Fiems, Dieter

Vinel, Alexey

English

Ghent University Academic Bibliography

1Connectivity Times in Vehicular NetworksDieter Fiems and Alexey VinelAbstract—We propose an analytical model that accuratelycaptures the service advertisement and access mechanisms inIEEE 1609.4/IEEE 802.11p multi-channel vehicular networkswhere road-side units announce non-safety services to passingvehicles on a dedicated channel. For a drive-thru scenario, wecalculate various performance measures including the servicediscovery probability, the mean time till discovery and thechannel utilization.I. INTRODUCTIONBy leveraging remote connectivity supplied by Road-SideUnits (RSUs), vehicles can exchange environmental/trafficdata gathered by on-board and on-the-road sensors, re-trieve/update maps, or access traditional Internet services likeweb browsing and cloud access via vehicle-to-roadside (V2R)communications. In a drive-thru scenario [1], where movingvehicles spend at most a couple of minutes in the coverage areaof a RSU, V2R communication links are expected to be short-lived and intermittent, due to the mobility of the vehicles andthe high cost to deploy a ubiquitous roadside infrastructure.Such scenarios pose specific performance issues which haveattracted attention in the research community. Spatially coor-dinated channel access in a drive-thru scenario is presentedin [2]. Assuming that the RSU coverage area can be dividedin zones by achievable throughput, the authors optimize theassignment of zones to vehicles such that the overall sys-tem throughput is maximized. In addition, [3] investigates astochastic model to assess the mean packet service time, thequeue length and the throughput per vehicle in a drive-thruscenario.The modeling frameworks above make abstraction of theimplementation of the service discovery process, which iscrucial to make the best of V2R connectivity opportunities.In particular, the time between service announcements is thekey to quick service discovery. If this time is small, the servicediscovery time will be small, while the probability to detectthe service will be high. There is however a trade-off. Asthe RSU has to switch its transceiver from the channel whereservices are provided to the advertisement channel, connectedvehicles experience disruption during advertisements, yieldinga considerably reduction of the channel utilization.The service discovery protocol is defined in the IEEE 1609.4vehicular communications standard, but an adequate analyticalmodel for its performance evaluation is missing in the litera-ture. While the mean service discovery time and the serviceD. Fiems is with Ghent University, Dep. TELIN, St-Pietersnieuwstraat 41,9000 Gent, BelgiumA. Vinel is with Halmstad University, School of ITE, Kristian IV:s va¨g 3,SE-30118 Halmstad, SwedenThis work has been partly supported by EU COST Action CA15127RECODIS ”Resilient communication services protecting end-user applicationsfrom disaster-based failures”, Knowledge Foundation (KKS) in Sweden andELLIIT Strategic Research Network.channel utilization are derived in [4], this work assumes thatthe error rate is constant and does not depend on the position ofthe vehicle in the RSU coverage area. This is however contraryto the nature of a drive-thru scenario where vehicles experiencechanging error rates while traversing the coverage area of theRSU [2]; also see [5] for supporting field measurements. Inthis letter, we introduce an analytical model for studying thediscovery process which accounts for the changing error rates.Our numerical results reveal that this additional modellingdetail is needed for an accurate performance evaluation.II. ANALYTICAL FRAMEWORKWe consider a vehicle moving at a constant speed v alonga path, experiencing location dependent bit error probabilities(or rates – BER). Without loss of generality, we assume thatat time t = 0 the vehicle starts in position z = 0, and that thevehicle is outside the range of the RSU at position z = Z.The RSU regularly announces the available drive-thru ser-vices, by transmitting a broadcast Service AnnouncementMessage (SAM) indicating services and the channel on whichthey can be accessed. Once an announcement is received,an interested vehicle tunes its transceiver to the announcedchannel and accesses the offered service(s) while it remainsin the coverage area of the RSU. The IEEE 1609.4 RSUperiodically switches the transceiver between the advertisingchannel (e.g. Service Channel 1 – SCH 1) and the advertisedchannel (e.g. SCH 2-4) with period τ , referred to as the SAMperiod, as depicted in Figure 1.During each SAM period, the RSU cannot provide serviceto the vehicles while tuned into the advertising channel. Thisservice-disruption time has a random duration X. The serviceperiod then corresponds to the remainder of the SAM periodand is denoted by Y = τ −X. Note that X is random as theIEEE 802.11p backoff delay is random. Apart from the backoffdelay B, the service disruption period includes the times Tswneeded to switch to and from the advertising channel and thetime to transmit the SAM message t0, that is,X = B+ 2Tsw + t0 . (1)The time to transmit the SAM message on the advertisingchannel includes mandatory idle time. We have, t0 = Th +L/R+ SIFS + AIFSN · σ, where Th denotes the SAM headerduration, L denotes the SAM payload size, R denotes theSAM data rate, SIFS denotes the Short Inter-Frame Space, σdenotes aSlotTime and AIFSN denotes the Arbitration Inter-Frame Space Number specified in IEEE 802.11p.Correct reception of the SAM message depends on the BER,which is assumed to depend on both location and speed of thevehicle. Let b(z, v) be the BER when the vehicle is in positionz with speed v. For ease of presentation, we further assume2that b(z, v) = 1 for z > Z. For further reference, let I be theindicator that the SAM message is received with errors.Given the assumptions above, we focus on computing thediscovery probability and the mean discovery delay, condi-tional on service discovery. The discovery probability is theprobability that the service is discovered while the vehicletraverses the coverage area, while the discovery delay is thetime between the moment the vehicle enters the coverage areaof the RSU, and the moment the SAM message is successfullyreceived. We also calculate the utilization ρ. This is the fractionof the time which is available for accessing services.A. Service disruption time and utilizationWe first focus on the mean backoff delay E[B]. As thebackoff delay does not depend on the error model, neither loca-tion nor velocity influences the backoff delay. Approximatingthe backoff procedure with a contention window of W slotsby a sequence of independent transmissions with probabilities2/(W + 1), we find the collision probability,p0 = 1−(1− 2 (W + 1)−1)N ,where N denotes the number of contending nodes. With aslight abuse of notation, let Bw be the backoff delay forwindow size w, and for collision probability p0 as given above.We find,E[Bw] =(1− w−1) (p¯0σ + p0t0 + E[Bw−1]) ,with p¯0 = 1−p0. This recursion follows from the observationthat the backoff delay is zero with probability 1/w while withprobability (1 − 1/w) it is equal to the sum of the backoffdelay with window size w − 1 and either the time slot σ0(if no other user sends) or the SAM transmission time t0 (ifanother user sends). As transmission starts when the windowsize is 1, we have E[B1] = 0. We can then explicitly solvethe recursion, yielding,E[B].= E[BW ] =12(W − 1)(p¯0σ + p0t0) .By equation (1), we further find the following expression forthe mean service disruption time,E[X] =12(W − 1)(p¯0σ + p0t0) + 2Tsw + t0 .Moreover, given E[X], we can also calculate the fraction oftime the service is available, say the utilization ρ. As theservice is periodically disrupted with period τ , we haveρ = (τ − E[X]) τ−1 . (2)B. SAM failure probabilityWe now focus on the SAM failure probability. Recall that Iis the indicator that the SAM message is received with errors.We therefore have p(z, v) = Ez,v[I], Ez,v being the expectationoperator given that the vehicle is in position z with velocityv at the start of the SAM period.The SAM message is correctly received when there is nocollision, and when all bits of the payload are correctly re-ceived. We hereby neglect the probability that the header of theTsw TswX YτSCH 1SCH 2–4σ t0 t0BdataSAMinterferenceFig. 1. Service Announcement Message (SAM) period.SAM message is not received correctly, as this header benefitsfrom additional protection. The SAM failure probability for avehicle with velocity v at position z when the transmission ofthe SAM message starts is,pt(z, v) = 1− p¯0L−1∏k=0(1− b(z + Th v + k v/R, v)) .The SAM failure probability depends on the backoff delay.Indeed, the location changes during the backoff delay. There-fore, let pb(z, v, w) be the failure probability when the vehicleis in position z with speed v at the start of the backoff periodwith window size w. Analogous to the the mean backoff delaycalculations, we find a recursion for pb(z, v, w),pb(z, v, w) = w−1pt(z, v) +(1− w−1)×(p¯0pb(z + vσ, v, w − 1) + p0pb(z + vt0, v, w − 1)).As the backoff delay is zero for w = 1, we have, pb(z, v, 1) =pt(z, v). As such, the recursion above allows for numericallydetermining pb(z, v, w) for any z, v and w.Accounting for the switching time Tsw, and suppressing thedependency on W in the notation, we finally find the failureprobability of the SAM message when the car is in positionz with velocity v at the start of the SAM period,p(z, v) = Ez,v[I] = pb(z + Tswv, v,W ) . (3)C. Conditional service disruption timeWe now consider the expectation Ez,v[XI] which relates tothe mean service disruption time, conditioned on the transmis-sion failure of the SAM message as follows,Ez,v[X|SAM not received] = Ez,v[XI]p(z, v).Define x(z, v) .= Ez,v[XI]. In view of equation (1) we have,x(z, v) = Ez,v[I](2Tsw + t0) + Ez,v[BI]= p(z, v)(2Tsw + t0) + Ez,v[BI] .Let B(z, v, w) be the mean of BI given that the vehicle isposition z with speed v at the start of the backoff period withwindow size w. Accounting for the switching time Tsw andthe window size W , we have,Ez,v[BI] = B(z + vTsw, v,W ) .3It now remains to calculate B(z, v, w). To this end, weproceed as for the mean backoff period and obtain a recursionby conditioning on the possible scenarios in the first time slot,B(z, v, w) =(1− w−1)×(p¯0(σpb(z + σv, v, w − 1) +B(z + σv, v, w − 1))+ p0(t0pb(z + t0v, v, w − 1) +B(z + t0v, v, w − 1))).Again, the recursion above allows for numerically determiningB(z, v, w) for any z, v and w.D. Discovery probabilityWe assume that the vehicle enters the coverage area at time0, and that the first (complete) SAM period starts at timeU,Ubeing uniformly distributed between 0 and τ . In other words,the vehicle enters the area at a random instant during the SAMperiod. Without loss of generality, we do not account for thepartial SAM period on entry. We can make the probability ofdiscovery during such a period arbitrarily small by extendingthe area, and assigning large BERs at large distances.Let pd be the probability the service is discovered whilethe vehicle is in range. To simplify the calculations, we firstcalculate the probability qk(z, v) that the service is not discov-ered during the first k (complete) SAM periods, assuming thatthe vehicle is in position z when the first SAM period starts.Accounting for the SAM failure probabilities, the constantspeed and the fixed length of the SAM periods, we have,qk(z, v) =k−1∏`=0p(z + `τv, v) ,where p is defined in (3).The vehicle leaves the range at location Z (or at time (Z−z)/v) if it starts from position z at time 0. Hence, b(Z −z)/v/τc SAM periods start while the vehicle is in range. Now,the vehicle is in position vU when the first SAM period starts,such that the probability that the SAM message is received is,pd = 1−∫ τ01τqK(u)(vu, v)du ,≈ 1−M−1∑m=01MqK(τm/M)(vτm/M, v) , (4)with K(u) = b(Z/v − u)/τc. In the second expression,the uniform distribution of U is approximated by a discreteuniform distribution with M points.E. Mean time till discoveryThe time till discovery now includes (i) the time U till thestart of the first SAM period, (ii) the length of a SAM periodduring each SAM period where the SAM was not receivedand (iii) the service disruption time of the SAM period wherethe SAM message is received.Let D denote the discovery time, where we define D tobe equal to the residence time Z/v of the vehicle in thecoverage area of the RSU if service is not discovered. LetParameter ValueSlot time σ 13 µsContention window size (W ) 15Interfering packets (N ) 5 – 20Short Inter-Frame Space (SIFS) 32 µsArbitration Inter-Frame Space Number (AIFSN) 6SAM payload size (L) 300 bytesSAM header duration (Th) 40 µsSAM data rate (R) 6 MbpsSAM transmission time (x0) 550 µsSAM period (τ ) 100 ms – 1000 msSpeed (v) 90 km/hDistance (Z) 1200 mChannel switching delay (Tsw) 4 msTABLE IOVERVIEW OF THE DIFFERENT PARAMETERS200 400 600 800 10000.880.900.920.940.960.98Location-dependent/constant BERN=5N=10N=15N=20Fig. 2. Channel utilization ρ vs. the SAM period τ for different numbers ofvehicles N as indicated.Ik be the indicator function that the SAM message was notreceived during the kth SAM period and let Xk be the servicedisruption time of the kth SAM period. We have,D = U+K−1∑k=0k−1∏`=0I`(1− Ik)(kτ +Xk) +K−1∏`=0I`Z/v , (5)with K = b(Z/v − U)/τc. Note that given U, the randomvariables Ik are conditionally independent,E[D|U] = U+K−1∑k=0qk(Uv, v)(kτ(1− p((U+ kτ)v, v))+ E[X]− x((U+ kτ)v, v))+ qK(vU, v)Z/v , (6)such that,E[D] =∫ τ0[u+ qK(u)(vu, v)Z/v +K(u)−1∑k=0qk(uv, v)×(kτ p¯((u+ kτ)v, v) + E[X]− x((u+ kτ)v, v))]duτ, (7)with p¯(t, v) = 1 − p(t, v) and K(u) = b(Z/v − u)/τc asbefore. Again approximating the uniform distribution of U bya discrete uniform distribution, we finally have,E[D] ≈ τ2+1MM−1∑m=0[qKm(umv, v)Zv+Km−1∑k=0qk(umv, v)×(kτ p¯((um + kτ)v, v) + E[X]− x((um + kτ)v, v))], (8)4with um = mτM and Km = K(um). In view of the definitionof D, we can also calculate the mean time till discovery,conditioned on the message being discovered. We have,E[D|discovered] = 1pd(E[D]− Z/v(1− pd)) ,where pd is the discovery probability, see (4).III. PERFORMANCE EVALUATIONWe now illustrate our approach by some numerical exam-ples. The values used correspond to the IEEE 802.11p/1609.4setup and are summarized in Table I. For the location-dependent BER, we translate the packet error probabilities of[5] to bit errors, that is, we setb(z, v) = 1− q(z)1/Lwith L the packet size in bits and with q(z) the locationdependent probability that the packet is correctly received, theRSU being in position 600 m (z is expressed in meters),q(z) =0.1 for z ∈ [0, 100) ∪ [1100, 1200)210− 25 |600−z|100 for z ∈ (100, 200] ∪ [1000, 1100)0.999 for z ∈ [200, 1000)0 otherwise.Figs. 2, 3 and 4 show the utilization ρ, the inverse ofthe discovery probability 1 − pd and the mean time tilldiscovery (in ms), conditional on the service being discoveredvs. the SAM period τ (in ms). For all figures, we depict theperformance measures for various N when location-dependentBER is and is not taken into account. In the latter case, weuse the average BER in the interval [0, 1200). Clearly, whenthe SAM period τ increases, the utilization increases as lesstime is spent on discovery. As the channel utilization does notdepend on the error model, see (2), the curves with location-dependent and constant BERs coincide. Moreover, if there arefewer contending vehicles, the utilization improves, as lesstime is spent on resolving contention. Fig. 3 shows that anincrease of τ implies a decrease of the discovery probability.Indeed, for longer SAM periods there are fewer occasions toconnect while the vehicle is in range. Moreover, the service ismore easily discovered if there are fewer contending vehiclesas the chance for service discovery in a single SAM periodis higher. In addition, the effect of location-dependent BER isapparent, the model without constant BER underestimating pd.Finally, the conditional mean time till discovery, first increasesand then decreases again for increasing τ for the location-dependent BER model (for N ∈ {5, 10, 15}), while it only in-crease for the constant BER model. The increase is expected: ifτ is longer, the time between discovery opportunities increaseswhich leads to longer discovery times. However, if τ furtherincreases, the probability that one cannot connect increasesas well. As we only consider the conditional discovery timeand the discovery time is typically shorter conditioned ondiscovery, we find that the conditional mean discovery timedecreases for increasing τ . Finally, for N = 20 and thelocation-dependent BER model, the discovery probability in asingle SAM period is considerably lower, such that the lattereffect immediately dominates.200 400 600 800 100010 1510 1110 710 31p dLocation-dependent BER200 400 600 800 100010 1510 1110 710 31p dConstant BERN=5N=10N=15N=20Fig. 3. Discovery probability pd vs. the SAM period τ for different numbersof vehicles N as indicated, and for position dependent and constant BER.200 400 600 800 100075001000012500E[D|discovered]Location-dependent BER200 400 600 800 1000050001000015000E[D|discovered]Constant BERN=5N=10N=15N=20Fig. 4. Mean (conditional) discovery delay E[D|discovered] vs. the SAMperiod τ for different numbers of vehicles N as indicated, and for positiondependent and constant BER.IV. CONCLUSIONWe have proposed and analyzed a stochastic model forservice discovery in a drive-through scenario. Accounting forlocation-dependent bit error probabilities, our model over-comes a fundamental limitation of prior work [4]. Our nu-merical results show that neglecting the effect of location onthe transmission errors, may lead to substantial differences indiscovery probabilities and mean discovery delays.REFERENCES[1] M. Xing et al. Maximum-utility scheduling for multimedia transmissionin drive-thru Internet. IEEE Transactions on Vehicular Technology 65(4),pp.2649–2658, 2016.[2] H. Zhou et al. Spatial coordinated medium sharing: optimal accesscontrol management in drive-thru internet. IEEE Transactions onIntelligent Transportation Systems 16(5), pp. 2673–2686, 2015.[3] R.F. Atallah et al. Modeling and Performance Analysis of MediumAccess Control Schemes for Drive-Thru Internet Access ProvisioningSystems. IEEE Transactions on Intelligent Transportation Systems16(6), pp. 3238–3248, 2015.[4] C. Campolo et al. Service discovery and access in vehicle-to-roadsidemulti-channel VANETs. In Proc. of International Conference onCommunication Workshop, IEEE, pp. 2477–2482, 2015.[5] A. Bo¨hm et al. Adaptive cooperative awareness messaging for enhancedovertaking assistance on rural roads. In Proc. of the 4th InternationalSymposium on on Wireless Vehicular Communications. pp. 1–5, 2011.

Connectivity times in vehicular networks

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Connectivity times in vehicular networks

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