Chapter 3 Mathematical analysis
3.4 The analyzed process of successful reservation ratio
Figure 3-6 shows an R-zone environment with the following four variables:
1. 𝜆𝜆: vehicle arrival rate for each lane 2. 𝑁𝑁𝑙𝑙: the number of lanes
3. 𝑣𝑣: the average speed of vehicles 4. 𝑎𝑎𝑅𝑅: the length of R-zone
Figure 3-6, the R-zone environment with four important variables
The estimating process of the actual number of contending vehicles will be given as follows: We separate the R-zone into several sub-zones, and a vehicle will go through the sub-zone 1 of R-zone (we donate it as the first stage) to the sub-zone 2 of R-zone (second stage), and so on. Assume there are 𝛼𝛼 number of vehicles entering the sub-zone 1 of R-sub-zone at the initial stage, after the channel contention, these 𝛼𝛼 number of vehicles will enter in the sub-zone 2, with some of which do not successfully get the channel reservation; meanwhile, there will have a number of new vehicles entering the sub-zone 1 of R-zone, then contend the channel with the previously vehicles that have not get the channel reservation successfully yet. These 𝛼𝛼 vehicles will go through the sub-zone 3 of R-zone, to the sub-zone 4 of R-zone, and so on till leaving the R-zone (our objective is to let 𝛼𝛼 reduce to 0, that is, these 𝛼𝛼 number of vehicles can contend
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the channel successfully). When the system operates for a while, the actual number of vehicle in contention on the R-zone will gradually approach to a constant 𝑘𝑘, which is the number of vehicles that have to contend the channel.
There are four parameters that will be used in the process for analyzing the successful reservation ratio, named 𝑎𝑎(𝑖𝑖, 𝑗𝑗), 𝛼𝛼, 𝑁𝑁(𝑖𝑖) and 𝑝𝑝𝑐𝑐(𝑎𝑎, 𝑐𝑐𝑐𝑐) . The first one 𝑎𝑎(𝑖𝑖, 𝑗𝑗), is to calculate the expected value of contending vehicle of the 𝑗𝑗-th sub-zone in the 𝑖𝑖-th stage, as shown in the figure 3-7. The second one 𝛼𝛼, is the number of contending vehicle at the initial stage. The third one 𝑁𝑁(𝑖𝑖), is the total number of contending vehicles of 𝑖𝑖-th stage. Finally, the fourth one 𝑝𝑝𝑐𝑐(𝑎𝑎, 𝑐𝑐𝑐𝑐), is the packet collision probability under the condition of 𝑎𝑎 number of contending vehicles and the contention window size is 𝑐𝑐𝑐𝑐, and the solution set is {𝑝𝑝|𝑠𝑠(𝑝𝑝, 𝑎𝑎, 1,0, 𝑐𝑐𝑐𝑐) = 0, 0 < 𝑝𝑝 <
1 and 𝑝𝑝 ∈ 𝑅𝑅}
Figure 3-7. The step by step process of contention for vehicles
The analysis process of successful reservation ratio will be described as follows.
At the first stage, there are 𝛼𝛼 vehicles flow in the reservation zone, that is, 𝑁𝑁(1) = 𝑎𝑎(1,1) = 𝛼𝛼 . After the first contention for the 𝛼𝛼 vehicles, the stage comes to the second
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one, we have to calculate the number of vehicles without getting the channel access, since the collision probability for a vehicle is 𝑝𝑝𝑐𝑐(𝑁𝑁(1), 𝑐𝑐𝑐𝑐(1)), we get n(2,2) = n(1,1) × 𝑝𝑝𝑐𝑐(𝑁𝑁(1), 𝑐𝑐𝑐𝑐(1)). At the same time, there are still newly vehicles flow in the reservation zone, the expected value is n(2,1) = 𝑇𝑇𝑐𝑐(1) × 𝜆𝜆 × 𝑁𝑁𝑙𝑙, where 𝑇𝑇𝑐𝑐(1) is the duration for the contention of second group. Notice that 𝑁𝑁(2) will be the summation of contending vehicles of first and second group, that is, 𝑁𝑁(2) = 𝑎𝑎(2,1) + 𝑎𝑎(2,2). At the third stage, the remaining 𝑎𝑎(2,2) vehicles will again contend the channel, we can use the similar way to derive 𝑎𝑎(3,3) = 𝑎𝑎(2,2) × 𝑝𝑝𝑐𝑐(𝑁𝑁(2), 𝑐𝑐𝑐𝑐(2)). The vehicle of the second stage and first group will contend the channel, we can use the similar way to derive 𝑎𝑎(3,2) = 𝑎𝑎(2,1) × 𝑝𝑝𝑐𝑐(𝑁𝑁(2), 𝑐𝑐𝑐𝑐(2)). At the same time, there are still newly vehicles flow in the reservation zone, the expected value is n(3,1) = 𝑇𝑇𝑐𝑐(2) × 𝜆𝜆 × 𝑁𝑁𝑙𝑙. Notice that 𝑁𝑁(3) will be the summation of contending vehicles from first to third group, that is, 𝑁𝑁(3) = 𝑎𝑎(3,1) + 𝑎𝑎(3,2) + 𝑎𝑎(3,3). The explicit flow chart shows in the figure 3-8.
Figure 3-8. The explicit flow chart of step-by-step contention of vehicles
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In general, the conducted equations are shown as follows:
(18) and
(19)
Finally, the system will approach to a steady state after a time interval 𝛽𝛽, which means that the real number of contending vehicles will reach a constant value. We assume that it reaches the steady state when safisfying the condition: 𝑁𝑁(𝛽𝛽) − 𝑁𝑁(𝛽𝛽 − 1) < 10−3, hence we get the number of vehicles in competition is 𝑁𝑁(𝛽𝛽).
In conclusion, since we derive the failure probability 𝑝𝑝�𝑁𝑁(𝛽𝛽)�
𝑝𝑝�𝑁𝑁(𝛽𝛽)� = {𝑝𝑝|𝑠𝑠(𝑝𝑝, 𝑁𝑁(𝛽𝛽), 𝑠𝑠𝑠𝑠𝑟𝑟𝑎𝑎, 𝑎𝑎, 𝑐𝑐𝑐𝑐) = 0, 0 < 𝑝𝑝 < 1 and 𝑝𝑝 ∈ 𝑅𝑅} (20) Here, the frozen probability is:
𝑝𝑝𝑓𝑓𝑟𝑟= 𝑝𝑝�𝑁𝑁(𝛽𝛽)� (21) And the successful channel reservation probability is:
𝑔𝑔(𝑖𝑖) = 1 − 𝑝𝑝�𝑁𝑁(𝛽𝛽)� (22)
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Chapter 4
The enviroment setup and evaluation results
4.1 Environment setup
Before discussing about the setup for the analysis and simulation, we have to derive the up-to-date real condition on the high-way, so that we can obtain more actual data corresponding to the current situation in Taiwan. According to the traffic flows that we have observed, there are two distinguishable periods of time, which are peak-hours and off-peak hours. In Taiwan, the peak-hours are often at 7-9 a.m. and 5-7 p.m. which are on-work time and off-work time, respectively; the rest of time are so called off-peak hours. In Jongli city of Taoyuan county where National Freeway No.1 passed through, and in NanKang district of Taipei City where National Freeway No.3 passed through, the traffic condition are almost similar that the average speed of vehicle is 100 km/hr with 0.5 vehicles per second of vehicle arrival rate for each lane in the off-peak hours, whereas the average speed of vehicle is 70 km/hr with 1.0 vehicles per second of vehicle arrival rate for each lane in the peak hours. The average speed of vehicle and arrival rate are summarized in Table 4-1.
Table 4-1. The real condition of high-way in Taiwan
Parameters peak-hour Off-peak hours
The average speed of vehicle 70km/hr 100km/hr
The vehicle arrival rate for each lane 0.8~1.2 veh/sec 0.4~0.6 veh/sec
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We conduct the mathematical analysis using an analytical program written in C++.
In our program, the parameters are declared as a form of macro, so that the developer can arbitrarily alter the value to see the variations of the successful reservation ratio.
With regard to the parameter setups, since the message transmitted between the RSU and OBU should have the highest priority, we consider the access category should be AC_VO. Also, the transmitting data rate is set to 3Mbps, which is the lowest regulated in the WAVE/DSRC spec, and the frame size is 1 Kb. More details are shown in the table 4-2.
Table 4-2. The parameter setup and the values for our analytical program
Analysis parameters Value
Access category (𝐴𝐴𝐶𝐶) AC_VO
The minimum of contention window size (𝐶𝐶𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 ) 3 The maximum of contention window size (𝐶𝐶𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 ) 7
Station short retry limit (SSRL) 7
Slot time (aSlotTime) 9𝜇𝜇𝑠𝑠
DCF Inter-frame space (DIFS ) 25𝜇𝜇𝑠𝑠
Short Inter-frame space (SIFS ) 16𝜇𝜇𝑠𝑠
Data rate (R) 3Mbps
Frame size (D) 1Kb
The length of reservation zone (𝑎𝑎𝑅𝑅) 20m as default
Number of lanes(𝑁𝑁𝑙𝑙) 4
Vehicle arrival rate(𝜆𝜆) 0.5 or 1.0 vehicle per second
Vehicle speed (v) 20m/s as default
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Moreover, we conduct the simulation using Estinet 7.0 simulator [18]. The simulation scenario is in a 1000 meters four-lane high-way, with four T-RSUs using independent SCH for transaction procedure and one R-RSU using CCH for channel reservation. In addition, the average vehicle speed and vehicle arrival rate for each lane has different value in accordance with the simulated conditions. Transmission range and data transmission rate of each RSU and OBU are set as the minimum value defined in WAVE/DSRC spec, that is, 300m and 3Mbps, respectively. The detailed parameters are given in Table 4-3.
Table 4-3. The simulation parameter setups
Simulation parameters Value
Average vehicle speed 70 or 100 kmph
Vehicle arrival rate 0.5 or 1.0 vehicle per second
R-Beacon interval 100 ms
Priority level of Reservation message AC_VO
CFP of SCH 100%
Packet error rate 0%
Transmission data rate 3Mbps
Transmission range 300m
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The following sections are organized as follows. In section 4.2, we will initially show the simulation results of proposed ETC system with varied length of R-zone and diffent vehicle arrival rate to observe the variation of the successful reservation probability, then we show the times of request message sent from vehicle with varied length of R-zone. Moreover, the default value of parameter is derived from table 4-1. In section 4.3, we will show the analytical results using our developed mathematical analysis within the parameter setup deriving from Table 4-2. Finally, in section 4.4, we compare the analytical results with simulation results, and we will find out both of these results are almost similar, which means that our mathematical analysis method has enough correctness.
4.2 Simulation results
Figure 4-1 illustrates the successful reservation ratio with varied R-zone length during the off-peak hours. We assume that the vehicle arrival rate is divided into three cases: 0.4, 0.5 and 0.6 (vehicle/sec). As what we have expected, the successful reservation probability with the case of vehicle arrival rate 0.6 is lower than others, this is because the number of vehicles in competition is higher than other cases so that the collision probability will be higher for each contention, which results in the reservation ratio lower. In addition, the reservation ratio will achieve 100% as the length of the R-zone reaches 6 meters, meaning that it is permitted for the R-R-zone length to be only set to 6m.
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Figure 4-1. The reservation ratio with variable R-zone length in off-peak hours
In addition, Figure 4-2 illustrates the case of peak-hour with arrival rates 0.8, 1.0, and 1.2. From figure 4-2, we learn that the reservation ratio reaches 100% if length of R-zone is greater than 10m. Hence we can conclude that if the R-zone length is set to 10m, it will satisfy the traffic flow for both the off-peak hour and peak hour cases in Taiwan high-way scenario.
Figure 4-2. The reservation ratio with variable R-zone length in peak hours 0%
Figure 4-3 illustrates the average times of request message sent by a vehicle within variable lengths of R-zone. From the figure, we will realize that the number of request times remains a constant for arrival rate 0.4 if the length of R-zone is greater than 4 meters. This is due to that the reservation ratio will reach 100% at that length, also meaning that the vehicle will not send request message as the displacement is over 4m, since the vehicle will absolutely get the channel reservation.
Figure 4-3. The avg. times of request sent by a vehicle within variable R-zone length
4.3 Analytical results
Figure 4-4 shows the successful reservation probability for a vehicle on the R-zone, with arrival rates: 0.3, 0.6, 0.9 and 1.2 (vehicle/second). The maximum length of R-zone is 20m, and the parameter on the x-axis is displacement of vehicles. From the figure, we observe that the reservation ratio is low when the vehicle arrival rate is high. Moreover, Figure 4-5 shows the case with variable data transmission rates, notice that the
0.00
specification of WAVE/DSRC regulates transmission rate should be between 3Mbps to 27Mbps, hence if the data rate is too slow, the reservation condition will be deteriorated resulted from the high transmission delay. As we have seen from the figure, the reservation ratio sharply declines between the distances from 2 to 6 meters for the transmission rate 1Mbps.
Figure 4-4 The length of R-zone is fixed 20m within variable vehicle arrival rate
Figure 4-5 The length of R-zone is fixed 20m within variable data transmission rate
0%
S:25, AR:0.3 S:25, AR:0.6 S:25, AR:0.9 S:25, AR:1.2
0%
DR: 1Mbps DR: 3Mbps DR: 5Mbps
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Figure 4-6 illustrates the case of short R-zone length, in which we adjust to 5 meters.
Since a vehicle does not have too many opportunities for contending the channel access if the R-zone length is too short, as we see from the figure, the successful reservation probability for a vehicle does not reach 100% at the end of the R-zone. In our developed ETC system, the length of R-zone is suggested to set as 20m.
Figure 4-6 The length of R-zone is fixed 5m within different vehicle arrival rate
4.4 The comparison between simulation and analytical results
At the end, we will compare the simulated results with analytical results, observing the difference among them.
Figure 4-7 illustrates the reservation ratio for the fixed 10m R-zone length, the purple and red curves stand for simulated result and analytical results, respectively, both of them are under same condition within 20 meters per second as vehicle speed, 2.0 as
10%0%
arrival rate, and the data transmission rate is 3Mbps. Other parameter setup such as packet size and number of lanes of R-zone are following the value shown in Table 4-2.
We see the ratio differentiation between these curves are at most 5% at 2m displacement, with slight gaps at other displacements. The other 2 curves in the graph has similar conclusion. Figure 4-8 expands the length to 20m, as we see, the reservation ratio is almost the same depicted in Figure 4-7 before displacement of 10m, which represents that even the length of R-zone expands to 30m or longer, the reservation ratio must be 100% at the end of the zone.
Figure 4-7 The comparison between analysis and simulation for 10m R-zone
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Figure 4-8 The comparison between analysis and simulation for 20m R-zone
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Chapter 5 Conclusion
In this thesis, we propose an explicit mathematical analysis for our developed contention-free based ETC system. In our mathematical model, we use a step-by-step approach to compute the reservation ratio with variable displacement for a vehicle.
Notice that the difference of our proposed mathematical model compared with others is that the contending nodes in our model is not always fixed 𝑎𝑎. Once a node gets the channel reservation, it will not contend for channel access again. In this thesis, we have shown a conductive method for computing the actual number of vehicles in contention within the reservation zone.
Finally, the evaluation results show that our analytical results almost match with the simulated results generated by Estinet 7.0 simulator, which means that our analytical model possesses enough accuracy for a set of parameters.
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References
[1] S. Tsugawa, “The current trends and issues on ITS in Japan: Safety, energy and environment”, Intelligent Radio for Future Personal Terminals (IMWS-IRFPT), pp. 1-2, Aug. 2011
[2] FarEasTone Telecommunication Co., Ltd., [Online]. Available: http://www.fetc.net.tw/.
[3] G-H Hsu; R-H Jan; C. Chen, “A novel non-payment vehicle searching method for multilane-free-flow electronic-toll-collection systems”, Advanced Communi-cation Technology (ICACT), pp. 904-909, 2012
[4] Y.L. Morgan, “Notes on DSRC & WAVE Standards Suite: Its Architecture, Design, and Characteristics”, IEEE Communications Surveys & Tutorials, Vol. 12, No. 4, pp. 504-518, 2010
[5] IEEE Standard for Wireless Access in Vehicular Environments (WAVE)--Multi-channel Operation, IEEE Std 1609.4-2010, Feb. 2011
[6] S. Eichler, ”Performance Evaluation of the IEEE 802.11p WAVE Communication Standard”, IEEE Vehicular Technology Conference, pp. 2199-2203, Fall 2007 [7] J. Alcaraz; J. Vales-Alonso; J. Garcia-Haro, “Control-based scheduling with QoS
support for vehicle to infrastructure communications”, IEEE Wireless Communications, Vol. 16, No. 6, pp. 32-39, Dec. 2009
[8] Y-W Lan; J-H Yeh; J-C Chen ; Z-T Chou., “Performance enhancement of IEEE 802.11e EDCA by contention adaption” IEEE Vehicular Technology Conference, pp. 2096-2100, Spring 2005
[9] M. Barradi; A.S. Hafid; J.R. Gallardo, “Establishing strict priorities in IEEE 802.11p WAVE vehicular networks”, IEEE Global Telecommunications Conference, pp 1-6, Dec. 2010
[10] M.I. Hassan; H.L. Vu; T. Sakurai; L.L.H. Andrew, “Effect of Retransmissions on the Performance of the IEEE 802.11 MAC Protocol for DSRC” IEEE Vehicular Technology, pp 22-34, Jan 2012
[11] J.W.Tantra; C-H Foh ; A.B. Mnaouer, “Throughput and delay analysis of the IEEE 802.11e EDCA saturation” IEEE International Conference on Communications, pp 3450-3454 Vol. 5,16-20 May 2005
[12] Z-H Xiao; Z-Q Guan; Z-H Zheng, “The Research and Development of the
Highway’s Electronic Toll Collection System”, Knowledge Discovery and Data
45
Mining (WKDD), pp. 359-362, Jan 2008
[13] A.S. Mustafa; M. Pitslava-Latinopoulou; G.A. Giannopoulos, “The multilane electronic toll collection system in Thessaloniki: Evaluation of its first 6 months of operation”, Vehicle Navigation and Information Systems Conference, pp. 699-703, Sep 1994
[14] W-Y Shieh ; T-H Wang ; Y-H Chou ; C-C Huang, “Design of the Radiation Pattern of Infrared Short-Range Communication Systems for Electronic-Toll-Collection Applications”, IEEE Intelligent Transportation Systems, pp 548-558, Sep 2008 [15] W-Y Shieh ; W-H Lee ; S-L Tung ; C-D Ho, “A novel architecture for
multilane-free-flow electronic-toll-collection systems in the millimeter-wave range”, IEEE Intelligent Transportation Systems, pp 294-301, Sep 2005
[16] J.D. Turner; R.M. Day, “Tolling applications using infra-red technology and the highest priority requirement: the enforcement system”, Electronic Techniques for Road Pricing and Tolling, IEE Colloquium on, pp. 1-6, Mar 1995
[17] R-H Jan, “A WAVE/DSRC-based Highway Electronic Toll Collection System”,
NSC project report, No. NSC 100－2221－E－009－71－MY2, Oct 2013 [18] Estinet Technology, [Online]. Available: http://www.estinet.com/.
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