Low Latency Scheduling Algorithms for Full-Duplex V2X Networks
Michail Palaiologos, Jian Luo, Richard A. Stirling-Gallacher, Giuseppe Caire
LLow Latency Scheduling Algorithms forFull-Duplex V2X Networks
Michail Palaiologos *† , Jian Luo * , Richard A. Stirling-Gallacher * and Giuseppe Caire † * Munich Research Center, Huawei Technologies Duesseldorf GmbH, 80992 Munich, GermanyEmail:{michail.palaiologos, jianluo, richard.sg}@huawei.com † Communications and Information Theory Group, Technische Universität Berlin, 10587 Berlin, GermanyEmail:[email protected]
Abstract —Vehicular communication systems have been anactive subject of research for many years and are importanttechnologies in the 5G and the post-5G era. One importantuse case is platooning which is seemingly the first step towardsfully autonomous driving systems. Furthermore, a key perfor-mance parameter in all vehicular communication systems is theend-to-end packet latency. Towards this goal, full-duplex (FD)transceivers can potentially be an efficient and practical solutiontowards reducing the delay in platooning networks. In thispaper, we study the delay performance of dynamic and TDMA-based scheduling algorithms and assess the effect of FD-enabledvehicles with imperfect self-interference cancellation (SIC). Bysimulations, we demonstrate the performance-complexity trade-off of these algorithms and show that a TDMA centralized schemewith low-complexity and overhead can achieve comparable per-formance with a fully-dynamic, centralized algorithm.
Index Terms —scheduling, latency, full-duplex, V2X
I. I
NTRODUCTION
Vehicular communications, most commonly refered to asvehicle-to-everything (V2X) communication systems, is oneof the most promising applications of fifth-generation (5G)systems that have the potential to dramatically increase theefficiency and safety of transportation. By exchanging valuableinformation, vehicles can interact with each other in a waythat the probability of collision can be reduced compared totodays transportation systems. One of the main applicationsof V2X communications is platooning. A platoon is a groupof vehicles where each vehicle is located behind another, sothat they all together form a chain of vehicles (Fig. 1).The exchange of control messages wirelessly betweenneighboring vehicles has to be at a high rate and with ultralow latency, so that the danger of platoon instability is mini-mized [1]. In order to achieve low end-to-end packet latency values, FD-enabled vehicles could be introduced as a potentialsolution. In particular, vehicles having distributed transceiversat different parts of the car body can easily realize full-duplextransmission, i.e. transmit and receive simultaneously at thesame frequency.It has already been demonstrated that FD can be leveraged inV2X scenarios towards increasing the sum-rate throughput ofthe network as well as reducing the latency [2]. However, themajority of the related literature is focused either on the outage End-to-end latency is the time that a packet spends in the network, startingfrom the time of arrival until the time of departure from the network
Fig. 1: Vehicular platoon networkprobability or the throughput performance of these networksby distributed resource allocation. In this paper, a centralizedresource allocation problem for a platoon network under thecoverage of a base-station (BS) is studied. We focus solely onthe latency performance associated with the communicationbetween the platoon vehicles and not between the BS and theplatoon leader (PL). Furthermore, it is assumed that the servingBS assigns orthogonal resources to neighbouring platoons.There have been many works in the past that have studiedcentralized scheduling policies and proposed different solu-tions [3], [4]. Recently, there have also been studies wheredifferent scheduling algorithms are implemented for relaynetworks, where line networks that are similar to platoonnetworks are examined [2], [5]. However, the assumption inmost of the existing literature is that the network nodes do nothave full-duplex (FD) capabilities.In this work, we study the effect of FD-enabled vehiclesin the latency performance of a platoon network under thepresence of imperfect self-interference cancellation (SIC). Fur-thermore, we propose two low-complexity and low-overheadTDMA-based scheduling schemes that allocate resources perframe (frame-based scheduling) and compare their perfor-mance with a slot-based scheduling algorithm as a benchmark.The remainder of the paper is organized as follows. Sec-tion II describes the system model. In Section III differentscheduling algorithms are presented where the effect of FD isalso taken into account. Section IV deals with the performanceevaluation of the scheduling algorithms and, finally, Section Vcontains concluding remarks and suggestions for future work.II. S
YSTEM M ODEL
Fig. 2 shows a directed graph representation G = { N , L } ,where N and L represent the set of vertices and edges ofthe graph, respectively. Let 𝑁 = | N | and 𝐿 = | L | be thenumber of vertices (nodes) and edges (links) in the networkrespectively (we use | · | to represent the cardinality of a set), a r X i v : . [ c s . I T ] J a n ig. 2: Platoon network graph modelwhile variables 𝑖 and 𝑙 denote the elements of sets N and L . N 𝐻 𝐷 and N 𝐹 𝐷 represent the set of half-duplex (HD)and FD vehicles, respectively. We allow arbitrary number andpositions of HD and FD nodes. 𝑁 𝑟 represents the number ofplatoon members (PMs), i.e. 𝑁 𝑟 = 𝑁 − . The terms node andvehicle are used interchangeably in this paper.Typically, a PM has to exchange information with the PLand with its preceding vehicle. Towards this, the underlyingassumption is that several flows are present in this network,where each flow is associated with a distinct transmitter -receiver pair, as illustrated in Fig. 3. The existence of flowsbetween the PL and the platoon tail vehicle in this flow modelallows us to evaluate the largest possible end-to-end latencyon a platoon network. Let F represent the set of existing flowsand 𝑆 ( 𝑓 ) the source node of flow 𝑓 , where 𝑓 ∈ [ 𝐹 ] and | F | = 𝐹 . Half of these flows are related to the transmission ofpackets from the PL to all PMs. Due to the distinct directionof the information flow of these flows we will refer to themas the "right-hand" flows. The other half of the flows will berefered to as the "left-hand" flows. The assumption is that avehicle can communicate directly only with its neighbouring vehicles, i.e. the ones that are only one-hop away (Fig. 2) dueto the low transmission power and the blocking effect of thevehicles at the selected frequency.It is assumed throughout that time is slotted. The capacity ofeach link 𝑙 at time slot 𝑡 is denoted as 𝐶 𝑙 ( 𝑡 ) . The transmissionrate of flow 𝑓 over link 𝑙 at time slot 𝑡 is given as 𝜇 𝑓𝑙 ( 𝑡 ) . Ateach time slot, packets from only one flow can be transmittedthrough an activated link. Due to the underlying flow model,routing constraints should be introduced, so that not all flowsare allowed to use all links. If the set of links that flow 𝑓 is allowed to use is denoted as L 𝑓 , then for all "right-hand"flows, i.e. flows 𝑓 ∈ [ 𝐹 ] we have that L 𝑓 = { 𝑙 : 𝑙 ≤ 𝑓 } .For the "left-hand" flows, i.e. 𝑓 ∈ [ 𝐹 + 𝐹 ] the set of linksthey are allowed to use is given by L 𝑓 = { 𝑙 : 𝐿 + ≤ 𝑙 ≤ 𝑓 } .Hence, 𝜇 𝑓𝑙 ( 𝑡 ) = ∀ 𝑡 , if 𝑙 ∉ L 𝑓 .III. S CHEDULING S CHEMES
A. TDMA Scheduling - Flow-based (FB)
Usually the goal in most of the publications related toTDMA scheduling is to obtain the minimum possible numberof slots (per frame), as in [3]. A TDMA scheduling approachwith the minimum frame length for the underlying platoonnetwork activates one link per frame under the assumption of one-hop interference . However, as it is illustrated in Fig. 3,links have to support a varying number of flows, dependingon their position in the network. Therefore there is a varyinglevel of (flow) "congestion" at each link. In order to model thiseffect, let S 𝑡 represent the set of links that are co-scheduled Fig. 3: Flow model - Numbers in red indicate the flow indexFig. 4: Bidirectional linksfor transmission in slot 𝑡 and 𝑇 represent the frame length innumber of slots. Then, the number of slots that each link 𝑙 isscheduled per frame is given as 𝑜 𝑙 = 𝑇 ∑︁ 𝑡 = 𝐼 { 𝑙 ∈ S 𝑡 } (1)where 𝐼 {·} is the indicator function (which returns 1 if theargument inside its brackets is true, otherwise it returns 0). Inorder to model the congestion in each link, we use variable 𝑑 𝑙 which is equal to the number of flows that have link 𝑙 intheir routing path and is given as 𝑑 𝑙 = 𝐹 ∑︁ 𝑓 = 𝐼 { 𝑙 ∈ L 𝑓 } (2)In order to take the traffic pattern into account, the numberof slots per link 𝑜 𝑙 needs to be proportional to the congestionof this link 𝑑 𝑙 . In the case of a platoon network, where thenumber of flows 𝐹 is small, the number of slots per link canbe exactly equal to the congestion level of this link, so that 𝑜 𝑙 = 𝑑 𝑙 . In this way, the slot allocation of each directional link 𝑙 ∈ L can be derived very simply from Fig. 3. Particularly,an edge coloring technique similar to the one in [3] can beused towards assigning a specific number of colors (slots) toeach link. In the case of our network, the topology in Fig.2 is a bipartite graph. It was proven in [6] that the minimumnumber of colors required to color all edges of a bipartite graphis equal to Δ , where Δ is the maximum degree of the graph.Thus, a per-link color allocation can be easily implemented atthe beginning of each frame, where the number of flows thatare incident to each node dictate the degree of this node and,hence, the exact edge color allocation.Instead of assigning a set of colors to each directional link 𝑙 , we could assign the same set of colors to each pair ofdirectional links that connect two neighbouring nodes. Conse-quently, the color assignment specifies only the bidirectionallink that needs to be activated in each slot. In Fig 4, 𝑙 𝑏 is theindex of bidirectional links of the platoon network and let L 𝑏 represent the set that contains all these links. This modificationallows an extra degree of freedom on the flow scheduling , sincethe flow that is activated in every slot can be decided after theig. 5: Frame structure - Bidirectional links activationtwo nodes that are the endpoints of the activated bidirectionallink exchange information on the sizes of their queue backlogs.Given the bidirectional-links network model in Fig. 4 andthe traffic pattern that is illustrated in Fig. 3, the number ofcolors per bidirectional link is given in a vector format as 𝑜 𝑙 𝑏 = (cid:2) 𝑜 𝑜 𝑜 𝑜 (cid:3) = (cid:2) (cid:3) (3)where the 𝑙 𝑏 - th element of this vector is the number of colorsallocated to bidirectional link 𝑙 𝑏 and is given by 𝑜 𝑙 𝑏 = ( 𝑁 𝑟 + ) − ( 𝑙 𝑏 − ) (4)Therefore, due to [6] and under the one-hop interferencemodel, the total number of colors (slots) required to supportthis color allocation is equal to Δ = max ≤ 𝑙 𝑏 ≤| L 𝑏 |− { 𝑜 𝑙 𝑏 + 𝑜 𝑙 𝑏 + } = + = (5)So, according to this slot allocation, the frame consists of 𝑇 = slots and is demonstrated in Fig. 5, where the bidirectionallinks activated in each slot are also demonstrated. B. Back-pressure
In the previous algorithm, although link congestion is takeninto account, there is no consideration for the backlog sizesof the queues. In a V2V platoon environment, where vehiclesare expected to transmit in bursts due to random changes ofthe surrounding environment, an efficient scheduling algorithmought to take into account the size of the backlogs. In order toincorporate the queue backlog information in the schedulingprocess, we implemented the back-pressure (BP) algorithm[4]. BP can be modeled as a binary integer programmingproblem, where a binary vector is introduced to capture thelink activations on a slot basis. In particular, this binaryscheduler vector
ΛΛΛ ( 𝑡 ) ∈ R 𝐿 is updated every slot as thesolution of the following optimization problem ΛΛΛ ( 𝑡 ) = arg max Λ 𝑙 ( 𝑁 + ) ∑︁ 𝑙 = 𝑊 𝑙 ( 𝑡 ) · 𝜇 𝑙 ( 𝑡 ) · Λ 𝑙 ( 𝑡 ) (6)Link 𝑙 is activated in slot 𝑡 only if the solution of theoptimization problem returns Λ 𝑙 ( 𝑡 ) = . 𝑊 𝑙 represents thequeue differential backlog.As flows have a different number of hops in their path, theirlatency performance will not be the same when their inputrates are equal. In order to deal with these fairness issues, thecomputation of the queue differential backlogs 𝑄 of the flowsmay depend on their hop count. To this extent, regarding thequeue backlog of each flow, instead of being raised to thepower of 1 for all flows, this exponent can vary depending on the number of hops in each flow [7]. If we use 𝛾 𝑓 to representthe exponent of flow 𝑓 , then 𝑊 𝑙 ( 𝑡 ) = max 𝑓 {( 𝑄 𝑓𝑖 − ) 𝛾 𝑓 − ( 𝑄 𝑓𝑖 ) 𝛾 𝑓 , } (7a) 𝑊 𝑙 ( 𝑡 ) = max 𝑓 {( 𝑄 𝑓𝑖 ) 𝛾 𝑓 − ( 𝑄 𝑓𝑖 − ) 𝛾 𝑓 , } (7b)where 𝑖 ∈ [ 𝑁 + ] and 𝑙 ∈ [ 𝐿 ] , 𝑓 ∈ [ 𝐹 ] for"right-hand" flows ((7a)) and 𝑙 ∈ [ 𝐿 + 𝐿 ] , 𝑓 ∈ [ 𝐹 + 𝐹 ] for "left-hand" flows ((7b)). In these two expressions, link 𝑙 isincident to nodes 𝑖 and 𝑖 − . Finally, the destination node ofa flow does not keep an internal queue dedicated to this flow.In order to resolve the conflicts of the network, a fewconstraint inequalities need to be added to the optimizationproblem of (6). These constraints, which can be expressedvia the binary scheduler vector Λ , basically capture the edgecoloring procedure on the topology graph. 𝜇 𝑙 ( 𝑡 ) = min { 𝑄 𝑓𝑖 ( 𝑡 ) , 𝐶 𝑙 ( 𝑡 )} , ∀ 𝑖 ∈ N , ∀ 𝑓 ∈ [ 𝐹 ] (8a) Λ 𝑙 ( 𝑡 ) ∈ { , } , ∀ 𝑙 ∈ L (8b) ∑︁ 𝑙 ∈{ 𝑖,𝑖 + ,𝑖 + 𝑁 𝑟 + ,𝑖 + 𝑁 𝑟 + } Λ 𝑙 ( 𝑡 ) ≤ , ∀ 𝑖 ∈ N 𝐻 𝐷 ∩ [ 𝑁 𝑟 ] , ∀ 𝑙 ∈ L (8c) ∑︁ 𝑙 ∈{ ,𝑁 𝑟 + } Λ 𝑙 ( 𝑡 ) ≤ , if 𝑖 = ∈ N 𝐻 𝐷 (8d) ∑︁ 𝑙 ∈{ 𝑁 𝑟 + , 𝑁 𝑟 + } Λ 𝑙 ( 𝑡 ) ≤ , if 𝑖 = ( 𝑁 𝑟 + ) ∈ N 𝐻 𝐷 (8e) ∑︁ 𝑙 ∈{ 𝑖 + ,𝑖 + 𝑁 𝑟 + } Λ 𝑙 ( 𝑡 ) ≤ , ∀ 𝑖 ∈ [ 𝑁 ] (8f) ∑︁ 𝑙 ∈{ 𝑖,𝑖 + 𝑁 𝑟 + } Λ 𝑙 ( 𝑡 ) ≤ , ∀ 𝑖 ∈ [ 𝑁 ] (8g) 𝜇 𝑓𝑙 ( 𝑡 ) = ∀ 𝑡, if 𝑙 ∉ L 𝑓 (8h)In particular, constraints (8c) - (8e) are related to the HDconstraint, while constraints (8f) and (8g) are necessary inorder to assure that no node is allowed to transmit (receive)to (from) more than one other nodes at any given time slot.Finally, (8a), (8b) and (8h) are due to the system model. C. TDMA Scheduling - Queue-based (QB)
In practise, it is rather difficult to perform an adaptivealgorithm such as BP. Additionally, the signalling overhead ofan adaptive algorithm such as BP is very large, as informationneed to be exchanged between the vehicles and the BS atevery slot. Note that the main advantage of BP is that it takesinto consideration variations in queue backlogs and channelconditions at every slot. But, in a platoon environment, whereall links are LOS, the variations of the link capacities areusually small from one slot to the next. Thus, one reasonableassumption could be that link capacities remain the sameduring each frame. In order to combine the advantage of thelow overhead of TDMA schemes and the dynamic behaviorof an algorithm such as BP, we introduce a TDMA schedulingscheme that utilizes the information of queue backlogs at thebeginning of each frame before the slot allocation.ore formally, the link that maximizes an objective function(similar with BP) can be obtained for each flow 𝑓 as arg max 𝑙 { 𝑊 𝑓𝑙 ( 𝑡 𝑆 ) 𝜇 𝑙 ( 𝑡 𝑆 ) } (9)where 𝑡 𝑆 is the begining of the 𝑆 -th time frame. This approachindicates that at least one slot is allocated per flow 𝑓 forthe upcoming frame, given that there is at least one non-empty queue in this flow’s path. Then, over these 𝐹 values,the number of times that each link 𝑙 is the solution of thisoptimization problem is the "demand" of each link, which isactually the number of colors that need to be assigned to thislink. In order to calculate the demand of each bidirectionallink 𝑙 𝑏 ∈ L 𝑏 , simply add the demand of each directional link 𝑙 𝑏 with the demand of its "mirror" link 𝑙 𝑏 + 𝑁 𝑟 + . As aflow can have at maximum 𝐿 / links in its path (Fig. 3), thecomputational complexity of this step, which has to run at thebeginning of each frame only, is of the order of 𝑂 ( 𝐹 · 𝐿 ) . So,each node has a specific degree and the edge coloring can becarried out based on the demand of the bidirectional links.If the size of the frame is equal to 𝑇 slots, then the actualnumber of allocated slots is equal to 𝑇 𝑎𝑐𝑡 = min { 𝑇, Δ } , where Δ is the maximum degree of the graph, after the demand ofeach link has been determined. If Δ > 𝑇 , the demand of thebidirectional links needs to be reduced (starting from the linkswith the highest demand) until Δ = 𝑇 . If Δ < 𝑇 , the demandof the bidirectional links needs to be increased in, e.g., asequential manner, until Δ = 𝑇 . Finally, in (9) we also dividethe differential backlogs with the link capacity of each linkat the beginning of each frame. Since the assumption is thatlink capacities remain the same during each frame, this actionaffects slightly the results. The rationale behind it is that weassign extra priority to links with bad channel conditions. D. Full-Duplex Consideration
The case of heterogeneous platoon networks, where bothHD and FD nodes exist, requires special attention, since theconflict-free independent sets that graph’s edges belong to aredifferent when the FD nodes positions vary. For example, ifnode 𝑖 = is FD, then bidirectional links 𝑙 𝑏 = and 𝑙 𝑏 = can belong to the same independent set and basically form asingle "FD link". As a result, these two links can be treatedas one and can be assigned the same colors. So, if the numberand/or the position of FD nodes in the network changes, thecolor assignment of the bidirectional links is also changed.Note that the TDMA schemes return results for the ac-tivation of bidirectional links only and do not include anyinformation for the scheduling of flows. At each slot, foreach activated bidirectional link, one of the contending flowsover this link can be scheduled based on its queue differentialbacklog. If an "FD" bidirectional link is activated, there are atleast three nodes involved in the scheduling decision, so thereare more queues involved. In order to satisfy this, the firststep would be to calculate the max differential backlog overall directional links. Then, instead of searching and comparingbetween the max differential backlog of the two "types" of TABLE I: Simulation Parameters Parameter Value
Platoon size, N 5Number of flows, F 8Vehicle length and separation 5 m and 33.33 mCarrier frequency and bandwidth 30 GHz and 200 MHzTransmit power 23 dBmShadowing: mean, standard deviation 0 mean, 8 dB standard deviationNumber of slots and slot duration 40000 slots with 125 𝜇𝑠 /slotSelf-interference cancellation level 10 dB, 40 dBRate of Poisson arrivals, 𝜆 Fig. 6: (a) Mean and (b) max latency for 2 different levels ofSIC and an input rate of 0.04 packets/slotflows (as in the HD case), first we need to sum the maxdifferential backlogs of all flows that belong to the same"type" and then compare these added differential backlogs inorder to determine if a "right-hand" or "left-hand" flow willbe scheduled. Hence, a more fair flow scheduling is achieved.IV. N
UMERICAL R ESULTS
In this section, the performance of the previously describedscheduling algorithms for a platoon network with both HDand FD vehicles is evaluated. The parameters that were usedfor the simulations are outlined in Table I. An example sizeplatoon of 5 vehicles is evaluated and a line-of-sight channelmodel with associated path loss is assumed between adjacentplatoon nodes. The frame length is fixed for fixed HD andFD locations and is given by Fig. 5. In Fig. 6, the meannd max end-to-end packet latency is demonstrated under thethree scheduling algorithms, for varying number and positionof FD nodes when the arrival rate is equal to . packets/slot.The actual values of the input rates are derived from the flowcontrol process in [8], so that network stability is guaranteed.The chosen arrival rates for all flows are assumed to be equaland strictly inside the capacity region. The arriving packetsizes are uniformly distributed in the range of [
40 : 32 : 136 ] kbits. Two distinct SIC levels are also studied.In Fig. 6, as expected, in the case where the SIC is atan acceptable level (i.e. equal to 40 dB) an algorithm suchas BP that takes scheduling decisions at every slot performsmuch better compared to the two TDMA scheduling schemes.However, the average delay of all these schemes remains lowfor a SIC of 40 dB, as it is not more than 1.53 msec. Possiblymore valuable for practical purposes is the information relatedto maximum latency in Fig. 6b. It can be seen that a TDMAsheduling scheme that takes queue backlogs into account (QBscheme) delivers latency performance close to the BP schemeand significantly better than the FB algorithm when thereare no FD vehicles or a single FD vehicle, while achievingthat with much lower complexity and signalling overheadcompared to BP.Note that although the QB algorithm outperforms the FBalgorithm, when a single FD vehicle is in position 1, itslatency performance becomes worse when adding more FDvehicles. The reason is that this algorithm does not take intoaccount the varying congestion levels in the links and thereforeover-schedules links with low congestion levels. In contrast,a simple scheme such as the FB algorithm, that takes intoaccount the congestion can only really take advantage of theexistence of FD nodes.It can also be seen from these two figures that, as shown in[2], relatively low levels of SIC are sufficient for satisfactorylatency performance in V2V networks, since, in practise,SIC of around 40 dB could be a reasonable assumption.Nonetheless, there is a limit on the acceptable levels of SIC. Infact, we can see that, even for a dynamic algorithm like BP, itsperformance deteriorates for SIC = 10 dB when FD vehiclesare added. On the other hand, FB scheme is very robust, sinceits latency performance is improved when adding FD vehicles,even when the SIC is equal to 10 dB.Regarding the weights 𝛾 𝑓 that have been used in thedifferential backlogs expressions in (7a) and (7b), they varydepending on the number of hops in each flow. It is not easy tocome up with a deterministic solution for these weights dueto the increased coupling between the flows [7]. Given thehop-count, a reasonable choice for flows with one hop in theirpath would be 𝛾 𝑓 = . , while for flows with 2 and 3 hops,a value of 𝛾 𝑓 = . appears to produce better results. Finally,for flows with the max possible number of hops, the exponentused in their differential backlog expressions is equal to 1.In Fig. 7 there is a single FD vehicle in the platoon indifferent positions. In this figure, the importance of the posi-tion of the FD-enabled vehicles is illustrated, which dependson the traffic pattern. Particularly, the best option is to have Fig. 7: Mean latency for input rate of 0.04 packets/slot and asingle FD vehicle - SIC = 40 dBa single FD vehicle in position 1, since this vehicle relayspackets from all flows. One FD vehicle in position 3 or 2cannot provide significant advantage, as the vehicle in position1 is HD and, hence, it will always "slow down" its receivingpackets. Finally, when there is a single FD vehicle, QB schemealways outperforms the FB scheme and it also keeps a smallperformance gap from BP for most FD nodes positions.V. C ONCLUSIONS
In this paper, we have proposed extensions to three schedul-ing algorithms to cover the case of having FD vehicles in aplatoon network where the latency performance was presented.It was demonstrated that the maximum latency performanceof a TDMA scheme such as QB, that takes the informationof the queue backlogs into account, delivers almost the sameresults with BP in the HD case, but with significantly reducedsignalling overhead and complexity. We have verified that thepractical SIC level of 40 dB already allows low packet delay.As a future step, distributed scheduling algorithms will beconsidered for more complex vehicular networks.R
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