Impact of the Generation Interval on the Performance of Sidelink C-V2X Autonomous Mode

Cellular-vehicle-to-everything (C-V2X) is gaining an increasing interest among the technologies under consideration for future connected and automated vehicles, especially for sidelink LTE-V2X Mode 4 and sidelink 5G-V2X Mode 2, where nodes autonomously perform resource allocations and transmissions, without relying on any infrastructure. In these cases, the allocation process has been designed based on the assumption of periodic packet generation constrained to a few possible allocation periods. Nevertheless, even assuming that the awareness messages are continuously exchanged, the packet generation might not always be exactly periodical or might come with a periodicity not constrained to the expected values, as for example with the Cooperative Intelligent Transport Systems (C-ITS) standard defined by the European Telecommunications Standards Institute (ETSI). The non-ideal periodicity of packet generation, if not properly taken into account, can significantly impact the operation and performance of C-V2X when vehicles autonomously select their radio resources. This paper provides an analysis of how a misalignment between packet generation and resource allocation affects the system performance and provides insights into how to design the parameter settings to improve the performance. A case study is provided, focusing on LTE-V2X Mode 4 and the cooperative awareness message (CAM) generation in agreement with the the ETSI specifications. Results show that the performance generally improves if the smallest allocation interval is adopted and if the reservation is maintained even when no packets are ready for transmission. It is also shown how the parameter controlling the maximum latency in LTE-V2X, jointly with the misalignment between the allocation and generation intervals, can further affect the packet reception rate.


I. INTRODUCTION
The transport systems and the automotive industries are undergoing key technological transformations since an increasing number of connected and automated vehicles is populating our roads, providing enhanced safety and efficiency. In this landscape, vehicle-to-everything (V2X) connectivity, enabling vehicles to cooperate with one another, The associate editor coordinating the review of this manuscript and approving it for publication was Walid Al-Hussaibi .
with roadside infrastructures, with pedestrians and with the other road elements, will improve the awareness and the perception of the scenario.
Sidelink LTE-V2X and sidelink 5G-V2X are two access layer technologies developed under the umbrella of cellular-V2X (C-V2X) and standardized by the 3GPP as access layer replacement for IEEE 802.11p. These C-V2X access layers are investigated for application in ITS stacks and related protocols, such as ETSI ITS in Europe. LTE-V2X was included in Release 14 of 4G as an evolution of device-to-device (D2D) VOLUME 9, 2021 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ initially imagined for public safety applications in Release 12 [1]- [5]. 5G-V2X is instead still under definition in Release 17 (the last part of the standardization is expected in 2022), based on the new radio (NR) of 5G [6]- [11], aimed at providing new capabilities and stringent quality of service (QoS) requirements for a more secure and smarter operation [12]- [15]. In 4G and 5G, two transmission modes support direct V2X communications, both transmitting in the sidelink channel over the PC5 interface, but differing on how radio resources are allocated [16]- [19]. In the first one (Mode 3 in LTE-V2X and Mode 1 in 5G-V2X), the resource selection, allocation, and reservation is performed by the network and commanded via the Uu interface to the nodes, which must be within the coverage of the cellular network. In the other one (Mode 4 in LTE-V2X and Mode 2 in 5G-V2X), the resources are autonomously selected by the stations, based on some local sensing mechanism, therefore allowing the vehicles to communicate even in out-of-coverage conditions. Once selected, the resources are used periodically for a certain time, and then a new resource selection is performed, i.e. through a procedure called resource reselection. According to [20], the centralized perspective of Mode 3 provides, in principle, more information to the scheduler resulting into a performance improvement. However, it poses non-negligible challenges in several conditions, such as at the cell edge (where outage can occur), in multi-operator (handover) scenarios and when high vehicle density is addressed. Beside these, it must be highlighted that V2X safety applications should be ubiquitous and cannot depend on the availability of an infrastructure-based cellular coverage. Thus, the autonomous mode plays a key role.
In the sidelink LTE-V2X autonomous mode, vehicles independently select their radio resources through a distributed scheduling protocol, namely the sensing-based semi-persistent scheduling (SB-SPS). Such a protocol assumes a periodic nature of the exchanged physical layer messages, estimates the occupied resources in the last period of time, predicts the future use of resources and then performs a semi-persistent reservation of the identified resources for a given period. Even if extended with new features, the basic operations are expected to be maintained in 5G-V2X.
The rationale for assuming periodic messages in the design of the resource allocation mechanisms is that V2X Day 1 applications 1 are based on the exchange of messages, which are continuously sent by each vehicle in broadcast. Such messages, called cooperative awareness messages (CAMs) in Europe, defined by the ETSI, and basic safety messages (BSMs) in the US, defined by the Society of Automotive Engineers (SAE), contain updates about the state and movements of the vehicle. Indeed, these and most of the messages that are currently under definition, such as the ETSI collective perception messages (CPMs) and vulnerable road user awareness messages (VAMs), have a repetitive nature and are in some specific cases periodic.
However, as detailed in further sections, focusing on CAMs as a case study and in order to better cope with the trade-off between timeliness and channel load, they tend to have adaptive generation intervals and are thus in general not periodic [21]: on the one hand, an higher beacon generation frequency is desirable in case of high speed, when the vehicle information needs to be updated more often; on the other hand, a lower message generation frequency, reducing the channel occupation and the collision probability, is preferable in low speed scenarios. Additionally, even when the packet generation is periodic, this periodicity might not be the same as the SB-SPS algorithm periodicity; whereas the packet generation is in fact designed without particular limitations, the periodicity of resource allocation is instead constrained by the time structure of LTE-V2X and 5G-V2X, which is based on a subframe length of either 0.25 ms, 0.5 ms, or 1 ms (the last one in LTE and any of the three in 5G, depending on the NR subcarrier spacing). The mismatch between the packet generation frequency and the periodicity of resource allocation can lead to inefficient allocations and major packet losses. Therefore, the proper set of system parameters cannot always rely on the assumption of exact periodicity and must be able to cope with a possible misalignment.
In this paper, we investigate the effect of a mismatch between the packet generation frequency at upper layers of the ITS stack and the allocation periodicity at physical layer in sidelink C-V2X autonomous mode, with reference, as a case study, to sidelink LTE-V2X Mode 4 (simply referred as LTE-V2X in the rest of the paper) and to the speed-dependent triggering mechanisms of CAMs as specified by ETSI [22]. We show a system level analysis performed via simulations under various traffic densities and vehicle speeds.
The key contributions of the paper can be summarized as follows: • We clarify how the allocation period and generation frequency interrelate and influence sidelink C-V2X autonomous mode; • We derive a model to calculate the average number of reselections for a vehicle moving at a constant speed as a function of several parameters; • We provide system-level results to analyze the performance of sidelink LTE-V2X Mode 4 varying the generation frequency, vehicle speed, and vehicle densities; and • We identify general guidelines for the setting of those parameters and procedures which are not constrained by specifications and mostly affect the system performance. The remainder of the paper is organized as follows. Section II describes the related work and state-of-the-art. Section III introduces LTE-V2X Mode 4 and 5G-V2X Mode 2. Section IV deals with the European protocol stack, the specific case of the generation of CAM messages and the relationship between message generation and packet transmission in LTE-V2X. Section V presents a case study with system level results. Finally, Section VI gives our conclusions.

II. RELATED WORK AND PAPER SCOPE
The first version of LTE-V2X was completed within 3GPP Release 14 in 2017, followed by refinements in Release 15. 5G-V2X is instead addressed through Releases from 15 to 17: the main applications and requirements are identified in Release 15; the first set of specification is introduced in Release 16, mainly dealing with architecture and physical layer; finally, 5G-V2X will be completed, with details on the access procedures, in Release 17, which is still under discussion.
Since its first introduction, attention has been posed to address the performance of LTE-V2X in general [5], [20], [23] or in comparison with IEEE 802.11p/ITS-G5 [24], [25]. A large number of papers have also investigated some specific aspects. Just as few examples, the use of network coding is proposed in [26] (raptor Q coding) and [27] (index-coding), and the exploitation of exponentially weighted measurements of the received power rather than simple average is suggested in [28]. Efficient scheduling and resource allocation have been also widely addressed for LTE-V2X in last few years, especially with the objective to optimize the resource allocation, as in in [29]- [31], improve the channel occupancy, as in [32], or provide the expected QoS, as in [33].
The 5G-V2X technology is instead under definition and, as a consequence, still less investigated. In [8], a first description of the features under development in 5G-V2X is provided, in [9], a link-layer performance comparison with the other solutions (IEEE 802.11p, IEEE 802.11bd, and LTE-V2X) is shown, and in [34] first investigations on novel semi-distributed transmission paradigms are proposed.
All the mentioned works have as a common simplifying hypothesis the use of a packet generation interval exactly equal to the allocation periodicity applied by either LTE-V2X or 5G-V2X access layers. Also in [35], [36], where congestion control is investigated and variable packet generation is considered, the issue of the mismatch between packet generation and resource allocation periodicity is not deepened. In [35], the generation interval is kept fixed and the effect of congestion control is rather to discard some packets at the higher layers. In [36], various generation periods are compared but always assuming the same value as allocation periodicity.
A packet generation interval exactly equal to the allocation periodicity, which is acceptable for general considerations and even correct under specific circumstances, is not expected to be always valid for many types of messages that are already defined or that are currently under definition. As the main example, also better discussed in Section III, CAM messages are generated depending on the dynamics of the vehicle and are not periodic in most of the cases. This is for example remarked in [21], where the authors analyze the CAM messages recorded by two car manufacturers during experiments performed on field in urban, sub-urban and highway test drives. In [21], it is shown that both the size of the messages and the time interval between consecutive CAMs are largely variable in time. The authors also derive a model for the generation of realistic messages in simulators.
A very few works do not rely on this assumption. In [37], where the feasibility of implementing the distributed congestion control algorithm specified in SAE J2945/1 standard on top of the C-V2X stack is investigated, the packet inter-arrival time is indeed adapted to the estimated congestion level, thus in principle causing a mismatch with the allocation period; however, how the authors deal with this is not detailed and the consequences are not analyzed from this point of view. More relevantly, based on the model presented in [21], a comparison of ITS-G5 and sidelink LTE-V2X is proposed in [38]. Taking into account a realistic generation of the CAMs, it is observed that LTE-V2X suffers of variable size and variable generation intervals, whereas ITS-G5 is inherently not impacted by these effects. Finally, in [39] the authors investigate the impact of aperiodic traffic, assuming the inter-packet distance following an exponential distribution. In their work, they observe that treating each packet as a new sporadic transmission is preferable than using periodical allocations and dropping packets when a resource is not available or randomly choosing a new one when needed.
In this work, we specifically focus on the impact of a mismatch between the packet generation interval and the allocation periodicity. Differently from previous works, the scope is here to elaborate on the implications in LTE-V2X of such mismatch. We provide a systematic investigation, clarifying which are the options possible at the implementation, and identifying the ways the scheduler can be configured to better cope with this issue.

III. RESOURCE ALLOCATION IN LTE-V2X MODE 4 AND 5G-V2X MODE 2
In this section, a brief description of LTE-V2X and 5G-V2X is provided, taking into account that the standardization process for 5G-V2X is not concluded. Only the main aspects will be here recalled and more details can be found for example in [8], [9], [40].

A. PHYSICAL LAYER OF LTE-V2X AND 5G-V2X
At the lower layers, sidelink numerology and building blocks of LTE-V2X and 5G-V2X are based on uplink, which is single carrier frequency division multiple access (SC-FDMA) in LTE-V2X and cyclic prefix orthogonal frequency-division multiple access (CP-OFDM) in 5G-V2X. LTE-V2X operates in 10 MHz or 20 MHz channels, whereas 5G-V2X can occupy up to 100 MHz when used in bands below 6 GHz (namely, sub 6 GHz). The resources are based on a time-frequency matrix structure: the time domain is divided into transmission time intervals (TTIs), of 1 ms duration in LTE-V2X and of either 0.25 ms, 0.5 ms, or 1 ms in 5G-V2X (sub 6 GHz); the frequency domain is organized in sub-channels, in turn VOLUME 9, 2021 composed of a certain number of subcarriers (spaced by 15 kHz in LTE and 15, 30, or 60 kHz in 5G). Multiple modulation and coding schemes (MCSs) are possible in both technologies.
There are two main PHY channels used to transmit the packets: i) the Physical Sidelink Shared channel (PSSCH) for data packets, also called transport blocks (TBs); and ii) the Physical Sidelink Control Channel (PSCCH) for the associated control information, also known as sidelink control information (SCI), which carries the information that the receiving stations requires to be able to receive and demodulate the PSSCH. The SCI is sent during the same TTI as the data, independently to the vehicle speed and for both LTE and 5G.
Additionally, the physical sidelink feedback channel (PSFCH) is added in 5G NR V2X to allow the receiver sending positive and negative acknowledgment. The TB and the associated SCI are transmitted in the same TTI. The transmission of one TB is performed in a single TTI and a number of adjacent sub-channels which depends on the packet size and the adopted MCS. In Mode 4, each station autonomously identifies the resources to allocate employing a SB-SPS. First of all, a parameter T b is set to define the periodicity for resource allocation. T b can be chosen equal to 20 ms, 50 ms, or any multiple of 100 ms up to 1 s [41]. When the first allocation is performed, starting from the interval T b and the number of subchannels required to transmit the given message, the station defines a grid of possible allocations in the next T b called candidate singlesubframe resource (CSSR). In order to estimate the future occupation of the CSSRs, the station uses the power measured in each subchannel and the content of the received SCIs during a sensing window of T sense = 1 s. The SCIs include an indication about the selected and reserved sub-channels by the neighboring stations. Among the CSSRs that are assumed available, the 20% which received less interference in T sense is passed to the medium access control (MAC) layer, which randomly selects the one to be used. Possibly, two parameters denoted as T 1 and T 2 can be used by the higher layers to set a minimum and maximum delay, respectively, between the message generation and its transmission. T 2 , in particular, can be used to guarantee a given QoS in terms of latency. The latency requirements are application-dependent. For example, safety-related use cases are expected to have very stringent requirements. In most of the cases, the latency deadline for CAMs is set to be equal or lower than 100ms.
Once selected, the same CSSR is kept periodically, with periodicity T b , for a certain time; this process is called SB-SPS and has been introduced to avoid the need for frequent changes of the resource selection, also called reselections. More specifically, the allocation is kept for a random number of periods, for example uniformly selected between 5 and 15 when T b = 100 ms. After that time, the same resource is still maintained with probability p k , which is a parameter set by the operator between 0 and 0.8. The SB-SPS is a key mechanism in order to let the other nodes estimating the future occupation and thus reduce packet collisions but is also prone to possible long bursts of errors [42].
The allocation process is exemplified in Fig. 1. Four subchannels are supposed in the example and the allocation period T b lasts six TTIs. Assuming one packet occupies one subchannel, this means that there are 4 × 6 = 24 possible CSSRs. The sensing interval during which the power is measured and SCIs are decoded is denoted as T sense and includes in the example three times T b , thus the power associated to each of the 24 CSSRs is the average of three values. The average power cannot be estimated in those TTIs in which the node is transmitting, due to the half-duplexing nature of current radios. The station selects a set of candidate resources from a selection window delimited in time by T 1 (here excluding for example the first TTI) and T 2 (here excluding for example the last TTI).

C. WHAT IS EXPECTED IN 5G-V2X MODE 2
The autonomous allocation procedure in 5G-V2X is called Mode 2 and, differently from LTE-V2X Mode 4, is split into several sub-modes [43]: Mode 2a is expected to inherit the same procedure of LTE-V2X Mode 4; Mode 2b was initially set to allow the stations assisting their neighbors in performing resource selection; this feature was later considered helpful in addition to other sub-modes and thus removed as a specific sub-mode; Mode 2c allows to specify a given pattern instead or in addition to the sensing procedure, so that with predefined allocations it is in principle possible to enable very low latency and very reliable transmissions for specific applications; Mode 2d allows a station to select and allocate resources for other stations, which is particularly helpful when vehicles are grouped such as in platoons.
Other relevant aspects of 5G-V2X are the addition of unicast and groupcast transmissions (only broadcast is possible in LTE-V2X), the already mentioned feedback channel to provide positive and negative acknowledgments, and a short-term sensing for non-periodical transmissions.
For the purpose of this paper it is to note that, despite the various additional features expected in 5G-V2X, still the SB-SPS allocation based procedure initially designed in Release 14, now called Mode 2a, is expected to be the main one to deal with recurrent messages similar to CAMs.

IV. RELATIONSHIP BETWEEN MESSAGE GENERATION AND PACKET TRANSMISSION IN LTE-V2X
LTE-V2X and 5G-V2X are intended as possible options for the access layers of protocol pillars that were initially defined with other technologies in mind. The European solution, which is the one considered in this paper, is defined by ETSI under the name of cooperative-intelligent transport systems (C-ITS). In Fig. 2, the architecture of the so-called C-ITS station (C-ITS-S) is reported, as defined in [44]. As observable, the protocol pillar includes three main layers in the middle of the figure: the facilities layer, which basically covers the session, presentation, and application layers of the OSI model; the transport and network layer, which corresponds to the two OSI layers bringing the same names; the access layer, which focuses on the data link (including MAC) and physical (PHY) OSI layers. In addition, management and security layers are foreseen as cross-layer entities, and applications are seen on top of the pillar.
The CAM messages, like the others defined or under discussion in ETSI, are generated and elaborated at the facilities layer in order to provide relevant information to the applications. At the transmitting C-ITS-S, the messages generated at the facilities layer are passed down to the access layer, where the transmission over the wireless medium is performed. Then, the reversed path is followed at the destination.
To be remarked once more is that what hereafter detailed about aperiodic message generations with specific reference to CAMs, is expected to be valid for most of the messages currently under definition, including for example CPMs and VAMs.

A. CAM PACKET GENERATION
As defined in [22], CAMs are packets generated at the facilities layer and exchanged between C-ITS-Ss to be aware of each other and to support Day 1 applications. CAMs are estimated to represent in the early stage of deployment at least the 70% of the traffic load. These messages contain status and attribute information of the originating C-ITS-S. Specifically, in the case of vehicles, the status information includes time, position, motion state and activated systems, among others. The attribute information includes other data such as the dimensions, vehicle type and role in the road traffic. Some of the data elements of the CAM are mandatory, such as the station ID, timestamp, position, and status data (i.e., speed, heading, acceleration and curvature). Beside the mandatory information, the optional information may include, for example, the vehicle role or category, basic sensors, signatures and certificates.
The CAM generation is managed by the cooperative awareness basic service, which defines, in particular, the time interval between two consecutive CAM generations. To grant an efficient use of the spectrum and prevent congestion in the wireless channel, the actual generation time interval is in general variable and depends on the time-dependent behaviour of the C-ITS-S; for instance, changes in direction, position, speed, vehicle condition or the fact of being a special vehicle (e.g., an ambulance) influence the generation frequency. The upper and lower limits of the transmission interval are set to 0.1 s and 1 s, respectively, corresponding to an instantaneous CAM generation frequency between 10 Hz and 1 Hz. Within these limits, the CAM generation can be triggered according to the C-ITS-S dynamics and the channel congestion status. In case the dynamics of the originating C-ITS-S lead to a reduced CAM generation interval, this interval should be maintained for a number of consecutive CAMs.
More specifically, in terms of C-ITS-Ss dynamics, a new CAM generation is triggered when there is a direction change of the vehicle above 4 • with respect to the previously transmitted message, or if the speed changed of more than 0.5 m/s, or finally, if the vehicle position changed of more than 4 m. Therefore, even when a vehicle is moving at constant speed and without changing its direction, the generation frequency depends on the vehicle speed. For example, the minimum packet generation periodicity (i.e., 1 Hz) corresponds to the vehicle moving at 14.4 km/h or below, while the maximum packet generation periodicity (i.e., 10 Hz) is obtained when the vehicle travels at a speed of 144 km/h or above. More in general, it was observed in [45] that the percentage of messages generated keeping the same generation interval as the previous one is only around 50%.
Assuming the generic vehicle moving at a constant speed, the generation interval, hereafter denoted as T g , can be derived as a function of the speed. Specifically, denoting the speed as v in m/s, considering the minimum value T g min = 100 ms and the maximum value T g max = 1 s, and taking into account the triggering condition after 4 m, it is which is shown in Fig. 3 (solid, black curve). As observable, the periodicity is larger at lower speed, where a less frequent update of the vehicle status is required, and smaller at higher speed, where the opposite is true. The behaviour of the curve shown in Fig. 3 is a consequence of the strictly linear increase in terms of generation frequency between its minimum and maximum values.

B. GENERATION AND ALLOCATION PERIOD
In the general case, the packet generation interval at the facilities layer T g and the SB-SPS allocation period of LTE-V2X at the access layer T b might differ from each other. In order to understand the implications of a mismatch between these two parameters, let us focus on the following two cases: i) when the allocation period is larger than the generation interval, i.e., T b > T g ; and ii) when the allocation period is shorter than the generation interval, i.e., T b < T g .
Case when T b > T g : This case is illustrated in Fig. 4 assuming a periodic message generation: the higher part of the figure focuses on the messages generated at the facilities layer, with the messages indicated with capital letters from A to E; the lower part of the figure refers, instead, to the access layer, showing the resource grid and the allocation periodicity, and exemplifying the allocation and transmission processes for the messages received from the facilities layer. In the shown example, the subchannels allocated and used by packet A first and B later, are not suitable for the transmission of C, since it would imply a transmission delay which is larger than the maximum tolerated delay (corresponding to the LTE-V2X parameter T 2 ). Therefore, a reselection is triggered in LTE-V2X to reserve a new resource, which allows C to be transmitted within the window with extremes T 1 and T 2 . This process is repeated also for the packet E. The reselection can be more or less frequent depending on the specific values of the generation and allocation periods. Example of CAM generation and allocation when T b > T g . The upper part illustrates the generation of five packets indicated with letters from A to E , and the selection window for each of these packets. The lower part illustrates the resource allocation process. The green squares represent the resources allocated for transmission. When the resource that was initially allocated is not within the selection window (see packets C and E ) a reselection is required.

FIGURE 5.
Example of CAM generation and allocation when T b < T g . The upper part illustrates the generation of five packets indicated with letters from A to E , and the selection window for each of these packets. The lower part illustrates the resource allocation. The green squares represent the resources allocated for transmission. When the resource that was initially allocated is not within the selection window (see packets C and E ) a reselection is required.
Case when T b < T g : This case is illustrated in Fig. 5 assuming a periodic message generation. When the generation interval is large compared to the allocation period, it happens that no packets are present in the transmission queue when the reserved resource is reached. How to deal with this situation in LTE-V2X does not appear defined in the specification and at least two options are possible: • Approach 1: to maintain the resource allocation but leave the resource empty (exemplified in Fig. 5(a)); • Approach 2: to Release the resource and repeat the allocation process when the next message is received from the facilities layer (exemplified in Fig. 5(b)). The two approaches are hereafter compared in terms of reselections and in Section V-C in terms of other performance metrics. 2 In the example of Fig. 5(a), Approach 1 is used: the resource previously allocated for the transmission of A, is left empty during the second allocation period because a new packet is not generated yet (see packet B). Although less frequent, a reselection can be anyway required also in this case (see packet C). Therefore, in Approach 1 the resource is maintained for multiple allocation periods according to the SB-SPS mechanism, while in Approach 2 the resource is maintained only for a single allocation period and then Released. In the example of Fig. 5(b), Approach 2 is used: the resource previously allocated for the transmission of A, is Released during the second allocation period because a new packet is not generated yet. When a new packet is generated (see packet B) a reselection is required.
In general, the less the two periods are aligned, the more the resources are allocated inefficiently. While the allocation period can take a few possible values (see Section III), the generation interval can be equal to any real number between 0.1 s and 1 s, depending on the vehicle dynamics. To remark this consideration, in Fig. 3 a vehicle is assumed to move at constant speed, and the corresponding T g varying the vehicle speed is shown compared to the possible values of T b between 100 ms and 1 s. Depending on the specific speed, which implies a given T g , and the allocation period T b , the situation can be the one described in Fig. 4 or the one in Fig. 5.
With the aim to determine the impact of this mismatch in terms of instability of the allocation process, we provide an analytical model for the average number of reselections 2 Focusing on Approach 2, two variants have been considered: the first one, denoted conventional, where neither SCI or TB are transmitted; the second one, denoted SCI with empty TB, where the SCI is transmitted, even if there is no data to transmit; the aim of the latter variant is to let the neighboring vehicles know that the resource is reserved. However, given that the allocation procedure mostly relies on the average measured power, the performance observed with the two approached was almost identical. For this reason, in this paper results are reported only adopting the conventional case.
per second, which depend on the setting of T b , T g , and T 2 . An increase of the number of reselections indirectly causes a reduction of the system performance, since it reduces the effectiveness of the SB-SPS mechanism to individuate unused resources; this consideration is confirmed by the system simulations shown in Section V.
The proposed model neglects the number of allocations due to the SB-SPS algorithm, which are instead considered in the simulations used to validate such model. In particular, we consider the probability that a single packet is allocated and then the expected number of reselections per second is given by the number of packets per seconds multiplied by the probability of reselections per packet. Under the Approach 1, the expected number of reselections per seconds can be approximated as where P (1) r is defined in (2), with m = T g /T b , while P (1) u = 1 − P (1) r . Under the Approach 2, the expected number of reselections per seconds is where P (2) r is defined as The derivation of (3) and (4)  Focusing on Approach 1, when T b = 0.1 s, we see that the number of reselections remains always constant at 0.5. Note that in this case the generation interval is greater or equal to the allocation period for any speed value (see Fig. 3) and that  T b = T 2 . With T b = 0.2 s, the generation interval is lower than the allocation period for any speed greater than 72 km/h (refer to Fig. 3). When the speed is exactly 72 km/h, T b = T g and Fig. 6 shows a local minimum. The same curve has a local minimum also at 38 km/h, which corresponds to a generation interval equal to 0.4 s (see Fig. 3), i.e., a multiple of T b . Indeed, a local minimum is expected for every value of the generation interval that is equal or multiple of the allocation period. For T b = 0.3 s, the generation interval is below the allocation period for speed values greater than 48 km/h (see Fig. 3). Interestingly, for the same speed value Fig. 6 shows a minimum equal to 0.17, which is lower than that obtained assuming T b = 0.2 s, i.e. 3.31. The same minimum is again achieved when T g is another multiple of T b . For any speed except around the local minima, the lowest T b = 0.1 s allows the minimum average number of reselections. Focusing on Approach 2, the average number of reselections is always higher or equal to the one of Approach 1. In particular, for any value of T b , the average number of reselections increases linearly for lower values of the speed, and then decreases in alignment with the case of Approach 1. In particular, the linear increase is maintained up to 36 km/h and 48 km/h for T b = 0.3 s and T b = 0.2 s, respectively. Similar results are shown in Fig. 7 assuming T b = 0.1 s and varying the maximum latency given by T 2 . Recall that T 2 is a parameter that can be set in LTE-V2X for QoS configuration. The figure shows that such maximum latency impacts remarkably on the number of required reselections. Indeed, the number of reselections for the case T b = 0.1 s in Fig. 6 was approximately constant for T 2 = 0.1 s; differently, when the maximum latency decreases, the number of reselections increases remarkably. Also in this case and for both T 2 = 20 ms and T 2 = 50 ms, there are local minima for the speed values corresponding to a generation interval equal or multiple of the allocation period. Indeed, as observable in Fig. 3, multiples of 0.1 s are for example obtained with speed equal to 36 km/h, corresponding to T g = 0.4, with speed equal to 48 km/h, corresponding to T g = 0.3, and with speed equal to 72 km/h, corresponding to T g = 0.2.

V. SYSTEM LEVEL RESULTS FROM THE CASE STUDY
In this section, we present system level simulation results for a case study in a highway scenario, adopting the open source LTEV2Vsim simulator [46]. 3 An insight on simulation settings and performance metrics is provided before discussing numerical results.

A. SIMULATION SETTINGS
In this subsection, the settings of the simulations are detailed in terms of scenario, propagation and packet loss modeling, facilities layer, and access layer. A summary is also provided in Table 1.

1) SCENARIO
We assume 50 or 100 vehicles/km moving on a 3 + 3 lanes and or 200 vehicles/km moving on a 6+6 lanes, considering a 2 km long straight highway with wrap-around (i.e., a vehicle exiting on one side of the scenario, enters from the other side in the same lane).
In order to better focus on the considerations subject of this research, the average speed of the vehicles is set to a specific value, assumed between 10 km/h and 150 km/h, in steps of 2 km/h. Each vehicle moves at a randomly selected speed with Gaussian distribution around the given average, with a standard deviation always equal to one-tenth of the average speed.

2) POWER SETTINGS, PROPAGATION, AND LOSS MODELING
The devices transmit in one 10 MHz large channel of the 5.9 GHz band (the specific channel that is used appears irrelevant to the scope of the paper), with a constant spectral power density of 13 dBm/MHz 4 and have an antenna gain at both the transmitter and receiver equal to 3 dBi. 5 The noise figure of the receiver is assumed equal to 6 dB. 6 For the path-loss, the WINNER+, scenario B1, with correlated log-normally distributed shadowing, characterized by a standard deviation of 3 dB and a decorrelation distance of 25 m is used, as in [1]. Given the highway scenario, line-of-sight (LOS) conditions are assumed. For each potentially received packet, the average signal-to-interference-plus-noise ratio (SINR) is calculated by taking into account the interference from all the other nodes. Once the SINR is calculated, the correct reception of each packet is statistically drawn from packet error rate (PER) vs. SINR curves, derived via link level simulations which take into account the impact of small-scale fading. In this work, the curves detailed in [47] are used, obtained assuming 1 transmitting antenna and 2 receiving antennas with 1×2 IRC (Hermitian noise covariance Matrix) equalizer, highway LOS fading model as per [48], channel estimate 4 A spectral power density of 13 dBm/MHz corresponds to 23 dBm if the full 10 MHz channel is used, which a common value for commercial devices. 5 An antenna gain of 3 dBi appears as a realistic average value over the Azimuth plane. An example antenna is the MobileMark SMW314. 6 A noise figure of 6 dB is for example indicated for the NXP RoadLINK SAF5400 modem. based on preamble and feedback loop, perfect control channel decoding, and perfect synchronization.

3) SETTINGS AT THE FACILITIES AND ACCESS LAYERS
At the facilities layer, messages of 350 bytes are supposed, which is the size of CAMs occurring with highest probability in [45]. Even if the size of CAMs is in general variable, as shown for example in [21], a fixed size is here assumed to focus the attention on the generation interval.
At the access layer, 5 subchannels of 10 physical resource block pairs (PRBPs) each are used as mandate by [49]. Additionally, the MCS 7 is used, which corresponds to QPSK modulation and 3 subchannels required to transmit a 350 bytes packet.

B. PERFORMANCE METRICS
We present simulation results based on the packet reception ratio (PRR), which is the average ratio between the number of neighbours correctly decoding a CAM at a given distance and the total number of neighbours at the same distance.
Specifically, we will consider the range with PRR > 0.9 and the value of PRR at a reference distance of 100 m.

C. RESULTS COMPARING DIFFERENT APPROACHES WHEN RESERVED RESOURCE IS REACHED WITH EMPTY QUEUE
In this subsection, results with T 2 = 0.1 s and variable T b are shown for the two approaches, namely Approach 1 and Approach 2, proposed for the handling of reserved resources with empty queue (see Section IV-B). Results are obtained with a density equal to 50 vehicles/km. Fig. 8(a) shows the range with PRR greater than 0.9 vs. the average speed for Approach 1, varying the allocation period T b . The figure shows that such a metric, which could be expected to decrease with the generation interval (implicitly decreasing when the average speed increases), actually follows a trend that is coherent with the variation of the number of reselections. Specifically, for T b = 0.1 s, the range with PRR > 0.9 is monotonically and slowly decreasing. Recall that in this case the number of reselections is constant as the speed varies (see Fig. 6). For T b = 0.2 s, the range with PRR > 0.9 is not monotonically decreasing with the speed and local maxima are found at 24 km/h (corresponding to T g = 3 · T b ), 36 km/h (corresponding to T g = 2 · T b ) and 72 km/h (corresponding to T g = T b ), where the range with PRR > 0.9 is 340 m, 340 m, and 330 m, respectively. Finally, for T b = 0.3 s, the range with PRR > 0.9 is also not monotonically decreasing with the speed and two local maxima are found at 24 km/h and 48 km/h, where the range with PRR > 0.9 is 340 m. In general, the value T b = 0.1 s looks always preferable for the speed values considered. Fig. 8(b) shows the range with PRR greater than 0.9 for Approach 2 and varying the allocation period. The metric is monotonically decreasing in this case, coherently with the variation of the number of reselections (i.e., monotonically increasing). For any value of T b , and for any speed, the performance is FIGURE 8. Range with PRR greater than 0.9 is shown as a function of the vehicle speed and varying the allocation period duration, with 50 vehicles/km, and considering two approaches for handling the reserved resources with an empty queue.
remarkably worse than the one obtained with Approach 1, confirming that frequent reselections have a significantly negative impact on the ability on LTE-V2X reliability, due to the inaccuracy that this causes in the estimation of available CSSRs.
Same conditions, but with a different point of view, are considered in Fig. 9(a) and Fig. 9(b), where the PRR obtained at 100 m is shown varying the average speeed with Approach 1 and 2, respectively. Focusing on Approach 1, this metric shows the same trend as the range with PRR > 0.9.  As an overall remark following the shown results, Approach 1, i.e., maintaining the resource allocation although leaving the resource empty, appears clearly the best approach. Therefore, in the rest of this Section, we will focus only on Approach 1. Focusing on this approach, it can be also concluded that under non-congested channel conditions and given T 2 = 0.1 s, the use of T b = 0.1 s always allows better performance than larger T b . More congested conditions and smaller values for T 2 are considered in the following subsections.

D. RESULTS VARYING THE VEHICLE DENSITY
In this subsection, we show the same performance metrics as in Section V-C, focusing on Approach 1, while considering two larger values for the vehicle density: 100 and 200 vehicles/km. Results are obtained with a maximum latency T 2 = 0.1 s, and varying the allocation period.  shows that the trend followed by the range with PRR > 0.9 as a function of the speed is in line with Fig. 8(a) and that an increase of the vehicle density worsens the performance, i.e. the metric decreases faster. For example, when T b = 0.1 and 100 vehicles/km, the range is 320 m at 10 km/h and 150 m at 150 km/h, respectively compared to 340 m and 280 m obtained with 50 vehicles/km. With 200 vehicles/km, range with PRR > 0.9 further worsens to 250 m at 10 km/h and 70 m at 150 km/h. It can also be noted that with the higher density, in a few very specific cases, adopting other values of T b than 0.1 s is the optimal choice. As specific examples, this occurs with an average speed between 70 and 72 km/h adopting T b = 0.2 and with an average speed between 44 and 50 km/h adopting T b = 0.3. In these specific cases, the generation period T g is compliant with the allocation period T b , thus the reselections do not increase relevantly and a larger allocation period T b allows to maintain the same allocation for a time which is on average longer. 7 The improvement compared to T b = 0.1 s is anyway small and the use of the latter seems a reasonable solution in all cases. Fig. 11(a) and Fig. 11(b) show the PRR at 100 m under the same conditions, i.e., assuming 100 and 200 vehicles/km, respectively, with different values of T b . In the scenario with 100 vehicles/km, the performance are worsened by the higher density and the decrease of the PRR is faster with the speed. Nevertheless, the trends remain the same. Overall, it is noted that, even if the value of T b allowing the highest PRR depends on the specific conditions, the use of T b = 0.1 s appears optimal in most of the cases and near to optimal in the few remaining, for any average speed (and the consequent generation period T g ) and density. It is to note that T b = 0.1 s is the minimum value that can be used with the maximum delay T 2 set to 0.1 s.

E. RESULTS VARYING THE MAXIMUM TRANSMISSION DELAY
In this subsection, we investigate the relationship between T g and T b assuming a smaller value of the maximum delay T 2 = 20 ms. Results are obtained with 50 vehicles/km.   Fig. 13 presents the PRR at 100 m. To note that T b = 20 ms constraints the delay to 20 ms and thus the case T b = 20 ms and T 2 = 100 ms is not considered.
Focusing on the cases with T 2 = 20 ms, Figs. 12 and 13 show that the use of the smaller T b = 20 ms is preferable at medium and medium-high speeds (between 30 and 130 km/h). For example, when the speed is 70 km/h, the range with PRR > 0.9 is 150 m for T b = 20 ms and T 2 = 20 ms, whereas it is reduced to 110 m for T b = 100 ms and T 2 = 20 ms. The conclusion is in line with what observed assuming T 2 = 100 ms, suggesting that the use of the smallest periodicity among those compliant with T 2 can be a good  solution in general. The point is that a lower T b implies overall less reselections. Exceptions are however observable when T g is exactly a multiple of T b for the majority of vehicles, i.e., when T b = 1 s and the average speed is below 14 km/h or T b = 100 ms and the average speed is above 144 km/h. In such cases, as explained hereafter commenting Fig. 14, a better individuation of the free CCSR is allowed by the larger T b . The performance trend is confirmed by Fig. 13 showing the PRR at 100 m.
As already anticipated, the conclusion is not that the choice of the shortest T b is in general the best solution. This can be further observed nothing that the case with T b = 100 ms and T 2 = 100 ms is also considered, it is noted that it always outperforms the case with T b = 20 ms (and T 2 = 20 ms). Please remark that this does not occur due to less time-frequency resources overall used, since instead the number of transmitted messages remains the same. The motivation is rather that a longer T b allows for a larger number of CSSRs and thus higher effectiveness of the SB-SPS. This consideration is further explained through Fig. 14, where the cumulative distribution function (CDF) of the sensed power averaged over the sensing period is shown for the selected subset of the CSSRs. With selected subset of CSSRs we mean the 20% of the available CSSRs, obtained based on both received power and information retrieved from the received SCIs, among which the next CSSRs to be used is randomly selected. As visible in Fig. 14, when T 2 = 100 ms, the power level is much higher for the case T b = 20 ms than the case T b = 100 ms. In particular, with T b = T 2 = 100 ms the average sensed power is always below -200 dB, meaning that none of the selected resources are used by neighboring nodes. With T b = 100 ms and T 2 = 20 ms, the total number of CSSRs is the same, but the selected ones are taken only from the first 20 ms, reducing the probability to have an average sensed power below −200 dBm to 0.74. When T b = T 2 = 20 ms, the entire pool of CSSRs is reduced to one fifth compared to T b = 100 ms and looking at the selected 20% the probability to have an average sensed power below −200 dBm falls to 0.09, which means that a non-interfered resource is chosen only in the 9% of cases.
Summarizing the results provided through Figs. 12-14, it can be concluded that: (i) given a certain T 2 , the smallest T b is always preferable when T g cannot be a multiple of T b , which is coherent with what concluded in Section V-D; (ii) that a larger T b is preferable only if T g is a multiple of such value; and (iii) that the use of a smaller T 2 causes a performance loss, implying a trade-off between latency and reliability.

VI. CONCLUSION
In this work, the effect of a mismatch between the packet generation at higher layers and the periodical structure of resources at the lower layers of sidelink C-V2X autonomous mode is investigated. The study is done focusing on LTE-V2X and CAM generation, but it is expected to provide general conclusions valid also for 5G-V2X and for most of the other messages currently under definition. Results have shown that performance reduces as soon as the packet is not generated using the same periodicity as the allocation process, although they appear always near to optimal if resources are reserved more frequently than needed, simply leaving them unused when the transmission buffer is empty. At the same time, it is also noted that the reduction of the maximum delay, which is a parameter left for optimization, has a negative impact on the reliability; thus, the maximum delay should be relaxed as much as allowed by the application, and then the allocation periodicity should be reduced to the minimum value compatible with such constrain. It follows that if the delay constraint can be set to 100 ms (i.e. the maximum allowed), a practical solution is to set the allocation period to 100 ms. Overall, it has been shown that the considered mismatch, expected to be common in real implementations, has a possible detrimental effect on the performance of the system and thus require careful setting of the parameters and appropriate definition of those procedures that are not specified.

APPENDIX ANALYTICAL MODEL
In this appendix, the analytical model for the average number of reselections is derived. Without loss of generality, let us consider that a reselection has been made for a packet arriving at t g , and therefore, the resource is allocated at t b that is uniformly distributed in [t g + T 1 , t g + T 2 ].

A. APPROACH 1
Under Approach 1, the next packet is generated at t g + T g , which falls within the allocation period [mT b , (m + 1)T b ), where m = T g /T b . Within such an allocation period, the next resource is allocated at (m + 1)T b + t b . Then, a new reselection is required if the resource is allocated after the maximum delay is expired and belongs to the subsequent allocation period, i.e.
Then the probability of reselection for a single packet generation is The expected value for the number of reselections per second n r , should be calculated also considering the probability that the resource is not reallocated but used for the packet at T g , i.e. P u = 1 − P r . In case the resource is used, a new reselection can be required for the following packet, in which case the time between two consecutive reselections would be 2 T g . We then approximate the average number of reselections as where we are neglecting all the terms after the second packet (i.e., when no reselection is required for the packet at 2T g ). The solution of the integral in (7) leads to the equation (3).

B. APPROACH 2
Under Approach 2, the next packet is generated at t g + T g . A reselection is always required unless t b + T b > t g + T g . In this case, the allocation is also required if t b + T b > t g + T g +T 2 . Then the probability of reselection for a single packet generation is The expected value for the number of reselections per second n r is analogous to (8). The solution of the integral in (9)