ESTIMATING ROAD TRAFFIC PARAMETERS FROM MOBILE COMMUNICATIONS R. Bolla, F. Davoli, A. Giordano Department of Communications, Computer and Systems Science (DIST University of Genoa Via Opera Pia 13, I-115 Genova, Italy (lelus, franco, al@dist.unige.it SUMMARY Mobile communications are widespread in a large part of industrialized countries and cellular networks, by which mobile radio-communications are supported, can give directly or potentially a huge amount of frequently updated information on the position of their users. This information can be used to estimate on-line the traffic conditions of important roads and highways, by exploiting the presence of mobile phones on-board a good deal of vehicles. This paper analyzes this possibility and proposes a mechanism, which gives the capability to estimate traffic parameters in the cells along a road with a partial presence of active cellular phones in the vehicles. The proposal has been tested by using an integrated vehicle and communication traffic simulator and different situations have been verified. The results are presented in the paper and they show a good level of accuracy and a satisfactory behavior of the proposed technique. INTRODUCTION Mobile communications are widespread in a large part of industrialized countries; their pervasiveness is quite evident in Europe, USA and Japan. Cellular networks, by which mobile radio-communications are supported, can give directly or potentially a huge amount of frequently updated information on the position of their users, as they need to keep track of the location of all mobiles and generate a non-negligible flow of location management traffic to this purpose. This information can be used to estimate on-line the traffic conditions of important roads and highways, by exploiting the presence of mobile phones on-board a good deal of vehicles. This paper analyzes this possibility and proposes a mechanism, which gives the capability to estimate traffic parameters in the cells along a road with a partial presence of active cellular phones in the vehicles. We suppose the presence of a cellular terminal to be detected at the vehicle s entrance within the monitored road stretch, and we suppose these terminals to be forced to signal every cell change. In these conditions, we can dynamically update the ratio between the number of vehicles that are equipped with a cellular mobile terminal and those that are not, and we can use this quantity to estimate the average vehicle density, flow and velocity in every cell. This proposal has been tested by using an integrated vehicle and communication traffic simulator. Different situations have been verified, with dynamic variations of conditions of part of the road (with accidents, meteorological changes and so on, and all results presented in the paper show a good level of accuracy and a satisfactory behavior of the proposed technique. 1
It is worth noting that registering every cell change requires more frequent signaling than with the usual location update information. However, this mechanism would affect only the handsets that are on-board the vehicles and may benefit of power feed by the latter; therefore, it would have little impact on battery power consumption. It is even more important to note that the whole process might be carried on by substituting the information from the cellular phones with that gained by interacting with equipped portals (e.g., telepass. THE TRAFFIC ESTIMATION MODEL We consider a road stretch in an area covered by a mobile cellular communication system; for the sake of simplicity, only one direction is taken into account. Let C = {1,,, M} be the set of M cells, numbered in ascending order according to the direction of motion, that are traversed from the road considered, and let s (i denote the road stretch that is included in cell i. Moreover, let L [km] the length of the sub-stretches s (i (supposed to be of equal length for simplicity n (i (t k the number of vehicles in s (i at time instant t k v (i (t k the number of vehicles in transit between s (i-1 and s (i in the time interval (t k-1, t k ] c (i (t k the number of vehicles that entered s (i from outside the road in the time interval (t k-1, t k ] o (i (t k the number of vehicles that left the road at s (i in the time interval (t k-1, t k ] n (i c (t k the number of cellular phones on the vehicles in cell i at time instant t k v (i c (t k the number of cellular phones on the vehicles on the road that passed from cell i to cell i+1 in the interval (t k-1, t k ]. We suppose that all entrances to and exits from the road under consideration be equipped with portals (e.g., toll stations, which can detect a passing vehicle, check the presence of an operating cellular phone on-board and identify it. Identifications will be referred to the cellular network, which will provide the values n (i c (t k and v (i c (t k for all cells i =1,,, M, at each instant t k, k=,1, In the case of presence of more than one phone on a specific vehicle, only one will be selected, disregarding the others. At every instant t k, toll stations will measure the values of c (i (t k and o (i (t k. For the sake of simplicity, let us suppose s (1 to possess a single access at the beginning of the road stretch and no exit. Under such hypothesis, we will have: n (1 (t k = c (1 (t k (1 Let us define the ratio vehicles/cellular phones in the first stretch as r (1 (t k = n(1 (t k n c (1 (t k By letting V indicate the average free speed of a vehicle on the road, and fixing t k = kt, k =,1,, with T = L/V (average time to traverse a road stretch covered by a cell, we can define (i r fast t k ( = r(i 1 (i 1 (t k 1 n c (t k 1 + c (i (t k o (i (t k n (i c (t k as the ratio vehicles/cellulars in cell i-1, at instant t k-1, which has entered cell i at time t k, updated with the quantities of incoming and outgoing vehicles and with the measured (by the network number of cellular phones at t k, and ( (3
(i r slow (t k = r(i 1 (i 1 (t k n c (t k + c (i (t k 1 o (i (t k 1 + r (i 1 (i 1 (t k 1 n c (t k 1 + c (i (t k o (i (t k n (i c (t k (3 as the weighted average of the same ratios in cell i-1 at instants t k- and t k-1, also updated with entrances and exits in i. We choose between the two updating mechanisms as follows r (i (t k = r (i slow (t k, r (i fast (t k, L V (i (t k 1 > T L V (i (t k 1 T In practice, we distinguish two types of road stretches (which are dynamically classified: slow, if its traversing time (L/V (i (t k-1 is less than half the average time to traverse a generic stretch (T = L/V, fast otherwise. In the fast stretches, the ratios are propagated from a cell to the next one every T seconds, by also updating them with entrances and exits (in the formulas, the latter are implicitly supposed to happen at the very beginning of the stretch. In the slow stretches, two ratios are suppose to cumulate, and the new ratio is obtained consequently as described above. At every instant t k, the cellular network provides the number of phones on the vehicles in each cell i and the total number. Let ρ (i (t k and q (i (t k, respectively, be the density and the flow of vehicles in s (i ; these values can be computed as ρ (i (t k = n c (i (t k r (i (t L k, i=1,,,m (5 q (i (t k = v c (i (t k r (i (t t k t k = v(i c (t k k 1 T As regards the velocity, it is computed indirectly as V (i (t k = q(i (t k ρ (i (t k ( r (i (t k, i=1,,,m ( i=1,,, M (7 NUMERICAL RESULTS Simulation results to test the proposed mechanism have been obtained with a microscopic vehicular traffic simulator, based on Gipps model [1, ], integrated with a telecommunication part that reproduces the operation of the mobile cellular network. The vehicular traffic simulator has been modified, to take into account special events, like road narrowing (for road works or incidents or particular meteorological conditions; the reason for this stems from the fact that monitoring mechanisms of this kind allow to detect congested situations in relatively short time and with relatively good precision, as regards the localization and entity of the phenomenon. The results reported refer to a single direction of movement on a three-lane road, with a single initial entrance and a final exit (i.e., no intermediate toll stations. This is a worst case condition, as the presence of points that absorb or inject traffic improves the precision of the estimates, since the quantities extracted or injected are known precisely (in the extreme case, if 99% of the traffic went out and the same quantity came in at the same toll point, the system would recompute the estimates on the basis of precisely known values. With no intermediate station, the precision of the estimates in the last stretch is tightly dependent from the proposed algorithm. 3
Evaluations have been performed on road stretches of and km, respectively. The instants of generation of incoming vehicles are chosen at random, but keeping a constant density and choosing desired velocities for the individual lanes, depending on the corresponding density. In practice, given certain input densities, different road characteristics have been chosen (giving rise to different velocities. The desired speeds are 9 km/h, 11 km/h and 13 km/h for the right, center and left lane, respectively. The results in the figures have been obtained on the -km road, with M= and L=1 km, by setting an input density of vehicles/km and imposing a time-varying percentage of cellular-equipped vehicles in the final cell. The variation consists of a three-step growth, starting from %, going up to % after min and then to 8% after min. Figs. 1and show the results of cell (i=, which is the farthest from the entrance to the road. Fig. 1 reports the estimated and the real densities over time (the variation in the percentage of cellular-equipped vehicles is also shown and the corresponding percentage error. Fig. gives the same type of information as Fig. 1, but relatively to the flow. Fig. 3 shows the average in the cells over the whole simulation, as regards all three estimated quantities. In general, a good precision is evidenced. The graphs in Figs. have been obtained under the same conditions as above, but for the addition of a slowdown at the beginning of the last cell. Substantially, the effect is to reduce the desired speed down to 5 km/h, over the three lanes. For instance, this might ensue in a situation of poor visibility conditions, as in fog or heavy rain. The two parts of Figs. show the behaviour of density and flow, respectively, both real and estimated, for cell 1, which is the central one in our global stretch. It can be noted that the slowdown imposed at the output reaches cell 1 between min and 5, causing the vehicle density to increase (and the velocity, not shown, to decrease. Also in this case, errors are quite low. It is worth noting that the system succeeds in becoming aware and in quantifying in real-time the anomalous situations where traffic parameters change abruptly. 7 5 3 1 % of veicles with cellular Real values Estimated values 1 1 8 13 7 3 7 5 1 8 75 81 88 95 (a 18 1 1 1 1 8 13 7 3 7 5 1 8 75 81 88 95 Time [min.]
(b Fig. 1. Real and estimated vehicle density (a and corresponding percentage of error (b in the last cell (i= versus time. 5 35 3 5 15 1 5 % of veicles with cellular Real values Estimated values 1 1 8 13 7 3 7 5 1 8 75 81 88 95 (a 1 1 1 8 13 7 3 7 5 1 8 75 81 88 95 Time [min (b Fig.. Real and estimated vehicle flow (a and corresponding percentage of error (b in the last cell (i= versus time. 5 Density Flow Velocity Error [%] 3 1 3 5 7 8 9 1 11 1 13 1 15 1 17 18 19 Cell (i Fig. 3. Average percentage error for estimated density, flow and velocity versus cell number. 5
1 1 Density [vehicle\km] 1 8 Real Estimated % of vehicles with cellular 9 8 7 5 % Vehicle with cellular 1 18 31 37 3 9 5 8 7 81 87 93 99 (a 3 Flow [vehicle\h] 5 35 3 5 15 1 5 1 18 31 37 3 9 5 8 7 81 87 93 99 Real Estimated % of vehicles with cellular 1 1 8 % Vehicle with cellular (b Fig. 5. Real and estimated vehicle density (a and flow (b in the middle cell (i=1 versus time; case with slow exit in last cell. CONCLUSIONS We have presented a methodology to estimate road traffic parameters from location tracking data in a cellular mobile network. To the best of the authors knowledge, our results are the first attempt in this case. The model of the system has been outlined and an evaluation by simulation has been reported and discussed, showing encouraging performance results. In particular, exceptional situations are immediately detected and quantified. References [1] P. G. Gipps, "A behavioural car-following model for computer simulation", Transpn. Res.-B, vol. 15B, no., pp. 15-11, 1981. [] P.G. Gipps, "A model for the structure of lane changing decision", Transp. Res. B, vol. B, no. 5, pp. 3 1, 198.