Fabrice Theoleyre
email: theoleyre@unistra.fr!

A Route-Aware MAC for Wireless Multihop Networks with a Convergecast Traffic Pattern

The MAC layer for multihop wireless networks has drawn considerable research attention in the last few years. We focus here on the wireless multihop networks with a convergecast traffic pattern: the whole traffic is destined to a sink/gateway. We propose first to select a k-tree core, i.e. a sub-tree of the shortest paths to the sink containing exactly k-leaves. In particular, these k-tree core nodes are chosen among the nodes that must forward most traffic. We design C-MAC, an optimized MAC layer for this kind of topology. C-MAC is derived from the CSMA-CA like approaches and consists in giving a larger priority to the k-tree core nodes. Moreover, a proper coordination among the k-tree core nodes permits to limit collisions among them. Simulation results show that organizing the transmissions in C-MAC permits to achieve a much larger throughput than the original IEEE 802.11-like protocol it is based on. This simple solution can be adapted to most CSMA-CA like protocols, and is particularly relevant for WSN or WMN in which traffic is mostly destined to the sink/gateway. MAC layer; convergecast traffic; k-tree core; CSMA-CA; route-aware MAC

INTRODUCTION

Multihop wireless networks are currently very popular and have been receiving a large attention of the research community. More specifically, many of these networks present a convergecast traffic pattern: all the packets are either destined or sent by the same entity.

Wireless Mesh Networks permit to offer a wireless connectivity while connecting only a subset of the Access Points to the wired Internet. Often, all the traffic passes through these gateways. Besides, Wireless Sensor Networks permit to instrument distributively an environment for house automation, smart buildings, sustainable development, etc. These networks are also often convergecast by nature: measurements are collected distributively by the sink.

The IEEE 802.11 technology has gained wide popularity when deployed in the infrastructure mode with an Access Point providing untethered connectivity to nomadic devices. The CSMA-CA mechanism has largely proven its efficiency to distribute the bandwidth among the stations in this kind of networks. With such a probabilistic approach, neither the number of packets nor the number of stations has to be fixed a priori. Moreover, the exponential backoff mechanisms allows the network to cope with a fluctuating number of contenders: the transmission probability will be self-adjusted. Indeed, if a collision occurs, the contention window is automatically doubled so that the traffic pressure is reduced.

However, there is a lot of evidence that the 802.11 MAC layer is not suitable for multihop wireless networks: the performance of packet forwarding over multiple hops quickly degrades with the number of hops due to channel contention and spatial problems such as hidden, exposed, masked, and blocked nodes [START_REF] Dhoutaut | Performance issues with IEEE 802.11 in ad hoc networking[END_REF], [START_REF] Ray | Evaluation of the masked node problem in ad hoc wireless LANs[END_REF], [START_REF] Iyer | Understanding the key performance issues with mac protocols for multi-hop wireless networks: Research articles[END_REF]. In particular, the chain topology is very common in multihop: packets have to be forwarded toward the destination. However, collisions among the different forwarders can occur, degrading the end-to-end performances. MAC layers that adopt a similar approach in WSN (e.g. IEEE 802.15.4) suffer from the same drawbacks when the load approaches the network capacity. Besides, the nodes close to the gateway/sink have often more packets to forward, and a bottleneck quickly appears around it [START_REF] Karnik | Throughput-optimal configuration of fixed wireless networks[END_REF].

On the opposite side, TDMA scheme permits a fine scheduling and limits bandwidth wastage. However, it requires a very tight synchronization and does not cope with variations: TDMA slots are assigned in advance, even when the traffic load changes frequently. Besides, to compute an acceptable scheduling while enabling radio reuse requires a complete knowledge of the radio environment: the scheduler must know the sets of links that interfere with each other. Consequently, one can adopt e.g. a centralized scheduler with SINR constraints [START_REF] Papadaki | Robust scheduling in spatial reuse TDMA wireless networks[END_REF] or a distributed slot assignment scheme with an a priori knowledge of interferences [START_REF] Macedo | Distributed latency-energy minimization and interference avoidance in TDMA wireless sensor networks[END_REF]. However, to measure the level of interferences among radio links is a complicated task in multihop networks, which requires to measure atomically the interferences [START_REF] Padhye | Estimation of link interference in static multi-hop wireless networks[END_REF].

We propose here to adopt an innovative solution, mixing the assets of both approaches. In C-MAC (Convergecast-MAC), most nodes execute the classical CSMA-CA algorithm to transmit their packets. Oppositely, we organize the transmissions of the most-constrained nodes. Instead of adopting a TDMA scheme which would require a global synchronization, we propose distributed MAC reservations, gateway-oriented: control frames that reserve the medium propagate from the gateway to the borders of the network, through the most constrained nodes.

This approach has the following promising assets:

• C-MAC extends the NAV of IEEE 802.11 by just introducing a new type of control frame. It is interoperable with the classical IEEE 802.11;

• it operates without any synchronization requirement;

• we jointly optimize routing and MAC by constructing a structure to collect the traffic: a k-tree core;

• we present a multichannel variant to multiplex transmissions across different channels. This feature limits greatly the number of collisions.

PRELIMINARIES

We focus in this article on multihop wireless networks with a convergecast traffic pattern: one single node, i.e. the gateway, is either the source or the destination of each packet transmission. If the network comprises several gateways, we will consider individually each gateway and all its associated nodes, i.e. we will neglect the impact of nodes with frequent gateway changes. Moreover, we will focus here on the MAC layer: the optimal gateway selection, the encapsulation scheme, etc. are out of the scope of this article.

IEEE 802.11 Behavior

IEEE 802.11 is widely deployed to provide a wireless access in hotspots. The CSMA-CA technique it implements is efficient to share the bandwidth among an unknown number of stations. Thus, we will shortly describe the basic functions of CSMA-CA protocol, and more particularly of IEEE 802.11 [8], on which we based the protocol presented here. In IEEE 802.11, each transmitter chooses a random backoff comprised between 0 and the contention window value (CW) 1 . If the medium is idle for more than DIFS time, it starts to decrement the backoff. As soon as the medium is detected busy, the backoff is paused and it will be redecremented when the medium becomes idle (still after the DIFS time). When the backoff is null, the node starts to transmit its data frame. The receiver decodes the data frame, waits for SIFS and sends an acknowledgement. If the source receives an ack, it considers the frame was correctly received. Else, it estimates a collision occurred: it doubles the contention window so that the backoff will probably be larger for the next retransmission. This exponential backoff helps to cope with a variable number of transmitters. Finally, when a node has correctly transmitted a frame, it reinitializes the contention window to the minimum value. This approach helps to converge to an accurate Contention Window value.

IEEE 802.11 is robust to collisions and performs well in cellular networks. [START_REF] Heusse | Idle sense: an optimal access method for high throughput and fairness in rate diverse wireless LANs[END_REF] studied the optimal contention window value to almost avoid all collisions. However, IEEE 802.11 performs quite poorly in multihop [START_REF] Dhoutaut | Performance issues with IEEE 802.11 in ad hoc networking[END_REF]. Thus, we aim here at optimizing the IEEE 802.11 approach in networks with a convergecast traffic pattern.

C-MAC GENERAL DESCRIPTION

We are convinced that jointly optimizing the routing and MAC layers seems a promising way for convergecast wireless networks. Since all the traffic is destined or generated by the gateway, we can self-organize the transmissions to avoid the classical bottleneck around the gateway.

C-MAC uses a reservation-oriented mechanism: a node becomes privileged during a small duration. We will distribute this privilege mode only to most constrained nodes so that no pair of nodes privileged simultaneously are interfering with each other.

We focus on convergecast networks, in which the routes form a tree rooted at the gateway. Thus, C-MAC uses this tree to distribute the privilege modes: it sends a token, which is forwarded hop by hop toward the leaves. When a node receives the token, it becomes privileged during a short time.

We consider now the example illustrated in figure 1. Each node chooses as parent the next hop toward the gateway, which forms a spanning tree, rooted at the gateway. Besides, we selected in this example 3 different branches, starting from the gateway. Each branch is linear: a node has only one child, except the gateway. Only the nodes of these branches can become privileged after receiving the token.

When it has finished to transmit its data frames, the node will then forward the token to its child, toward the leaves.

If the gateway sufficiently inter-spaces the tokens it generates, we can avoid interferences among privileged nodes. Indeed, the previous token will have been forwarded sufficiently far to avoid collisions. node, i.e. along one single branch. Moreover, only the nodes part of the tree will be able to gain a special access to the medium. Consequently, we would like to obtain a tree with the following characteristics:

• to limit interferences among and inside the branches, they should be as linear as possible (i.e. we should avoid zigzag);

• we should bound the number of branches in order to limit the time a branch has to wait before receiving the next token;

• we want to minimize the distance of normal nodes to the tree, i.e. the packets should be forwarded mostly by the nodes that can become privileged.

The k-tree core structure was originally introduced in [START_REF] Peng | Algorithms for a core and k-tree core of a tree[END_REF] and is particularly convenient for our purpose. Intuitively, the k-tree core proposes to extract from a tree the k leaves that minimize the average distance from a node to the closest k-tree node.

More formally, l(T ) denotes the number of leaves in the tree T and d(A, B) denotes the distance in hops between nodes A and B. We also define the distance from one node N to a set S as the distance from N to the closest node in S:

d(N, S) = min M ∈S (d(N, M )) (1)
If KT is a set of k-tree core nodes associated to the tree T , the following definition holds:

KT ⊂ T (2) l(KT ) = k (3)
Objective : min

N ∈T d(N, KT ) (4)
[10] proposes a centralized algorithm to select a k-tree core from any tree topology. The nodes report to the root of the tree the most convenient leaves. Intuitively, we must select the best k branches to form the k-tree core. To achieve this objective, each node computes a metric representing the suitability to select its branch (from it to the best leaf). This metric is computed from the leaves to the root. When the root obtained all the metrics from its children, the best branch can be selected. Eventually, this process can be repeated k times although some optimizations exist to reduce the convergence delay.

We will now explain how we construct such a k-tree core for C-MAC.

Approach

In existing approaches, the k-tree core is selected when the graph is already a tree. We adopt consequently the following heuristic:

1) We construct first the tree of shortest paths towards the gateway. The k-tree core aims at minimizing the distance to the tree. Thus, a node chooses preferentially as parent the node with the largest subtree size if several candidates are available. Intuitively, if this node is chosen as a k-tree node, it will save more hops for normal nodes;

2) We select then the k leaves that minimize the average distance to the k-tree core. Besides, we force the root to be part of the final k-tree core.

We will now detail the construction process.

Tree Construction

Algorithm 1: Self-stabilizing Tree construction We first construct a self-stabilizing tree as described in algorithm 1. All control information is piggybacked in hello packets. In particular, the gateway sends its hellos with a strictly increasing sequence number. A node propagates the largest sequence number received from its parent. In this way, we are able to detect tree disconnections when the sequence number does not increase for a sufficiently long time (∆ seqnum seconds). In this case, a node just reinitializes its parent and its distance to the gateway.

Besides, a node changes its parent when a neighbor announces a smaller distance to the gateway. The node just switches its parent and updates both its sequence number and distance to the gateway.

Several neighbors may announce the same distance to the gateway. In this case, a node chooses as parent the node which announces the largest subtree size. This will optimize later the k-tree core. Each node updates its subtree-size when it receives an hello from one of its children: a node simply sums up the cardinalities of the subtrees of its children.

The reader can note that the tree will be correctly maintained, even if one radio link or one node disappears: each node will monitor the tree connectivity and it will choose another parent if a starvation in the sequence number is observed.

The worst case corresponds to a linear topology: during one hello packet period, only one node is added to the tree. We denote by D the network diameter, and by n the number of nodes. The time complexity of algorithm 1 is

O(D) = O(n).

K-tree Core Selection

We elect the k-tree core as highlighted in algorithm 2.

Similarly to [START_REF] Peng | Algorithms for a core and k-tree core of a tree[END_REF], we use the concept of savings. The k-treecore must be chosen to minimize the average distance to the closest node of the core. saving(leaf, root) represents the number of hops saved if the path (leaf, root) is a core compared to the average distance to the root. A larger saving means that we should choose the path (leaf, root): it will minimize the number of transmissions exterior to the core.

Let's consider the example illustrated in figure 2 to explain intuitively how to compute savings. When A has to compute its saving value, it extracts the savings of its children B and C. Let's imagine that B has the largest saving. A will update its own saving to the sum of saving(B, root) and the size of the subtree rooted at A. Intuitively, if A is chosen in the core, all its descendants will save one transmission through the link (A, D).

The reader can consequently remark that this saving value as introduced in [START_REF] Peng | Algorithms for a core and k-tree core of a tree[END_REF] can be computed distributively.

In parallel, each node reports in its hellos the k best savings to select the best k leaves. More precisely, the savings are computed as follows (algo 2):

1) A node N orders all the savings announced by its children; 2) The largest saving value is updated taking into account the fact that N will become part of the ktree core;

Algorithm 2: k-Tree Core savings computation

14 for i ∈ [0..k -1] do 15 savingExport ←savingExport ∪ mySavingList [i];
3) N piggybacks in its hellos this new value accompanied with the k-1 other largest values, forwarded as is.

The savings are correctly computed, according to lemma 3.3 [START_REF] Srivastava | Cluster based routing using a k-tree core backbone for mobile ad hoc networks[END_REF].

The root (i.e. the gateway) has to be part of the k-tree core since it will forward all the traffic in up/download. Thus, it initiates the creation of k branches by selecting the k largest savings values among its children. The root associates to each branch a branch id and the associated neighbor id. This information is piggybacked in hellos: each node verifies if it has been selected by its parent. If this is the case, it extracts the corresponding branch ids. Then, it chooses the i th largest saving value for the i th branch for which it has been selected. The corresponding children are announced and they prolongate the branches in the same way.

Savings are reported from the leaves to the root while elected k-tree nodes are reported in the inverse direction. In the worst case, the tree depth (denoted T ) is equal to the number of nodes (n). Thus, the time complexity for computing savings and electing k-tree nodes is in O(T ) = O(n).

Figure 3 illustrates a k-tree core with 3 branches. Thus, each node reports the 3 largest savings. The leaves (e.g. nodes B or F ) report a unique saving of 1 (themselves). On the contrary, G has several children. It reports the largest saving (from H) incremented y its subtree size (7 + 6) and the 2 other savings from K and M without modification. Finally, the root A is able to select the 3 largest savings to create the branches. In particular, node G is chosen twice since it announces 2 of the largest savings. The k-tree core is then propagated, each node selecting its children. In particular, G has been selected for 2 different branches and has to select the two largest savings (i.e. corresponding to nodes H and K).

Properties

We can remark that the algorithm is deterministic but relies on unreliable transmissions. For instance, a node may have two neighbors, closer to the root and with the same subtree cardinality. In that case, unreliability for hello transmissions will conduct the node to choose pseudo-randomly one of these nodes as parent.

C-MAC MECHANISMS

We propose here to use the tree constructed previously to regulate the transmissions in the network: we focus on the k-tree core nodes since they will carry, by construction, most of the traffic. In particular, we give them a privileged access to the medium. A reservation mechanism, propagated by the gateway, limits interferences among these constrained nodes.

Normal Nodes

Any node which is not part of the k-tree core executes the normal CSMA-CA algorithms, as in IEEE 802.11. Thus, it has to wait a DIFS before decrementing its backoff. It may either use a RTS-CTS to limit the hidden terminal problem if the frames are long or directly transmit them.

We adopt also the exponential backoff algorithm of IEEE 802.11 to cope with different densities. The contention window is doubled upon a collision to reduce the collision's probability.

Medium Access for Privileged Nodes

The most-constrained nodes become iteratively privileged: they have the largest priority to transmit their frames. Since we control the number of nodes privileged simultaneously, we can grant an immediate medium access without contention to these nodes.

To be compatible with IEEE 802.11, we re-use the PIFS value, dedicated originally to the Point-Coordination-Function of IEEE 802.11 when the Access Point polls the stations. Thus, a privileged nodes has only to wait for PIFS after it detects the medium is free. Since all the other nodes have to wait for DIFS, the privileged node will always win for the contention. Besides, the privileged node will not break a transmission since PIFS is superior to SIFS: it will wait the current exchange among another pair of nodes is finished.

Let's focus on the example described in figure 4. We assume that two nodes S 1 and S 2 are backlogged (i.e. they have a large buffer of data to transmit). When S 1 becomes privileged, it just has to wait PIFS before gaining the medium access. It will eventually send several data frames before finishing to be privileged, waiting every time PIFS. When S 1 is not privileged anymore, it is authorized to transmit any data frame. Thus, S 2 will be able to sense an idle medium during DIFS and its backoff: it will then transmit its data frame. Such a mechanism is efficient because we choose the most-constrained nodes to be privileged. Other nodes have less traffic to forward and we do not need to regulate their transmissions: the IEEE 802.11 mechanism works well.

The reader can note that C-MAC can profitably acknowledge data in bursts when a node is privileged. D 1 would send an ack only after receiving the second data frame. However, we did not implement this option for the performance evaluation to have a fair comparison with IEEE 802.11.

Privilege Forwarding

C-MAC regulates the medium access by focusing only on most-constrained nodes. These constrained nodes can become privileged to have an exclusive access to the medium. However, we must limit interferences among nodes becoming privileged simultaneously. Besides, we argue a TDMAlike approach presents too strong limitations compared to CSMA-CA approaches. Firstly, it requires a fine grained synchronization and a guard time has to be reserved to avoid collisions among the different slots. Besides, the scheduling should be derived from the contention graph, which is usually not trivial to compute. A TDMA-like approach presents also a low flexibility: the scheduling has to be entirely recomputed when the traffic or the conditions vary. Finally, we aim at keeping the compatibility with the classical IEEE 802.11 approach. Thus, we will use the convergecast nature of the network: the gateway is the root and can distribute the bandwidth to its neighbors, and more specifically to its neighboring branches. Thus, we chose to use a new control frame we call Clear-To-Receive (CTR). This CTR acts as a token to become privileged and should reserve the medium for the newly privileged node. Consequently, the CTR acts like the Clear To Send of IEEE 802.11: destination has only to wait for PIFS before transmitting its data frame. Using PIFS instead of SIFS permits to limit collisions with ongoing transmissions while having a larger priority than other nodes (using DIFS). When the gateway sends a CTR, it will gain access to the medium and will not release it when its neighbor become privileged: the medium is not idle for a duration equal or longer than DIFS.

Besides, this CTR acts as token and is forwarded along the branches of the k-tree core. A node has to forward the CTR when it remained privileged for a duration longer than T slot . Thus, each CTR constitutes a kind of wave. Each wave propagates along a branch and dies when it reaches the leaves of the k-tree core. If the gateway inter-spaces sufficiently the CTR it generates for each branch, it can avoid the interferences. Thus, a gateway generates a new CTR for another branch when the other one is estimated CT R hop apart (i.e. it has to wait CT R hop * T slot ).

Let's focus on the example in figure 5. We reported the subset of nodes in fig. 1 that interests us in this example. We assume that the gateway generates a new CTR for a different branch every 2 slots. In this case, the CTR is forwarded along the first branch, and the sink generates a new CTR after C ends its privileged slot. We did not represent the ack for a sake of clarity.

Two k-tree core nodes can be privileged simultaneously if they are sufficiently far from each other (more than 2 hops). For instance, D and G can transmit their data frames to their parent without collision.

We represented possible concurrent transmissions from non k-tree nodes on the lower part of the figure. A privileged node maintains the reservations made by the CTR: all the frames are interspaced by either PIFS or SIFS. Thus, a normal transmission can take place if no other privileged transmission already reserved the medium. For instance, the node 5 can send a data frame to its parent 4 during the privileged slot of B without collision: no signal is sensed since B is assumed to be out of interference range.

Transmissions are unreliable although a packet loss is very prejudicial for CTR: the whole privileged slot is conditioned by the correct reception of this packet. Thus, a CTR must be acknowledged by:

• a data packet from the destination: the next hop has data packets and starts its transmission because it has received the CTR;

• a CTR: if the next hop has no data to transmit, it forwards without delay the CTR to its own child. Thus, this implicitly acknowledges the previous transmission.

Collisions may occur between different k-tree nodes if CT R hops is too small or if two interfering k-tree nodes are privileged simultaneously. These repeated collisions would also create hello packet losses, triggering tree and k-tree core reconfigurations. Meanwhile, a k-tree node implements a classical retransmission strategy: it tries to retransmit its packets long retry times, as in IEEE 802.11. During the first short retry retransmissions, the k-tree node transmits directly after PIFS, and for the last retransmissions, it chooses a random backoff after having waited PIFS: we would solve contention among k-tree core nodes. If this is not sufficient, the node drops the packet (either a CTR or a data packet) and consider that the privileged slot is lost. Thus, one of the two competing k-tree nodes will win and keep the privilege token/slot. We limit unfairness because the retransmission mechanism is based on a pseudo-random strategy.

CTR self-adaptation

The reader can note that the gateway can regulate the bandwidth assigned to each branch. Indeed, it can fix a different T slot value for each branch, reserving de facto a different bandwidth for each of them. However, we let an adaptive algorithm fixing dynamically these values to a future work.

In the same way, the gateway could be able to test different values for the CT R hops parameter. After having measured the achievable throughput, the gateway could be able to adjust dynamically the value. In particular, when the CT R hops is too small, many collisions would occur between k-tree nodes during their privileged time. These collisions will negatively impact the throughput, and CT R hops would be re-increased. The AIAD (Additive-Increase Additive-Decrease) method could be particularly interesting to find dynamically the optimal value.

Upload/Download Transmissions

In a convergecast network, the traffic can follow two directions: in upload (from the nodes to the root) and in download (from the root to the nodes). C-MAC can deal with both cases.

Obviously, non-k tree nodes follow the classical IEEE 802.11 approach. Thus, they are able to transmit to their parent and children in a similar manner, without any specificity.

For k-tree nodes, C-MAC operates in the following manner: upload: this case is illustrated in fig. 5. Just after having received the CTR from its parent, a node transmits all its buffered packets to its parent; download: this case is illustrated in fig. 6. When node B receives a CTR, it can transmit its packets to C. If necessary, B can use an RTS/CTS to avoid the hidden terminal problem: neighbors of node C may not be aware of the existence of a privileged slot. This reservation is then active for the whole burst. In our case, node B mixes download (to C) and upload (to A) directions in the same privileged slot. When a k-tree node has to forward a packet to a normal node, it uses the non privileged mode: these transmissions are not part of the k-tree core. For instance, B will send a data packet to the node 2 using the normal CSMA-CA mode after having chosen a random backoff (with the usual DIFS). To avoid unfairness, a k-tree node has to share equally the bandwidth between the up and download directions: a node should forward roughly as much traffic as it receives.

Forwarding Delay

For non-k tree nodes, packets are forwarded according to the classical CSMA-CA mechanism. Thus, the delay remains unchanged compared to IEEE 802.11.

On the contrary, k-tree nodes can only forward packets after having received a CTR. To avoid any synchronization requirement, each k-tree node forwards its CTR to its child. In other words, we create a kind of precedence along the tree. Thus, the forwarding delay is different according to the direction in the k-tree: download: the privileged slots are directly consecutive. Thus, a node has to wait at most T slot (i.e. the end of its slot) before forwarding the data packets.

For instance, the node B receives its packets in the privileged slot of A and forwards them to C just after that (fig. 6); upload: we face an inverse situation. A node receives the data packets from one child just after having forwarded to it the CTR. Thus, it has to wait for the next CTR from its parent. Thus, it has to wait exactly CT R hops * privileged duration * nb branches. This buffering delay in upload also exists when a ktree node receives a data packet from its children not present in the k-tree core. In particular, each k-tree node will buffer all the data packets received between two CTR (i.e. CT R hops * privileged duration * nb branches seconds). As a side effect, C-MAC is consequently efficient to aggregate the data packets from its children.

The reader can also remark that the the data packets of non-k tree and k-tree nodes can be aggregated in the same manner. When a node receives packets from one k-tree child, it waits for the next CTR before forwarding them. This gives the occasion to receive the other packets from its other nonk tree children. In figure 5, data packets from 2 and D can be aggregated for the next transmissions of C.

Multichannel Extension

Although C-MAC was not conceived for this specific purpose, it can be very easily adapted to work in a multichannel environment. Indeed, all the transmissions use by default a common channel (e.g. channel 0) while transmissions of privileged nodes can use different orthogonal channels. If strictly more than 2 channels are available, different channels are used for different branches: CTR can be generated safely more frequently. The gateway mentions the channel id used for the privileged transmissions directly in the CTR.

More precisely, the CTR are transmitted over the common channel. Let's focus on the example described in figure 7. The node A forwards the token by sending a CTR. It will automatically switch to the privileged channel to receive frames. The node B first acknowledges the CTR by a CTR-ACK and then switch to the reserved channel for sending its data frames. The data frame exchange takes place on this interference-free channel. Thus, the node B can use safely SIFS for all its transmissions since it is alone to transmit. Besides, each node maintains a Network Allocation Vector (NAV) per channel as highlighted in figure 7. In this example, the node C is aware of the ongoing transmission and will send its data frame to A only when the reservation elapsed, i.e. it extracted the T slot value from the CTR.

Since the CTR can suffer from collisions or bad transmissions, the source of the CTR may retransmit it after switching back to the common channel. The CTR retransmission process is identical to the single-channel case. This mechanism maximizes the probability that the token is correctly forwarded along the branches.

The reader can note that the performances of C-MAC will not improve for more than CT R hop + 1 channels. Indeed, the gateway may act as a bottleneck since it is blocked for the whole T slot duration after sending a CTR (i.e. it cannot transmit simultaneously two CTR on two different channels). Moreover, a new CTR can be safely generated on the same channel when the other one is CT R hop apart. With the additional common channel, this gives the aforementioned limit. However, we could cope with this particular situation by having multi-radio gateways. This would relax this constraint.

INTEGRATION

We will now describe how C-MAC can efficiently cohabit with the other protocols present in the multihop network.

MAC Layer Independency

Although we used IEEE 802.11 to explain the C-MAC approach, the philosophy of C-MAC can be implemented with many other CSMA-CA approaches. Exhaustivity is impossible, but we will here describe how C-MAC can cohabit with various solutions in Wireless Sensor and Mesh Networks.

Busy Tones can be used to limit the hidden terminal problem [START_REF] Haas | Dual busy tone multiple access (DBTMA)-a multiple access control scheme for ad hoc networks[END_REF]. They permit to notify the transmissions in the vicinity. C-MAC can be easily adapted to use for instance busy tones in reception and/or emission.

In WSN, we can also add a preamble [START_REF] Hill | Mica: a wireless platform for deeply embedded networks[END_REF] before each transmission to wait for the destination to wake up. For ktree node, a preamble is required to transmit the CTR or a data packet to one child. Then, other packets can be transmitted without preamble since the destination will wait for the end of the privileged slot.

C-MAC would also be useful when only short preambles are used, such as in Single Channel Polling (SCP) [START_REF] Ye | Ultra-low duty cycle MAC with scheduled channel polling[END_REF]. To reduce power consumption, nodes agree on a schedule to wake-up synchronously: shorter preambles are sufficient to cope with clock drifts. However, the nodes may have buffered packets when they slept. This would lead to a traffic storm when all nodes wake-up. C-MAC could be implemented when all the nodes are awake to regulate the transmissions, during the active period.

Energy Consumption

C-MAC was not designed to save energy but rather to optimize the network capacity. Thus, it consumes similar energy as other CSMA-CA protocols. However, C-MAC can be easily adapted to be integrated with other solutions saving energy in WSN.

As highlighted previously, C-MAC can be adapted to work with various other MAC layers. In particular, the preamble sampling techniques permit to save energy efficiently.

In the same way, topology control solutions permit to choose the most accurate neighbors. By choosing to use the most economical radio links, the network can save energy globally. Thus, C-MAC can perfectly be executed after a topology control algorithm has been executed. In this way, C-MAC would use efficient radio links. Finally, C-MAC could also use a metric based on energy to choose the radio links in the tree. In that way, C-MAC would use only most thrifty transmissions.

PERFORMANCE EVALUATION

We have simulated C-MAC in OPNET with the parameters presented in Table 1.

We have compared the performance of our proposal with the standard IEEE 802.11 DCF, one representative CSMA-CA protocol. We conjecture that the mechanisms of C-MAC could be adapted to any CSMA-CA approach, when the traffic to forward is large (e.g. when nodes wake up simultaneously to transmit data frames after a long sleeping duration or after having detected an event).

We did not compare C-MAC with a TDMA-like approach since such a solution would require a global synchronization. Besides, an efficient conflict-free scheduling algorithm must be implemented to organize the transmissions. This approach would require to know a priori the conflict-graph which is practically a difficult problem. However, we plan to experiment in the future C-MAC and compare it in realistic conditions to a TDMA-like approach, adopting for instance the approach described in [START_REF] Rhee | DRAND: Distributed randomized TDMA scheduling for wireless ad-hoc networks[END_REF].

We first evaluate the impact of the parameter's values in C-MAC in a grid network of 7x7 nodes, the sink being located at the center of the simulation area. Then, we focused on random circular topologies of nodes to generalize these results. Data traffic consists of several constant-bitrate (CBR) flows, their rate being represented in the figures below as the offered load in packet per second (pps). Each node transmits a CBR to the central sink, to represent a convergecast traffic pattern. We focus on the upload direction since the download direction offers less constraints in fairness and delay with C-MAC.

We have averaged the results presented below over several different simulation runs and have plotted the 95% confidence intervals. We have run simulations with and without the RTS/CTS option and obtained results that are not significantly different, so we have decided not to represent them in the figures.

We have evaluated the performance of three MAC layers according to three metrics:

1) End-to-end delay: the delay between packet generation and its reception by the final destination; 2) Aggregated throughput: the volume of all received data in the network per unit time in Mbps; 3) Jain index defined as:

( n i=1 X i ) 2 n n i=1 X 2 i , (5)
where X i is the throughput obtained by flow i, measures throughput fairness of different flows in the network. A low Jain index means poor fairness; 4) Overhead: the ratio of the volume of control and data packets transmitted per node and the volume of data packets received by the sink. The volume is measured either in number of packets or in bits.

Tuning C-MAC Parameters

First, we measured the influence of the number of branches in the k-tree core (i.e. the k value) for a grid of 49 nodes. We chose an offered load of 13 pps so that the network operates in saturation: all the generated packets cannot be delivered to the sink. We are consequently able to study the impact of the C-MAC parameters in saturated mode. Figure 8(a) illustrates the throughput for different k values. When the k-tree has one single branch (i.e. it is a core), the throughput is minimal: C-MAC does not achieve to balance the load in the network, and some data packets are dropped. On the contrary, more branches permit to forward more packets while avoiding collisions. However, it also increases the delay (fig. 8(b)). Indeed, the sink generates a new CTR iteratively for each branch. When a branch has just forwarded a CTR, it has to wait for the sink to send a new CTR for all the other branches. On average, a k-tree core node has to wait longer before having again the right to be privileged. We consider that 5 branches constitutes a good trade-off for the delay and throughput. Then, we measured the influence of the privileged duration, i.e. the time between a k-tree core node receives a CTR and it has to forward it (fig. 9). A k-tree core node has the right to send its data frame to its parent only during this privileged duration. If this duration is too small, the overhead for forwarding the CTR becomes large. If this duration is long, the end-to-end delay increases. The throughput reaches a maximum when the privileged duration is around 5ms (fig. 9(a)). In the same way, the end-to-end delay reaches a minimum for the same values (fig. 9(b)). Moreover, C-MAC is relatively insensitive to a small variation for this duration (the graphs are in log-scale). We verified also that 5ms constitutes the best privileged duration for other nongrid networks.

Finally, we measured the influence of the CTR interspacing, the time separating two consecutive CTR generated by the sink (fig 10). The CTR inter-spacing is represented in hops (the sink has to wait CT R hops * T slot before generating a new CTR). If the sink generates too frequently new CTR, they will surely collide with each other: data packets will be retransmitted, having a negative impact on the throughput (fig 10(a)). On the contrary, if CTR are more than 6 hops : it increases the buffering delay, as described in section 5.6. In consequence, we consider that a CTR interspacing of 3 hops constitutes a good trade-off.

Grid Network

We first evaluated the robustness of the algorithm electing the k-tree core. In a grid network, the optimal assignment would use shortest paths toward the sink and balance the load among the different branches. Thus, we compared the performance of C-MAC with the distributed algorithm we presented in section 4 and with a centralized static k-tree core (we chose statically the k-tree core as represented in figure 11(a)). We first reported the throughput of C-MAC and IEEE 802.11 in figure 12(a). IEEE 802.11 uses the tree to route packets toward the gateway. Since IEEE 802.11 is not routeaware, its performances are not impacted when it uses a static or a dynamic routing tree. Besides, we can remark that the throughput of C-MAC is the same for the centralized and our distributed k-tree core construction. Thus, our algorithm seems robust. Finally, we can remark that C-MAC uses the same routes as IEEE 802.11 but optimizes the throughput by reducing the number of collisions and by giving a privileged access to k-tree core nodes. C-MAC achieves a gain of almost 100% for the throughput. Then, we measured the delay (fig. 12(b)). When CBR flows are small, C-MAC achieves larger delays than IEEE 802.11: a node in the k-tree core that receives a packet has to wait for a CTR before being authorized to forward it. However, the collisions in IEEE 802.11 quickly increase the congestion when the network is more heavily loaded. Thus, C-MAC achieves quickly better delays than IEEE 802.11. We can also remark that the delays are similar whatever the k-tree core algorithm we used (either static or distributed).

We plotted the Jain index in figure 12(c). IEEE 802.11 quickly saturates and drops many packets, in priority from sources far from the sinks: the route length being larger, these packets have a larger chance to be dropped by a forwarder. On the other side, C-MAC achieves a good fairness for larger loads. Obviously, when the network saturates, the packets through shorter routes have a larger probability to be delivered, and the fairness index decreases.

Finally, we measured the overhead in bits for both C-MAC and IEEE 802.11 (fig. 12(d)). We can remark that the overheads are similar for low traffic values: the CTR generated by C-MAC are negligible. In the same way, the additional bits inserted byC-MAC in the hello packets have a very limited impact on the global overhead. For a large traffic, long flows suffer from collisions, decreasing the packet delivery ratio. Thus, both protocols generate more packets to deliver the same number of data packets to the sink. Mechanically, the global overhead increases.

Random Convergecast Networks

We compared the performance of C-MAC and IEEE 802.11 in a random network (fig. 13): 60 nodes are randomly located in a circular area while maintaining an average degree of 8. Besides, the sink is located in the center of the simulation area to limit side effects. We keep on using the default values as mentioned in table 1. We can remark that C-MAC supports a larger throughput than IEEE 802.11. While We also measured the impact of the density (fig. 14): we adjust the simulation area to increase the average degree. Each source generates 20 pps so that congestion begins to appear in the network. We discard topologies that are disconnected. When the density is low, the throughput decreases: routes are longer and some nodes become disconnected because they only have unreliable links with their neighbors. C-MAC outperforms IEEE 802.11 for small and average densities. When the network is almost single hop, the throughput is maximum, and IEEE 802.11 and C-MAC perform in a similar manner: the k-tree core is very limited and almost all the nodes transmit their packets directly to the sink, without CTR. The gain over IEEE 802.11 is equal to for smallest densities and to 16% for medium densities (av. degree of 15). Finally, C-MAC and IEEE 802.11 achieve a similar delay since we are in saturated mode (fig. 14(b)). Finally, we measured the overhead for these topologies (fig. 15). Firstly, we can remark that C-MAC and IEEE 802.11 achieve more or less the same overhead for a low and a very large traffic (fig. 15(a)). We can remark that for a very low traffic, C-MAC generates slightly more control packets than IEEE 802.11: in this case the CTR overhead is not enough mutualized and its cost is not negligible. However, the overhead is not sensitive in this case since the network capacity is not reached. For CBR flows of about 30 to 50 pps, C-MAC is more efficient than IEEE 802.11 to deliver packets to the sink/root. This decreases the average number of data and control packets generated for each delivered data packet.

We also plotted the repartition of the overhead for CBR flows of 20 pps to have a more detailed view of the origin of control packets (fig. 15(b)). We can remark that hello packets and CTR-END are negligible. We have also a small amount of CTR packets for C-MAC (below the ack). Besides, data constitute the vast majority of transmissions, with the associated acks. We can conclude that C-MAC presents an acceptable overhead. We also verified we obtained the same type of result when we measured the number of packets without taking into account the packet sizes.

Multichannel Feature

We evaluated in figure 16 the multichannel feature of C-MAC. When more than 1 channel is available, the channel 0 is used by default while the other channels are used for the k-tree nodes that become privileged. When C-MAC operates with more than 2 channels, the sink will alternate the channels it uses for the different branches of the k-tree core. Thus, the sink can generate CTR more frequently, and thus increases the network capacity.

We measured first the throughput (fig. 16(a)). While the network saturates with one single channel, the multichannel version of C-MAC supports a larger load. The gain is the largest when we have two channels: a k-tree node that receives a CTR becomes privileged and uses an orthogonal channel, avoiding entirely the collisions with non k-tree core nodes. Since CTR seldom suffer from collisions in the control channel (channel 0), this multichannel mechanism performs well. The reader can remark that when the number of channels is almost the number of branches, the frequency of CTR cannot be increased, and the throughput saturates. Moreover, the gain is reduced because non k-tree core nodes may start to have difficulties to send their data packets if the receiver is a k-tree core node, deaf to transmissions on the channel 0. We can also remark that using different channels limits the number of retransmissions and transitively the end-to-end delay (fig. 16(b)). In conclusion, C-MAC can exploit very efficiently a collection of orthogonal channels, multiplexing the transmissions without any need of synchronization or multiradio nodes.

RELATED WORK

The MAC layer has recently received a large attention for multihop wireless networks. IEEE 802.11 [8] is the predomi-nant protocol for hotspots, i.e. single hop wireless networks for multimedia. The CSMA-CA mechanism is flexible and particularly efficient to cope with traffic variations. However, IEEE 802.11 has been proved to perform very poorly in multihop [START_REF] Dhoutaut | Performance issues with IEEE 802.11 in ad hoc networking[END_REF].

In wireless mesh networks, some researchers have proposed to assign different channels for multi-radio mesh nodes [START_REF] Kyasanur | Routing and linklayer protocols for multi-channel multi-interface ad hoc wireless networks[END_REF], [START_REF] Ramachandran | Interference-aware channel assignment in multi-radio wireless mesh networks[END_REF], [START_REF] Raniwala | Architecture and algorithms for an IEEE 802.11-based multi-channel wireless mesh network[END_REF], [START_REF] Hoang | Channel assignment for multicast in multi-channel multi-radio wireless mesh networks[END_REF]. [START_REF] Raniwala | Architecture and algorithms for an IEEE 802.11-based multi-channel wireless mesh network[END_REF] focuses on the routing metric to construct the tree rooted at the gateway, and then assigns a channel per link, taking into account the traffic load. [START_REF] Ramachandran | Interference-aware channel assignment in multi-radio wireless mesh networks[END_REF] starts from the gateway, assigning the channels to the most constrained links. [START_REF] Hoang | Channel assignment for multicast in multi-channel multi-radio wireless mesh networks[END_REF] extends it to cope with multicast. However, these approaches require multi-radio capable nodes and color the radio links in a centralized manner. [START_REF] Kyasanur | Routing and linklayer protocols for multi-channel multi-interface ad hoc wireless networks[END_REF] proposes that a subset of interfaces stay static while the other ones switch from one channel to another. However, it works only for multiradio nodes. To the best of our knowledge, no MAC protocol was proposed to cope with wireless mesh nodes with one single interface, typically adapted to the convergecast traffic pattern.

In wireless sensor networks, most approaches focused on energy savings, like [START_REF] Ali | Medium access control issues in sensor networks[END_REF]. In [START_REF] El-Hoiydi | Low power MAC protocols for infrastructure wireless sensor networks[END_REF], the PSM mode of IEEE 802.11 is modified to work in WSN. In SMAC, each node wakes up periodically and publishes this periodicity in its hellos [START_REF] Ye | An energy-efficient MAC protocol for wireless sensor networks[END_REF]. A node just has to know this scheduling to know when to send the frame. Single Channel Polling (SCP) proposes a global synchronization scheme in which all the nodes wake up simultaneously and sense once the channel [START_REF] Ye | Ultra-low duty cycle MAC with scheduled channel polling[END_REF]. However, contention may be large since a node wakes up only seldom, leading to collisions and energy wastage. [START_REF] Kulkarni | An address-light, integrated MAC and routing protocol for wireless sensor networks[END_REF] already jointly optimized the MAC and routing layer. However, it focused on very low traffic conditions. Since C-MAC could be adapted to work with CSMA-CA like approaches, we could extend these protocols to adapt for them the concept of privileges in C-MAC.

Other propositions adopted a TDMA-like approach in WSN. For instance, [START_REF] Rhee | DRAND: Distributed randomized TDMA scheduling for wireless ad-hoc networks[END_REF], [START_REF] Rhee | Z-MAC: Hybrid MAC for wireless sensor networks[END_REF] computes a distributed scheduling to assign timeslots to each node. [START_REF] Macedo | Distributed latency-energy minimization and interference avoidance in TDMA wireless sensor networks[END_REF] adapts the scheduling to interferences measured by the nodes. [START_REF] Kaushik | Channel allocation and medium access control for wireless sensor networks[END_REF] proposes to adopt a multichannel approach, coloring each radio link to avoid interferences. However, it uses a dedicated separated low power radio for transmitting pulses.

WSN present often a convergecast traffic pattern: this particular property can be used to optimize certain functions. [START_REF] Zhang | Reliable bursty convergecast in wireless sensor networks[END_REF] optimizes the retransmissions when several bursts of traffic have to arrive to a sink. [START_REF] Voigt | Improving sensor network robustness with multi-channel[END_REF] extends DMAC [START_REF] Lu | An adaptive energy-efficient and low-latency MAC for data gathering in wireless sensor networks[END_REF], rearranging the slots attributed to each node. [START_REF] Chen | Adjustable convergecast tree protocol for wireless sensor networks[END_REF] proposes to balance the load for the convergecast tree, optimizing the routing and not the MAC layer as C-MAC does. [START_REF] Huang | Radial coordination for convergecast in wireless sensor networks[END_REF] focuses also on controling the data flows in the routing layer to limit collisions.

C-MAC uses a k-tree core structure as introduced originally in [START_REF] Peng | Algorithms for a core and k-tree core of a tree[END_REF]. [START_REF] Wang | Finding a k-tree core and a k-tree center of a tree network in parallel[END_REF] provides a parallelized version of the algorithm. Then, [START_REF] Srivastava | Cluster based routing using a k-tree core backbone for mobile ad hoc networks[END_REF], [START_REF] Srivastava | Distributed algorithms for finding and maintaining a k-tree core in a dynamic network[END_REF] extended it to provide a distributed version, adapted for routing in ad hoc networks. They use any spanning-tree before selecting the k-tree core while we use only shortest paths to the gateway and we try to create straight branches that forward most traffic. Indeed, our objective here is different since we focus on regulating the transmissions at the MAC layer. [START_REF] Wang | Efficient algorithms for a constrained k-tree core problem in a tree network[END_REF] proposed to upper bound the k-tree core diameter. [START_REF] Li | K-tree trunk and a distributed algorithm for effective overlay multicast on mobile ad hoc networks[END_REF] uses this k-tree core for multicast. To the best of our knowledge, the k-tree core structure was never used before for organizing the transmissions in the MAC layer although it is particularly adequate.

CONCLUSION & PERSPECTIVES

In this paper, we studied the wireless multihop networks with a convergecast traffic pattern. We proposed to organize the network into a k-tree core. This structure coupled with a specific MAC protocol helps to organize the transmissions and to reduce the collisions. By giving a different medium access in CSMA-CA to the nodes that carry most of the traffic, we reduce the number of collisions, which may occur only with nodes with less traffic. Besides, C-MAC does not need any synchronization mechanism, and is much more flexible than a classical TDMA scheme. Finally, C-MAC is entirely compatible with IEEE 802.11, i.e. it can cohabit transparently with non-C-MAC enabled nodes. We have also shown that C-MAC operates efficiently in multichannel environments and optimizes the throughput while avoiding the deafness problem. Simulation results demonstrated that C-MAC with a k-tree core outperforms IEEE 802.11.

One important future research consists in validating C-MAC in a realistic environment, but it requires to have access to the IEEE 802.11 firmware to allow a k-tree core node to use PIFS for its transmissions. Besides, it could be interesting to jointly optimize the routes and the k-tree core structure. Indeed, C-MAC optimizes the transmissions for a tree of shortest paths. However, shortest routes could not be the best solution for balancing the load to reduce contention. We expect also to compare C-MAC and a TDMA-like approach in realistic conditions. In particular, TDMA requires to know exactly the conflict graph and needs to compute a conflictfree scheduling. We plan to measure the impact of conflict graph imprecisions, and to verify that C-MAC achieves similar or better results without synchronization and without computing a complex and less flexible scheduling. Finally, we plan to adapt C-MAC to SCP in order to reduce the collisions when all the nodes wake-up simultaneously. This feature would be particularly accurate in Wireless Sensor Networks for event detection since the traffic is mostly in bursts in these cases.

Fig. 1 .

 1 Fig. 1. Tree structure of C-MAC (here a 3-tree core)

Fig. 2 .

 2 Fig. 2. Savings to find a k-tree core

Fig. 3 .

 3 Fig. 3. K-tree core selection and savings computation (3 branches)

Fig. 4 .

 4 Fig. 4. MAC access for privileged nodes

  Fig. 5. CTR forwarding and data transmissions in upload (nodes → root) with CT R hops = 2

Fig. 6 .

 6 Fig. 6. CTR forwarding and data transmissions in download (nodes ← root)

Fig. 7 .

 7 Fig. 7. C-MAC behavior in multichannel

Fig. 8 .

 8 Fig. 8. Regular grid of 49 nodes, 13 pps -impact of the number of branches in the k-tree core

Fig. 9 .

 9 Fig.9. Regular grid of 49 nodes, 13 pps -impact of the privileged duration (i.e. time before a CTR is forwarded)

Fig. 10 .

 10 Fig.10. Regular grid of 49 nodes, 13 pps -impact of the CTR interspacing (hops that separate two consecutive CTR generated by the sink)

Fig. 11 .

 11 Fig. 11. k-tree core election in a grid of 49 nodes

Fig. 13 .

 13 Fig. 12. Regular grid of 49 nodes with a convergecast traffic

Fig. 14 .

 14 Fig. 14. Circular Random Network of 60 nodes -CBR of 20pps

Fig. 15 .

 15 Fig. 15. Circular Random Network of 60 nodes -CBR of 20pps

Fig. 16 .

 16 Fig. 16. Regular grid of 49 nodes with a convergecast traffic -multichannel extension

or 21 (h dist ≤ myDist and h stSize > myParentStSize) then 22 myParent ←h id; 23 myDist ←h dist + 1; 24 myParentStSize ←h stSize;

	1 / * My parent	* /
	2 myParent ←∅ ;
	3 / * The subtree size of my parent	* /
	4 myParentStSize ←0 ;
	5 / * My sequence number	* /
	6 mySeqnum ←0 ;
	7 / * My distance to the root/gateway	* /
	8 myDist ←MAX;
	9 while hello received do
	10	/ * Extract info from hello	* /
	11	h id, h stSize, h seqnum, h dist
		←extractInfo(hello);
	12	/ * To detect tree disconnections	* /
	13	if myParent = h id then
	14	mySeqnum ←h seqnum;
	15	/ * Tree is disconnected: seqnum did
		not change for ∆ seqnum seconds	* /
	16	if noChange(mySeqnum, ∆ seqnum ) then
	17	myParent ←∅;
	18	myDist ←MAX;
	19	/ * To keep shortest routes to the
		gateway	* /
	20	if (h dist + 1 < myDist)

TABLE 1

 1

	Simulation parameters -default values
	Bit rate	11Mbps
	Packet reception threshold	-86dBm
	Transmit power	5mW
	Frequency	5Ghz (5180→5805)
	RTS/CTS	inactive
	Packet size	128 bytes
	Privileged duration	5ms
	CTR inter-spacing	3 hops
	Number of branches for the k-tree core	5

TREE CONSTRUCTIONC-MAC aims at enabling the most constrained nodes to gain a privileged access to the radio medium while limiting interferences. Thus, a token can be forwarded only to one

ACKNOWLEDGEMENTS

The author would like to thank Catherine Rosenberg (University of Waterloo, Canada) for providing helpful advices and sharing its expertise in this research topic.

This work was partly supported by the French Government and the Competitive Clusters Minalogic and System@tic under the contract FUI SensCity.


MD Franck Morschhauser
email: franck.morschhauser@chru-lille.fr

Kamal Bouabdallah

Stephan Stilgenbauer

Catherine Thieblemont

Sophie De Guibert

Florian Zettl

Lawrence M Gelbert

Kellie Turner

Siva Rama

Prasad Kambhampati

Lily Q Li

P Kellie Turner

Sean Buchanan

Susana Barriga

Melissa M Bear

Martin Wilhelm

Georg Hess

Affiliations

Clinical activity of abemaciclib in patients with relapsed or refractory mantle cell lymphoma -a phase II study

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2

Mantle cell lymphoma (MCL) accounts for ~6% of all non-Hodgkin lymphomas (NHLs) with an aggressive clinical course in patients, especially after early relapse. [START_REF] Arora | Novel therapies for relapsed/refractory mantle cell lymphoma[END_REF] Lack of cure for relapsed/refractory (R/R) MCL with conventional therapy [START_REF] Arora | Novel therapies for relapsed/refractory mantle cell lymphoma[END_REF] has resulted in a search for targeted therapies. CDK4 & 6 inhibitors have emerged as therapeutic options for R/R MCL because MCL cell lines and patient-derived samples that express high levels of cyclin D1 are highly sensitive to CDK4 & 6 inhibitors. [START_REF] Gong | Genomic Aberrations that Activate D-type Cyclins Are Associated with Enhanced Sensitivity to the CDK4 and CDK6 Inhibitor Abemaciclib[END_REF] Oral abemaciclib is a potent and selective CDK4 & 6 inhibitor that reduced tumor growth in human xenograft models with MCL. [START_REF] Dempsey | Abstract LB-122: LY2835219, a selective inhibitor of CDK4 and CDK6, inhibits growth in preclinical models of human cancer[END_REF] In a Phase I study of patients with MCL, palbociclib, another CDK4 & 6 inhibitor, was shown to overcome resistance to ibrutinib, a first-in-class BTK inhibitor. [START_REF] Martin | A Phase I Trial of Ibrutinib Plus Palbociclib in Previously Treated Mantle Cell Lymphoma[END_REF] Here, we evaluated the efficacy, safety, and pharmacokinetic profile of abemaciclib in patients with R/R MCL in a Phase II trial.

In this multi-center, open-label, single arm trial, patients ≥18 years of age with R/R MCL received 200 mg oral abemaciclib Q12H (every 12 hours) each day of a 28-day cycle (Online Supplemental Appendix). The study enrolled 28 patients in 8 centers in France and Germany from March 2013 to September 2015 (Online Supplemental Figure 1). Most patients were male (60.7%) and white (96.4%) with a median age of 70 years (range, 53-83) (Online Supplemental Table 1). Median number of prior therapies was 3 (range 1-6) and majority of the patients (67.8%) had received ≤3 prior lines of therapies. 7 patients had received prior stem cell transplant and median time to treatment from stem cell transplant was 46 months (range, 18-87 months). During the study, patients completed a median of 6 cycles (range, 1-32).

Fluorescence in-situ hybridization (FISH)/cytogenetics showed that all evaluable samples (n=5) from patients had the t(11;14)(q13;q32) translocation, which is a genetic hallmark of MCL and 4 (14.3%) among them overexpressed cyclin D1 (Figure 1A). In addition, cyclin D1 was overexpressed in 16 more patients (57.1%) as evidenced by immunohistochemistry although the t(11;14)(q13;q32) translocation could not be verified in these patients due to lack of evaluable samples. (including bone marrow evaluation). [START_REF] Cheson | Report of an international workshop to standardize response criteria for non-Hodgkin's lymphomas. NCI Sponsored International Working Group[END_REF] Key secondary objectives included the objective response rate (ORR), duration of response (DoR), progression-free survival (PFS) and overall survival (OS). Single-agent abemaciclib demonstrated a DCR of 71.4% (95% CI; 51. 3, 86.8). ORR was 35.7% (95% CI: 18.6, 55.9) including 2 CRs (7.1%) (CR, n=1; CRu, n=1) and 8 PRs (28.6%) (Table 1; Figure 1A). Median time to best response was 110.5 days. At the end of cycle 2). A correlation could not be made between efficacy, and gene translocation and cyclin D1 expression due to the small number of samples and lack of sufficient information on the biomarkers.

In the subgroup of patients who had received ≤3 prior therapies DCR was higher (84.2%; n=16; 95%CI: 60.4, 96.6) than those who received >3 prior therapies (44.4%; n=4; 95% CI: 13.7, 78.8). A similar trend was observed for ORR (47.4%; 95% CI: 24.5, 71.1 vs 11.1%; 95% CI: 0.3, 48.3), DoR (12.39 vs 6.67 months), PFS (12.85 vs 5.09 months) and OS (NR vs 8.18 months; Online Supplemental Table 2). Thus, abemaciclib was more clinically active in patients who had received ≤3 prior therapies than those who received higher numbers of prior therapies.

In patients who received temsirolimus, an mTOR inhibitor, as prior therapy (n=14), ORR was 14.3% (95% CI: 1.8, 42.8) vs 57.1% (95% CI: 28.9, 82.3) in those who did not receive temsirolimus. Dose reductions and dose omissions were reported for 78.6% and 75% of the patients, respectively. Median relative dose intensity was 71.5%. Median time to dose reduction was 28 days (range, 15-117) for those who had received ≤3 prior therapies and 15 days (range, 15-43) for patients who had received >3 prior therapies.

A c c e p t e d M a n u s c r i p t

Safety was assessed per Common Terminology Criteria for Adverse Events (CTCAE) v4.0.

The most frequent TEAEs of any grade were diarrhea, thrombocytopenia, fatigue and neutropenia (Table 2). Diarrhea was the most common TEAE and was reported by 75% of the patients with most (60.7%) experiencing low grade diarrhea (grade 1 or 2) in cycle 1. Grade 3 diarrhea occurred less frequently (14.3%). Per protocol, diarrhea was managed with over-thecounter medications, such as loperamide, or dose reduction. 12.5% of patients required dose reduction due to diarrhea, and no patient discontinued due to this adverse event. 50% of the patients who experienced diarrhea received anti-diarrheal medication (loperamide). Fatigue was also predominantly of low grade; grade 3 and 4 events were reported for thrombocytopenia (n=11) and neutropenia (n=9) and were likely related to study drug. A total of 42.9% of the patients reported at least 1 serious adverse event (SAE). 5 patients experienced grade ≥3 events, likely related to the study drug (n=1 each of lobar pneumonia and lung infection, dehydration and pyrexia, nausea, grade 5 sepsis, and somnolence). There were 5 fatal events reported that were considered by investigators as due to AEs (1 patient due to grade 5 meningitis that was unrelated to study drug, 1 patient due to grade 5 sepsis possibly related to study drug, 1 patient due to grade 4 sepsis unrelated to study drug, 1 patient due to grade 5 reversible posterior leukoencephalopathy unrelated to study drug, and I patient due to grade 3 lung infection possibly related to study drug; Online Supplemental Figure 3). PK evaluations included assessing plasma concentrations of abemaciclib and its metabolites by LC-MS method. The median abemaciclib t max after a single dose was 5.7 hours (range, 3.9-8.0 hours) (Figure 1B). The mean (coefficient of variation) steady-state abemaciclib trough concentration was 364 ng/mL (85%), indicating a high degree of interindividual variability in exposure. After single and multiple doses of abemaciclib, the mean accumulation ratio based on C max was 2.14 for abemaciclib and 3.91 to 5.17 for its metabolites, LSN2839567, LSN3106726, and LSN3106729 (Online Supplemental Table 3).

A c c e p t e d M a n u s c r i p t

In this single arm Phase II trial, abemaciclib monotherapy demonstrated clinical activity and a manageable safety profile in patients with R/R MCL. The ORR of 35.7% achieved with abemaciclib was similar to the 33% ORR with bortezomib 6 , 28% with lenalidomide, [START_REF] Goy | Single-agent lenalidomide in patients with mantle-cell lymphoma who relapsed or progressed after or were refractory to bortezomib: phase II MCL-001 (EMERGE) study[END_REF] and 47% with temsirolimus [START_REF] Rule | Ibrutinib versus temsirolimus: 3-year follow-up of patients with previously treated mantle cell lymphoma from the phase 3, international, randomized, open-label RAY study[END_REF] , which are approved agents for MCL treatment. This study did not investigate the effect of abemaciclib in patients who previously received BTK inhibitors or lenalidomide as these compounds were not approved at the time of enrollment; the results post temsirolimus, however, suggest a potential influence of prior pathway specific treatment. Compared to this, ORR was higher with BTK inhibitors; 81% with alacabrutinib [START_REF] Wang | Acalabrutinib in relapsed or refractory mantle cell lymphoma (ACE-LY-004): a single-arm, multicentre, phase 2 trial[END_REF] and 68% with ibrutinib [START_REF] Wang | Targeting BTK with ibrutinib in relapsed or refractory mantle-cell lymphoma[END_REF] . However, de novo or acquired resistance to BTK inhibition [START_REF] Zhao | Unification of de novo and acquired ibrutinib resistance in mantle cell lymphoma[END_REF] followed by uncontrolled growth of resistant MCL cells have led to poor prognosis. Therefore, the current challenge in the treatment of R/R MCL is to overcome the resistance to BTK inhibitors by choosing combination therapies targeting non-overlapping pathways.

Simultaneous inhibition of BTK and BCL2 with ibrutinib and venetoclax in a Phase II trial, improved patient outcomes at 16 weeks (CR: 42%) compared to historical controls at the same time point (9%). [START_REF] Tam | Ibrutinib plus Venetoclax for the Treatment of Mantle-Cell Lymphoma[END_REF] A CR of 37% was demonstrated in a Phase I trial of R/R MCL patients who were treated with a combination of ibrutinib and palbociclib. [START_REF] Martin | A Phase I Trial of Ibrutinib Plus Palbociclib in Previously Treated Mantle Cell Lymphoma[END_REF] Prolonging cell cycle arrest using a CDK4 & 6 inhibitor was reported to have reverted ibrutinib resistance. [START_REF] Chiron | Cell-cycle reprogramming for PI3K inhibition overrides a relapse-specific C481S BTK mutation revealed by longitudinal functional genomics in mantle cell lymphoma[END_REF] These data are promising and indicate that abemaciclib may have a potential role in the treatment of R/R MCL.

It is important to explore the CDK4 & 6 inhibitors in combination with BTK inhibitors with potential synergistic effects.

Previous PK assessments performed in Colo-205 xenograft tumors showed that continuous inhibition of CDK4 & 6 and the resulting cell-cycle arrest were associated with an abemaciclib plasma concentration of approximately 200 ng/mL. [START_REF] Tate | Semi-mechanistic pharmacokinetic/pharmacodynamic modeling of the antitumor activity of LY2835219, a new cyclin-dependent kinase 4/6 inhibitor, in mice bearing human tumor xenografts[END_REF] In this study, although the mean steady state trough abemaciclib plasma concentrations in patients were higher than the levels associated with durable cell cycle arrest in preclinical models, the range of the observed A c c e p t e d M a n u s c r i p t concentrations was consistent with patients with solid tumors. [START_REF] Tate | Semi-mechanistic pharmacokinetic/pharmacodynamic modeling of the antitumor activity of LY2835219, a new cyclin-dependent kinase 4/6 inhibitor, in mice bearing human tumor xenografts[END_REF] Similar to abemaciclib, its major metabolites, LSN2839567 and LSN3106726, also inhibit CDK4 & 6 with similar potencies in in vitro biochemical and cell-based assays and the metabolite exposure achieved in patients with MCL at a dosage of 200 mg twice daily exceeds the 50% inhibition concentration (IC 50 ) for CDK4/cyclin D1 and CDK6/cyclin D1. [START_REF] Burke | Abstract 2830: The major human metabolites of abemaciclib are inhibitors of CDK4 and CDK6[END_REF] Thus, the exposure of abemaciclib and its active metabolites is consistent with what is expected to yield biological activity. However, the optimal abemaciclib dose in MCL based on the relationship between exposure, efficacy, and safety requires further elucidation.

In conclusion, this study demonstrated that single-agent abemaciclib dosed on a continuous schedule has clinical activity in patients with R/R MCL who received multiple prior systemic therapies. The safety profile of abemaciclib in this patient group is generally consistent with other abemaciclib studies on advanced breast cancer except for higher thrombocytopenia. persistent or recurrent grade 2 nonhematologic toxicity that did not resolve to baseline or grade 1 within 7 days with supportive care, dose can be reduced or suspended. Supportive care and concomitant medications were allowed. Any concurring anticancer therapy was not allowed.

Efficacy and safety measurements

Radiological tumor assessments were made by computed tomography (CT) and magnetic resonance imaging (MRI) at baseline (≤28 days before the first dosing of abemaciclib) and at the end of every 2 cycles for the initial 6 cycles and thereafter at the end of every 3 cycles until objective progression was observed. Patient's survival status was followed until death or study completion.

Pharmacokinetics

For PK evaluations, blood samples were collected on Days 1 and 15 pre-dose and 1, 2, 4, 6, and 8 hours post-dose. Plasma concentrations of abemaciclib and its metabolites were determined using a validated LC-MS method (Charles River Laboratories, Montreal, Canada).

Maximum concentration (Cmax), time of maximum concentration (t max ), steady state trough concentration (C trough ), area under the concentration-time curve from time zero until the last observed concentration (AUC 0-last ), and accumulation ratio based on C max were computed by non-compartmental methods using WinNonlin Professional Edition.

Statistical methods

The study tested the assumption that the true DCR was significantly different from a prespecified null DCR (25%). If the observed DCR was 50%, then a sample size of 20 patients was estimated to provide a 95% confidence interval (CI) that the DCR will be between 27% and 73%

A c c e p t e d M a n u s c r i p t 3

 3 Primary objective was disease control rate (DCR) based on the Response Criteria for NHL

  Additional clinical trials of abemaciclib in combination with current preferred therapies such as a BTK inhibitors are needed to determine the synergistic effects and positioning of CDK4 & 6 inhibitors in MCL.

  Abbreviations: C max = maximum observed plasma concentration; t max = time of maximum observed drug concentration; AUC(0-last) = area under the concentration time curve from time 0 to last observed concentration; C trough = observed plasma concentration prior to next dose; RA, C max = accumulation ratio based on C max ; n = number of observations a Median and range b In multiple dose, PK values were calculated on days 12 (n=1), 14 (n=10), 15 (n=9), or 16 (n=1) c n=21 A c c e p t e d

Table 1 . Summary of Overall best response

 1

	Best Overall Response	Abemaciclib (N=28), n (%) (95% CI)
	Disease control rate (CR+CRu+PR+SD)	20 (71.4) (51.3, 86.8)
	Overall response rate (CR+CRu+PR)	10 (35.7) (18.6, 55.9)
	Complete response (CR)	1 (3.6) (0.1, 18.3)
	Complete response unconfirmed (CRu)	1 (3.6) (0.1, 18.3)
	Partial response (cPR)	8 (28.6) (13.2, 48.7)
	Stable disease (SD)	10 (35.7) (18.6, 55.9)
	Progressive disease, n (%) (95% CI)	2.0 (11.8) (0.9, 23.5)
	Not assessed, a n (%)	6.0 (21.4)
	Time to events	Abemaciclib (N=28), n (%) (95% CI)
	Median progression-free survival, months (95% CI) 8.2 (4.34, 16.03) b
	Median overall survival, months (95% CI)	16.0 (6.77, NR)

c a Patients without post-baseline tumor assessment values at the time of data base lock b Number of PFS events were 19 c Number of OS events were 17

Table 2 . Treatment-emergent adverse events

 2 Anti-tumor Activity and Pharmacokinetics of abemaciclib. A. Change in Tumor Size at Best Response. Best overall response was based on investigator assessment. Number above or below each bar is the number of treatment regimens prior to study entry. Cyclin D1 expression and t(11;14)(q13;q32) translocation in each patient is shown below the response. Abbreviations: CR, complete response; CRu, complete response unconfirmed; PD, progressive disease; PR, partial response; SD, stable disease. B. Abemaciclib plasma concentration-time profiles following oral administration of single (left panel) and multiple (right panel) doses of 200 mg abemaciclib every 12 hours, depicted as individual (gray continuous lines) and geometric mean (black broken line).

	Events occurring in ≥20% of patients (N=28) Diarrhea Thrombocytopenia	All Grades n (%) 21 (75.0) 14 (50.0) M Grade 1 n (%) 7 (25.0) 2 (7.1) a n u s c r i p t Grade 2 n (%) Grade 3 n (%) Grade 4 n (%) 10 (35.7) 4 (14.3) 0 1 (3.6) 6 (21.4) 5 (17.9)
	Fatigue	12 (42.9)	4 (14.3)	7 (25.0)	1 (3.6)	0
	Neutropenia Anemia Nausea Vomiting Creatinine increased A c c e p t e d 11 (39.3) 10 (35.7) 9 (32.1) 8 (28.6) 7 (25.0)	0 2 (7.1) 6 (21.4) 6 (21.4) 3 (10.7)	2 (7.1) 6 (21.4) 1 (3.6) 2 (7.1) 3 (10.7)	2 (7.1) 1 (3.6) 2 (7.1) 0 1 (3.6)	7 (25.0) 2 (7.1) 0 0 0

Table 3 . Pharmacokinetics of abemaciclib and its metabolites in relapsed or refractory MCL Geometric Mean (CV%)

 3 25% or lower DCR. DCR and its 95% CI were estimated using the Clopper-Pearson method. DoR, PFS, and OS were analyzed using Kaplan-Meier methods.

	M a n u s c r i p t
	A c c e p t e d

Acknowledgements

This study was funded by Eli Lilly and company. The authors thank the investigators and staff who conducted this study, and the patients and their families for their participation. Nirmala Xavier, employee of Eli Lilly and Company, provided medical writing support for this manuscript.

Supplemental Methods

Patients

Patients ≥18 years of age with R/R MCL to standard therapy were eligible. Additional inclusion criteria included assessable disease based on the Response Criteria for NHL [START_REF] Chiron | Cell-cycle reprogramming for PI3K inhibition overrides a relapse-specific C481S BTK mutation revealed by longitudinal functional genomics in mantle cell lymphoma[END_REF] , an Eastern Cooperative Oncology Group performance status (ECOG PS) score ≤2 and adequate organ function (absolute neutrophil count ≥1.5 × 10 9 /L, platelets ≥75 × 10 9 /L, hemoglobin ≥8 g/dL, bilirubin ≤1.5 times upper limits of normal [ULN], alanine aminotransferase ≤3 times ULN, aspartate aminotransferase ≤ 3 times ULN, and estimated creatinine clearance ≥50 ml/min). [START_REF] Tate | Semi-mechanistic pharmacokinetic/pharmacodynamic modeling of the antitumor activity of LY2835219, a new cyclin-dependent kinase 4/6 inhibitor, in mice bearing human tumor xenografts[END_REF] Key exclusion criteria included any serious medical condition that precluded participation, symptomatic CNS metastasis, recipient of autologous or allogenic stem-cell transplant ≤75 days prior to receiving treatment, pregnant or lactating female patients, and the presence of any active infection. The institutional review boards of the participating institutions approved the study protocol. Written informed consent was obtained from all participants before entering the study, and ethical principles of the Declaration of Helsinki and Good Clinical Practice were followed.

Study design

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Elisabeth Pereira

Sophie Faure

David J Aitken

Photochemical behaviour of 5-formyl and 5-acetyl uracils in the presence of ethene

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