Padovan Sequence based Backoff Algorithm for Improved Wireless Medium Access in MANETs

Padovan Sequence based Backoff Algorithm for Improved Wireless Medium Access in MANETs Dalil Moad, Soufiene Djahel, and Farid Nait-Abdesselam University of Paris Descartes, France Lero, UCD School of Computer Science and Informatics, Ireland {dalil.moad, naf}@parisdescartes.fr, soufiene.djahel@ucd.ie Abstract In this paper, we propose a novel Backoff scheme, dubbed Padovan Backoff Algorithm (PBA), to improve the efficiency of IEEE 802.11 MAC protocol when operating in DCF mode. PBA will enable significant reduction of the number of collisions when more than one node try to access the shared wireless medium concurrently, leading to an enhanced network performance. The Binary Exponential Backoff (BEB) scheme used in IEEE 802.11 has been proven to not be the optimal backoff algorithm for MANETs. This is mainly due to the exponential increase of the Contention Window (CW) size when a collision occurs, which results in picking the random backoff timer from a large interval that may lead to a longer waiting time before the node tries to retransmit again. Therefore, this waiting time for the idle medium could be important, especially in dense networks where consecutive collisions are more likely to happen, and thus causes a severe degradation of the network performance. To overcome the above issue, PBA employs a different scheme that reduces the size of CW as compared to BEB, thanks to the Padovan sequence. The obtained simulation results reveal that the PBA allows more efficient network resources utilization and outperforms the legacy BEB scheme in different scenarios. Keywords IEEE 802.11, Backoff Algorithm, MAC Protocols, Padovan Sequence, DCF Mode, MANETs, Throughput. I. INTRODUCTION Wireless networks refer to the use of radio frequency signals to share information and resources between wireless devices. The increasing popularity of such networks is mainly due to their intrinsic properties of cheap, easy and flexible deployment, self-organization and configuration etc. Among wireless networks we can mention, Wireless Local Area Networks (WLAN), Mobile Ad hoc NeTworks (MANETs) [13], Wireless Mesh Networks (WMN) [5] and Vehicular Ad Hoc Networks (VANETs) [14]. These networks can be grouped into two main classes, infrastructure based wireless networks (e.g. WLAN) and infrastructure-less networks (e.g. MANETs, VANETs (V2V communication)...). The former class requires a central unit to manage the networks unlike the latter class which does not need such unit; as the networks in this class are self-organized and selfconfigured. Nowadays, Mobile Ad hoc Networks (MANETs) have emerged as a promising wireless communication paradigm enabling wireless ad hoc communication in situations where the services ensured by both wired networks and WLAN are unavailable, such as in case of emergency, disaster and battlefield etc. The nodes in this network exchange information directly over wireless links if they are within the transmission range of each other. Otherwise, the communication is ensured by the intermediate nodes that relay the packets from the source to the destination through multi hop transmissions. Due to the rapidly changing topology of such networks and the instability of links, efficient medium access mechanisms are needed to maximize the usage of the limited shared bandwidth. IEEE 802.11 protocol is well famous and widely used as main Medium Access Control (MAC) protocol in wireless networks which have seen an unprecedented market expansion during the last decade. IEEE 802.11 [4], known as Wi-FI for its widely used IEEE802.11b specification, is currently the dominant standard for medium access in wireless networks. In IEEE802.11 based Mobile Ad Hoc Networks (MANETs), communication between two adjacent nodes (i.e. within transmission range of each other) is carried out directly, while farthest nodes can avail from an extended coverage ensured by intermediate relay nodes through multi-hop communication. The IEEE 802.11 standard [3] defines a common MAC layer that offers various functions supporting wireless access operations. In general, this layer establishes, manages and maintains communication between IEEE802.11 nodes (i.e. nodes equipped with wireless cards) by coordinating their access to the shared radio channel and employing protocols that improve the communication over the shared wireless medium. Often considered as the cornerstone and brain of the network, IEEE 802.11 MAC layer employs a dedicated physical layer, such as 802.11 b/g/ac/ad etc., to perform several tasks such as carrier sensing, transmission, and reception of IEEE 802.11 frames. IEEE 802.11 MAC protocol provides two types of access modes: Distributed Coordination Function (DCF) and Point Coordination Function (PCF). In the first mode, Carrier Sensing Multiple Access with Collision Avoidance (CSMA/CA) is used as a primary access mechanism, and it is designed to support best effort traffic that does not require any specific service guarantees. In the second optional access mode (i.e. PCF), the access point plays a major role by performing a polling through which it determines which station is allowed to transmit resulting in a contention-free communication. PCF mode is usually preferred in scenarios/applications requiring strict QoS guarantees. As stated above, PCF is an optional access mode that can be utilized only in the presence of an access point, concurrently with DCF mode. Since the focus in this paper is on MANETs, therefore DCF mode will be used as the main access scheme of all the nodes in the network. In this mode, a node shall ensure that the medium is idle before attempting to transmit a data or control frame. It picks a random backoff value smaller than or equal to the current contention window (CW) size, and decrements the backoff timer by one after each time slot when the medium is idle. A node may also wait for DIFS (DCF Inter Frame Space) time slots after a successful transmission or EIFS (extended inter frame space) period in case of collision. If the medium is found busy, the node freezes its backoff timer and sets its network allocation vector (NAV) to the expected duration of transmission indicated in the received frame (i.e. RTS, CTS or DATA frames). Transmission should start whenever the backoff timer reaches zero. These different steps are summarized in Figure 1. If a CTS (Clear To Send) or an ACK (ACKnowledgement) frames associated with a DATA packet are not received within a predefined period of time (i.e. timeout), then the sender node assumes that the transmission was failed. A transmission failure, such as collision, triggers the backoff procedure which consists in selecting

a random waiting time chosen in the range of the current contention window (CW). After each successful transmission, the size of CW is initialized to CW min, while it is doubled in case of an unsuccessful transmission attempt. When the CW reaches CW max it remains unchanged till it is reset to CW min after reaching the number of retransmission limit or the DATA packet is delivered successfully to the intended receiver node. While it is commonly established that CW size is crucial and playing a key role in improving the overall network performance, it still presents certain limitations as doubling it in case of unsuccessful transmission may not be the most efficient way to ensure better performance, especially in dense network scenarios. Indeed, the unnecessary idleness of the medium causes the deterioration of the network performance as more packets could be transmitted over the channel during the idle unused slots where the nodes are decrementing their relatively large backoff values due to the exponential increase of CW size. Therefore, In the light of the above observations, we propose in this paper to use silver ratio of Padovan sequence to set and update the size of CW, instead of using the Binary Exponential Backoff (BEB) scheme, aiming to combat the devastating effect of the idleness resulted from the doubling the CW size after each collision. The proposed Padovan algorithm design relies on the Padovan sequence that is characterized by a plastic ratio or silver ratio as it will explained in next sections. The remainder of the paper is organized in the following way. Section II is devoted to the background and the related work on the Backoff algorithms design. The detailed description of our proposed algorithm is then introduced in section III, followed by the performance evaluation and simulation results in section IV. Finally, Section V concludes the paper. Figure 1: DCF mode: CSMA/CA scheme basic mechanism II. RELATED WORK The control of the access to the shared wireless media is ensured by the Media Access Control (MAC) protocols. Binary Exponential Backoff (BEB) [12] is the most widely used algorithm in distributed MAC protocols category. It is mainly used to avoid collisions or at least reduce their number when more than one wireless node attempt to transmit simultaneously. In IEEE 802.11 MAC protocol operating under DCF mode, the nodes willing to transmit a frame wait for the channel to become free before they start the transmission, as described in Figure 1. According to the outcome of the transmission the CW of IEEE802.11 is updated by the BEB algorithm as described in the following. In BEB based DCF mode, at any given time, only one transmitting node uses channel while other nodes in its transmission or carrier sensing range defer their transmission as they sense a busy medium. Similarly, the nodes within the transmission range of the receiver node will defer their transmission when they receive the CTS (Clear to Send) frame. Before accessing the medium, each node waits for DIFS time slots and a random backoff time (Bo) uniformly distributed in the interval [0, CW]. The CW is an integer whose range (i.e. CWmin and CWmax) is determined by the physical layer characteristics. Every node decreases its backoff timer by one every time slot if the medium is still idle, and freezes it if any activity is detected on the medium, and resumes it when the medium is sensed idle again for a period equals to DIFS. Transmission shall start whenever the backoff timer counter reaches zero. If the destination node receives the RTS (Data) frame properly, it sends back a CTS (ACK) after a Short InterFrame Space (SIFS) period. If either CTS or ACK frames are not received by the sender after a predefined timeout value the sender node concludes that the previous transmission (RTS or Data frames transmission) was failed, and updates its current CW size according to BEB algorithm as described below, then after an Extended InterFrame Space (EIFS), the node selects a new backoff timer. After each failed transmission, the CW is doubled up to a maximum value of CW max. CW new = min[2 (CW old + 1) 1, CW max] (1) Random backoff value (Bo) is calculated as follows: Bo = random(0, CW ) SlotT ime. (2) Such that Bo is a random variable uniformly distributed in the interval [0, CW-1]. To improve the efficiency of the BEB algorithm discussed above a number of novel backoff calculation schemes have been proposed in the literature. In the following, we summarize the most significant contributions in this context. Multiplicative Increase and Linear Decrease (MILD) algorithm [6] and the Linear Multiplicative Increase and Linear Decrease (LMILD) [9] algorithm are among the pioneer works proposed to enhance IEEE 802.11 efficiency. In LMILD, the nodes involved in a packet collision increase their contention windows multiplicatively, while the nodes that overhear this collision increase their contention windows linearly. After a successful transmission, all the nodes decrease their contention windows linearly. In MILD, once a collision occurs, instead of doubling the CW, this latter is increased by a multiplicative factor equals to 1.5. Moreover, upon successful transmission after a collision the CW is linearly decreased. Both schemes achieve significant improvement of the throughput under the assumption that the nodes are aware of the collided packets in their transmission ranges. However, this assumption is very difficult to satisfy in real world, especially in highly dense MANETs scenarios. In [7], the authors propose to dynamically tune the contention window and approximate the backoff value by p-persistent backoff. This latter is calculated based on the estimation of the number of active nodes in the network, which doesn t match a real network scenario. The Enhanced Distributed Channel Access (EDCA) scheme is proposed in [1] to improve the performance of the DCF function by providing certain levels of QoS according to the type of traffic

Algorithm 1 Padovan Backoff Algorithm 1: if (The medium is sensed idle more than DIFS) then 2: Send MAC frame 3: end if 4: if (retry-count==0) then 5: max-backoff = CW min 6: else 7: max-backoff = P(retry-count) 8: end if 9: if (max-backoff > CW max ) then 10: max-backoff = CW max 11: end if 12: backoff = Random (0,max-backoff) max-backoff: Backoff s upper bound. CW min : Minimum contention window. CW max : Maximum contention window. backoff: Backoff timer. P(retry-count): Padovan term. retry-count: Retransmission number. to be transmitted. The performance enhancement is achieved by offering prioritized access to different classes of traffic. EDCA mechanism defines 4 access categories each of which is assigned a CWmin,CWmax and Arbitrary Inter-Frame Space (AIFS) value which corresponds to DIFS in BEB. This mechanism is mainly designed to support traffic types with high requirements in terms of QoS such as video and audio packets. Besides the aforementioned pioneer schemes, some recent works have further investigated the BEB algorithm and designed alternative schemes to further improve the network performance. Among these works, [15] for example dealt with the increasing number of collision in dense networks and proposed the so-called Constrained-send DCF (CDCF) to limit the transmission probability of the competing nodes, and thus reduce the collision probability. In [16], the authors designed the Dynamic Contention Window Adjustment (DCWA) scheme to ensure that the maximum throughput can be achieved (approached) under saturated load conditions. Finally, in [8], a comparative study between standard DCF algorithm and Power Line Communication (PLC) MAC protocol is carried out under different network scenarios (e.g. topologies with hidden and exposed nodes, all the network nodes in the same coverage etc.). The obtained results show that PLC MAC outperforms DCF MAC. III. THE PROPOSED SOLUTION In this section, we present our MAC protocol in which we use Padovan sequence to design a new Backoff calculation scheme. As explained above, in BEB algorithm when a collision occurs the first response is to increase the contention window (CW) size exponentially (i.e. a node doubles its CW), which introduces unnecessary idle time in the channel and thus reduces the network overall performance. We, therefore, argue that doubling the contention window is not always the best or optimal solution to deal with the packets collision problem because the backoff time chosen from the new CW could be larger than the required waiting time to ensure collision free medium access. Therefore, we propose in the following the Padovan sequence based backoff scheme summarized in Algorithm 1 to ensure better management of the CW size. The Padovan sequence is the sequence of integers P(n) defined by the following initial values: P (0) = P (1) = P (2) = 1 (3) The recurrence relation is given below: P (n) = P (n 2) + P (n 3), n >= 3. (4) P (n + 1)/P (n) = 1.32472 (5) The main characteristic of Padovan sequence is the plastic number [10] which is also referred to as the silver number, but this name is more commonly used for the silver ratio (1 + 2). In mathematics, the plastic number is a mathematical constant which represents the unique real solution of the equation 6. x 3 = x + 1 (6) In 1928, Dom Hans van der Laan gave the name plastic number to this mathematical constant. The word plastic does not refer to a specific substance, but means something that can be given a threedimensional shape. This is because, according to Padovan [10], the characteristic ratios of the numbers, 3/4 and 1/7, relate to the limits of human perception in relating one physical size to another. This value is obtained by dividing the term (N+1) of Padovan sequence by the term N, as shown in Figure 3. This figure shows the evolution of the plastic number while Figure 2 depicts the increment behavior used in PBA and BEB. In Figure 3, we can clearly observe that after certain number of terms of the sequence, the ratio tends to a fixed number equals to 1,32472. Figure 2 shows the evolution of the size of CW generated by BEB (see the blue curve) and PBA (see the red curve) in case of successive collisions (i.e. successive unsuccessful transmissions), and highlights that PBA can reach the CW max after larger number of retransmissions as compared to BEB in which the CW reaches the maximum value after a few attempts only. This means that the wireless nodes using PBA can get faster access to the medium and, therefore, a better utilization of the available bandwidth can be achieved. However, the slow evolution of CW size in PBA may result in an increased collision probability in case of large number of contending nodes within transmission range of each other. The Algorithm 1 describes the detailed functioning of our proposed Padovan Backoff Algorithm. In this algorithm, each node increases its CW up to the maximum contention value CW max after an unsuccessful transmission, and resets it to a minimum value equals to CW min after a successful transmission according to the following formulas: CW new = { min(p CWold, CW max) if collision CW min if success Where P represents the Padovan number. While CW is updated, the backoff timer value Bo is calculated as follows: (7) Bo = random(0; CW ) SlotT ime (8) The recurrence relation can be then solved explicitly, given that: P(n) = ((1 + r 1) / (r n+2 1 (2+3r 1))) + ((1 + r 2) / (r n+2 2 (2+3r 2))) + ((1 + r 3) / (r n+2 3 (2+3r 3))) where r i is the i th root of: x 3 +x 2-1=0. Even the other form of the solution can be also calculated as explained below: P(n)=((r 2 1)(r 3 1)r n 1 )/((r 1 r 2)(r 1 r 3))+((r 1 1)(r 3 1)r n 2 )/((r 2 r 1)(r 2 r 3)) +((r 1 1)(r 2 1)r n 3 )/((r 1 r 3)(r 2 r 3))

bandwidth among the contending wireless nodes, and thus if it can be adopted in real wireless cards or not. The FI is defined as follows: Figure 2: Contention window size vs. consecutive transmission failures in PBA Figure 3: Plastic number evolution where r i is the i th root of x 3 -x-1=0. IV. SIMULATION SETTING AND RESULTS After describing the details of our proposed scheme in previous sections, we now focus on evaluating its performance through computer simulations using OPNET 14.0 [2]. The main goal of our simulation is to study the efficiency of our algorithm compared to Binary Exponential Backoff algorithm. To implement our Backoff algorithm, the IEEE802.11 MAC implementation in OPNET has been modified to include the functionality of our proposal. Moreover, various simulation scenarios (network topologies and nodes mobility) are considered in the performance evaluation so as to show the benefits behind using Padovan ratio to update the CW size. In our simulation, the network size varies between 20 and 100 mobile nodes and their mobility speed varies from 2m/s to 10m/s. In order to highlight the strength of our scheme as compared to the standard BEB algorithm we have chosen to evaluate the following metrics. Normalized THroughput (NTH): the NTH of a node id is defined as follows: N throughput = T hroughput id Availablebandwidth This metric is measured for all simulation scenarios under both PBA and BEB. It is indeed a good indicator to compare the efficiency of these two algorithms. Fairness Index (FI): this metric is introduced by Jain in [11] and is considered as an important property that allows us to verify whether our PBA scheme can guarantee a fair share of (9) F I(T h1, T h2,...t hn) = NX( T i hi)2 T i h2 i (10) where Thi denotes the acquired throughput of a traffic flow (i.e. node if we have one traffic flow only per node) i and N is the number of the contending flows. Note that if only M of N flows acquire equal bandwidth (while other flows get none), then the FI is M. Hence, an F I value close to 1 indicates that PBA is N respecting the fairness property. Now, we present the simulation setting and configuration of the different parameters used in our experiments to assess the performance of PBA and BEB. Our simulation is conducted using CBR traffic during 300 seconds, which is a duration long enough to capture the behavior of our proposed scheme under different scenarios. Simulation settings and parameters configuration are summarized in table I. Parameters Values Area 1000 X 1000 square meters Physical layer Direct sequence MAC protocol IEEE 802.11b Transmission range 250m Traffic type CBR Topology Random Data rate 11 mbps CBR packets size 500 bytes Simulation time 300 seconds Slot time 20E-06s SIFS 10E-06s DIFS 50E-06s No. of simulation epochs 5 Network simulator OPNET 14.0 [2] Table I: Simulation settings In Figure 4, the NTH acquired by each sender node is plotted. The results shown reveal that the achieved average normalized throughput is much higher in case of small number of senders (i.e. less than 40 senders) while it decreases when the number of senders gets larger (i.e. more than 40 senders). Inn this latter case, each sender node gets almost half of the bandwidth acquired in the former scenario where the network is relatively of small size (i.e. less than 40 nodes). Since the network topology is randomly deployed then it is composed of separated dense clusters of nodes connected among them, hence the throughput gained within each set is independent from that acquired in other sets. We can also observe from these results that the our PBA scheme outperforms the BEB scheme under all simulated scenarios. To assess the impact of the network density on the performance of both PBA and BEB schemes in terms of throughput, we vary the number of nodes between 20 and 100 as shown in Figure 5. The results graphed in this figure clearly highlight the supremacy of PBA over BEB under various network densities as the average throughput gained by each node in the network has increased significantly in our scheme (see the blue curve) compared to that obtained in BEB (see the red curve). The increase of the throughput achieved in our scheme is due to the reduction of the unnecessary time that nodes must wait to access the medium, thanks to the Padovan sequence. This throughput, however, is inversely proportional to the network density as under high network density the number of contending nodes within the same transmission range increases significantly, leading lo lower throughput. As the gained throughput by each node may also vary according to the speed at which the node is moving, therefore we plot in Figure

Figure 4: Normalized throughput vs. the number of sender nodes in the network Figure 6: Average network throughput under varying mobility speed of nodes: case of network size equals to 20 Figure 5: Impact of network size on the obtained average network throughput Figure 7: Average network delay vs. network size 6 the measured average throughput in a network of 20 nodes under a mobility speed ranging from 2 m/s to 10 m/s. The results shown in this figure indicate a gap of approximately 70 kbps between PBA and BEB, which represents a substantial improvement of PBA over BEB. These results reveal also that PBA is more sensitive to the mobility speed compared to BEB as the acquired throughput under PBA decreases slightly when the nodes move faster (i.e. at a speed higher than 4m/s). However, even under higher mobility PBA still outperforming BEB as it guarantees a higher throughput (the gap is still around 55 kbps). In Figure 7, we compare the average transmission delay achieved by both schemes.as we can see from the graphed results, PBA achieves lower or similar delay compared to BEB in most simulation scenarios. This is justified by the fact that when BEB is used, in case of collision a long idle time is observed, which consequently increases the average delay in the network, as opposed to PBA which use Padovan sequence to lower this idle time as much as possible. It is also worth to mention that the average delay achieved both PBA and BEB schemes is inversely proportional to the network size. The Figure 8 plots the Fairness Index (FI) values measured under both our scheme and BEB scheme in a random network topology and under varying number of the sender nodes (20... 100). The depicted results highlight that both schemes achieve similar fairness level which is close to 1 in most cases. Hence, this proves that using Padovan sequence to manage the CW size ensures the fair share of the bandwidth among the competing wireless nodes. V. CONCLUSION In this paper, we have proposed a novel backoff computation scheme that ensures a significant improvement in the efficiency of IEEE 802.11 MAC protocol operating in DCF mode, especially in Figure 8: Fairness index: our scheme vs. BEB dense MANETs scenarios. It is well known that IEEE 802.11 BEB scheme is not an optimal backoff algorithm, especially in dense networks, because the exponential increase of the Contention Window (CW) size after each unsuccessful transmission may result in an under-utilization of the channel bandwidth. Therefore, the network performance may experience a severe degradation. To overcome the above limitation of BEB, we have devised an original backoff mechanism based on Padovan sequence in which the CW is updated according to the evolution of the Plastic number rather than doubling its value as in BEB. The obtained simulation results reveal that the Padovan Backoff Algorithm (PBA) ensures more efficient network resources utilization and outperforms the legacy BEB scheme under various scenarios. These results highlight also that PBA achieves higher throughput compared to BEB, especially in dense network scenarios, and maintains the fairness index close to 1.

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