highest for this scheme, benefiting the overall voting process from the better results provided by SVM using data with sequence length 2 compared to the worse accuracy using length 1. The great impact of the better results provided by SVM could be seen for sequence length 1, where the poor prediction results of the other two algorithms could be partially compensated.
IV. CONCLUSIONS Prediction approaches to gain knowledge about future user positions can help to aid the triggering of cell handovers. The approach for mobility prediction presented here is reduced to the most common denominator available for a multitude of heterogeneous networks, i.e. cell residence. Using this trace data, it has been shown, that prediction of user movements is possible. Three different algorithms have been investigated and it has been demonstrated, that each of it showed similar behavior depending on the maximum length of available path sequences. Additionally it should be considered that the overall accuracy for predictions is one measure for algorithm performance. Complementing this, a detailed analysis per base station allows to investigate problematic locations for the prediction. For the success of handovers the most important predictions occur when moving into highly populated cells. Finally it could be demonstrated that a combination of more than one algorithm reduces the overall rate of erroneous

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1 2

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. .. + X .. ~Scheme 1 [
4 5

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Fig. 4. Reduction of error rates through majority voting

predictions. Future work is going to integrate these algorithms with the classical measures for handover triggering.
REFERENCES
[1] Akyildiz, I.F.; Wang, W.: The Predictive User Mobility Profile Framework for Wireless Multimedia Networks, IEEE/ACM Transactions on Networking, Vol. 12, No.6, pp. 1021-1035, 2004

To examine this effect and to present a method to compensate the degradation of quality, we tested the application of the three pattern detection algorithms in parallel and accepted only predictions, where two or more of the algorithms delivered the same result. Three schemes are evaluated and the results are shown in figure 4. The ordinate shows the gain (i.e. the percentage, by which the error rate could be reduced) which could be achieved by using three predictors in parallel for the different sequence lengths. Scheme 1 shows a simple voting mechanism, where all algorithms used data of the same sequence length. This means for each value of the abscissa, the results of all three algorithms have been combined for the final prediction, while before they have been treated independently (fig. 3). This scheme shows a continuous raise, which means that up to 30% of the errors could be eliminated using all three

algorithms together. Scheme 2 kept data of sequence length 1 fixed as input to the SVM algorithm, which denotes to have on algorithm with low quality of nearly 50% errors (see fig. 3) inside the voting scheme. For each value along the abscissa the other two algorithms delivered for voting same results as taken for the single predictions. In spite of the worse predictions by SVM, figure 4 shows how this effect can be compensated by the other two algorithms. Scheme 3 kept data of sequence length 2 fixed as input to SVM, which means better error reduction up to 45% compared

[2] Bhattacharya, Amiya; Das, Sajal K.: LeZi-Update: An InformationTheoretic Approach to Track Mobile Users in PCS Networks, Proceedings of ACM/IEEE International Conference on Mobile Computing and Networking, MobiCom '99, Seattle 1999 [3] Cheng, C.; Jain, R.; Berg, E.v.d.: Location Prediction for Mobile Wireless Systems, in: Furht, B. (Hrsg.): Wireless Internet Handbook, S. 245-264, CRC Press, Boca Raton 2003 [4] Liang, Ben; Haas, Zygmunt J.: Predictive Distance-Based Mobility Management for Multidimensional PCS Networks, IEEE/ACM Transactions on Networking, Vol. 11, No. 5, 2003 [5] Markoulidakis, J.G. et al.: Mobility modeling in third-generation mobile telecommunication systems, IEEE Personal Communications 1997 [6] Michaelis, S.; Wietfeld, C.: Evaluation and comparison of prediction stability for user movement pattern detection algorithms, European Wireless, Athens 2006 [7] Poon, W.T.; Chan, E.: Traffic Management in Wireless ATM Network Using a Hierarchical Neural-Network Based Prediction Algorithm, Proceedings of the International Conference on Computers and their Applications, ICSA 2000 [8] Quinlan, J.R.: C4.5: Programs for machine learning, Morgan Kaufmann, San Mateo 1993 [9] Roy, A.; Das, S.K.; Misra, A.: Exploiting Information Theory for Adaptive Mobility and Resource Management in Future Cellular Networks, IEEE Wireless Communications, 2004 [10] Song, L.; Kotz, D. et al.: Evaluating location predictors with extensive Wi-Fi mobility data, Proceedings of IEEE InfoCom, 2004 [11] Witten, Ian H.; Eibe, Frank: Data Mining: Practical machine learning tools with Java implementations, Morgan Kaufmann, San Francisco 2000

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