 Research
 Open Access
New delayefficient TDMAbased distributed schedule in wireless mesh networks
 JaeHyun Kim^{1}Email author,
 JaeRyong Cha^{1} and
 HanJoon Park^{1}
https://doi.org/10.1186/168714992012369
© Kim et al.; licensee Springer. 2012
Received: 4 June 2012
Accepted: 5 November 2012
Published: 26 December 2012
Abstract
Time division multiple access (TDMA)based medium access control (MAC) protocols can guarantee quality of service (QoS) in wireless environments. However, in an environment where multihop packet transmissions are necessary for realtime communications, each node may experience the wellknown queuing delay. This queuing delay increases multihop packet transmission delay, resulting in not meeting the delay bound of realtime applications in multihop wireless networks. This article first introduces two kinds of queuing delays that can occur in multihop wireless networks. Then, this article proposes a new delayefficient TDMAbased distributed scheduling scheme to eliminate the secondary queuing delay. For the performance analysis of the proposed scheme, the scheduling overhead is first evaluated in terms of power consumption. Next, the multihop packet transmission delay of the proposed scheduling scheme is derived and validated through a simulation, before comparing the result with that of the conventional minimum length scheduling scheme which employs distance2 graph coloring. According to the simulation and analysis results, for a deterministic packet arrival, the proposed scheme works well irrespective of the packet interarrival rate and outperforms the conventional graph coloring. However, in case of a nondeterministic packet arrival, the multihop packet transmission delay of the proposed scheme is slightly higher than that of the conventional graph coloring because the probability that each node has more than two packets increases at the beginning of the frame. However, the multihop packet transmission delay of the conventional graph coloring is intolerable when the packet interarrival rate is high.
Keywords
1 Introduction
Wireless mesh networks (WMNs) are emerging communication networks consisting of nodes that automatically establish an adhoc network and maintain mesh connectivity. Because of their advantages over other wireless networks, WMNs are progressing rapidly and are inspiring numerous applications in commercial and tactical environments. With the popularity of WMNs, supporting quality of service (QoS) over multihop radio links is becoming an issue because multihop packet transmission delay increases quickly with the increase in the number of hops [1]. Previous studies on WMNs have mostly been studied based on 802.11 wireless local area networks (WLANs). One of the major drawbacks of such networks is that it is difficult for them to support QoS, which is essential for supporting realtime applications, particularly in multihop wireless networks. This is because packet transmission delay is accumulated at each hop on a path. Meanwhile, scheduling schemes based on time division multiple access (TDMA) have been proposed for WMNs. Most TDMA scheduling schemes [2–13] for WMNs have been proposed for determining the minimum length schedules. However, although such schemes reduce the frame length, they may bring about queuing delay, which can increase the multihop packet transmission delay in WMNs.
Recently, TDMAbased QoSaware scheduling schemes [14–19] have been proposed for supporting various applications such as voice and video calls in WMNs. However, these schemes necessarily need a centralized base station for achieving their goals, such as a minimum length schedule considering the scheduling delay, delayconstrained schedule of flows, and link activation schedule to bound endtoend delay [1]. Brief descriptions of these schemes are presented in the following section. Therefore, this article proposes a new delay efficient TDMAbased distributed scheduling scheme for eliminating secondary queuing delay, which is defined in subsequent sections, and for ultimately reducing the multihop packet transmission delay in WMNs.
2 Related study
This section introduces conventional studies related to the TDMAbased QoSaware scheduling scheme. Recently, various TDMAbased QoS awarescheduling schemes have been introduced for WMNs [1].
In [14], the authors schedule different types of flows for satisfying bandwidth and delay requirements. In the first phase, the algorithm attempts to allocate interferencefree slots (using multiple channels) to a flow based on the maximum bandwidth requirement of the flow. The second phase is invoked for a flow if the first phase fails to allocate sufficient slots to satisfy even the minimum bandwidth requirement.
In the mechanism proposed in [15], first, a given network is transformed into a conflict graph whose vertices represent links and there is an edge between two vertices if two links conflict (interfere) with each other. Determining the order of transmission, in such a conflict graph, for a conflictfree TDMA schedule with minimum scheduling delay is NPcomplete. Therefore, the authors formulate this problem as a linear programming optimization problem. Given the minimum scheduling interval and relative activation times, the authors show how to determine the minimum length TDMA schedule (actual assignment of links to slots) in polynomial time.
To prevent computational complexity of the optimum solution, the authors in [16] have proposed a ‘bottleneck first scheduling’(BFS) scheme, where scheduling decisions at stations having higher traffic loads are made before those having lower traffic loads. At each station, scheduling decisions for constant bit rate (CBR) packets with more hops to their destinations are made first. Through simulations, the authors show that the delay of BFS is better than ‘earlier deadline first’ (EDF) and ‘first come first serve’ (FCFS) scheduling.
In the mechanism proposed in [17], the nodes (and thus links) in the network are first labeled either even or odd (twoslot scheduling). Then, while determining paths, only those paths that go through nodes having alternate labeling are considered. Using subchannelization of OFDMA, secondary interference between two links in the same slot is prevented by assigning different channels to the links. Once the slot requirements and routing paths are determined, each node employs a local (wirelinetype) scheduling policy. The scheduling policy determines the order in which packets leave the buffer at each node, and the authors show that such a mechanism provides twoapproximation bounds for the endtoend delay. The problem of finding feasible routes (to and from gateway to network nodes) in an evenodd labeled (tree) network is formulated as a linear program and heuristics using Dijkstra’s shortest path algorithm have been proposed.
The authors of [18] have proposed a ‘loadbalanced weighted shortest path with a retry’ routing heuristic. In this heuristic, first, the shortesthop algorithm is used to determine a path. If one or more edges on the path are blocked, those are removed from the graph and the heuristic is applied again to find a suitable path. Next, a call admission control (CAC) algorithm is applied which considers the unsolicited grant service/realtime polling service in WiMAX. To manage the jitter value of a connection, the path from a source node to a destination node is partitioned into two segments;one segment is from the source to the penultimate node (the node just before the destination), and the other segment is the link between the penultimate node and the destination. The delay requirement is that the total delay on both the segments should be less than the delay constraint. Because of the split, to ensure the jitter constraint of the path, the scheduler only needs to look at the second segment between penultimate node and destination. This is achieved by fixing an offset value and scheduling the packets within the limit of the jitter grant interval.
In [19], an online algorithm that works in three phases has been proposed. In the first phase, the algorithm constructs an auxiliary graph from the given topology graph. A vertex in the auxiliary graph is a fourparameter tuple of the form (node, slot, channel, hop). An edge is formed between two vertices if a set of rules is satisfied. The rules model the interference and delay constraints. In the second phase, Dijkstra’s shortest path algorithm is run to output the delayconstrained schedule while finding a routing path, assigning a channel, and scheduling links in the process. In the third phase, an unfavorable schedule is filtered to incorporate an arbitrary interference graph. The authors compare this algorithm with an offline optimal solution and show that it accepts around 90% of the calls with respect to the optimal solution.
3 System model
In this article, we model WMNs with a topology graph connecting the nodes that are present in each other’s wireless range. The network can be represented with a directed connectivity graph G(B,E) , where B={b_{1},…,b_{ m }} is a set of nodes and E={e_{1},…,e_{ g }}is a set of directed links, and two nodes (u and v) are neighbors if (u,v)∈E . In the network, F is a set of flows, and a flow f(∈F) is specified by a node set R(f)={p_{1},…,p_{ q }}, where p_{ k } is the k th node in a flow (2≤q ; k=1 : the source node, 1<k<q : the intermediate node(s), and k=q: the destination node).
4 Queuing delay in multihop wireless networks
In this section, we describe two main factors that cause an increase in the multihop packet transmission delay in multihop wireless networks. In previous studies [2–13], TDMA scheduling is generally used to determine the minimum length schedules. However, such schedules may cause additional queuing delays, which have a negative influence on delaysensitive networks. The QoS of realtime applications in multihop wireless networks may not be guaranteed if additional queuing delays occur.
For example, in Figure 1, multiple flows pass through the Node R1toR2 link. These flows share a slot for transferring packets. Assume that the network employs the minimum length schedule. Then, Node R1 allocates only one slot for transferring packets to node R2. It is also assumed that Node S1 and Node S2 are supposed to send a packet to Node R1 in the 1^{st} slot and the 2^{nd}slot, respectively. Moreover, Node R1 is scheduled to send a packet to Node R2 in the 3^{rd} slot. It is also assumed that, in each node, the arrival of a packet from application layer is concurrent with the start of a frame. In the 3^{rd}slot in the frame, Node R1 has two packets to send:one from Node S1 and another from Node S2. However, Node R1 can transfer the packet received from node S1 in the current frame and can transfer the packet received from Node S2 in the next frame because it can transfer only one packet per link in a frame as prescribed by the minimum length schedule. In conclusion, the minimum length schedule may work well in singlehop wireless networks with high throughput and short delay. However, in multihop wireless networks, it may cause secondary queuing delay because only one common slot is allocated for multiple flows.
Therefore, this article proposes a new distributed scheduling scheme to eliminate the secondary queuing delay, thereby ultimately reducing the multihop packet transmission delay.
5 Proposed scheduling scheme
In this section, the operational procedures for the proposed scheduling scheme are described in detail. The operational procedures are classified into two phases: Phase I and Phase II. In Phase I, each node obtains paths using the adhoc ondemand distance vector (AODV) routing protocol [20] and gathers the information on its onehop neighbors. These two tasks are also performed in the conventional schemes [9, 21] prior to the TDMA scheduling, although both the routing algorithms and the approaches for obtaining the neighbor information are slightly different. Moreover, these tasks are generally excluded during the overhead analysis in the conventional tasks, as these tasks are considered as input parameters for scheduling. Therefore, we also exclude Phase I during the overhead analysis for performance comparison with the conventional schemes. However, we have performed these tasks during the simulation.
On the other hand, Phase II involves three steps for slot allocation: an initial frame length synchronization (IFLS) process, a multihop slot allocation (MSA) process, and a global frame length synchronization (GFLS). First, IFLS determines the initial frame length L_{init}, which can be used initially for slot allocation in the network. Second, the MSA process allocates a different slot to each flow in a link to eliminate the secondary queuing delay. For example, in Figure 1, two flows exist between Node R1 and Node R2. Therefore, the proposed scheme allocates two different slots for two flows in the Node R1toR2 link. Although such a slot allocation can eliminate the secondary queuing delay, it results in a large frame length. In such a case, it is important to consider the order of the slots allocated on a path. Therefore, we show the delay effect by an allocation order as well as demonstrate the manner in which slots should be allocated sequentially in a flow after the routing path is established.
Meanwhile, the multihop nature of WMNs allows spatial reuse of the TDMA slots. Different nodes can use the same time slot if they do not interfere with each other [22]. Finally, after the MSA process, we obtain the minimum frame length, which can be used globally in the network. After all three processes are completed, all the nodes in the network transfer packets in their allocated slots. This article describes the details of Phase II from the following section onward. The description of two tasks performed in Phase I is not included, because it is beyond the scope of this article as mentioned before.
5.1 Initial frame length synchronization: IFLS
where N is the total number of nodes in the network. Once initial frame length synchronization is completed, then each node carries out the MSA process using the same initial frame length L_{init}.
5.2 Multihop slot allocation: MSA
In this section, we describe the proposed MSA process in detail. First, we assume that each node follows global slot synchronization. Thus, all nodes know the starting time of each frame. Before the description of the proposed MSA process, we first introduce the delay effect caused by an allocation sequence of TDMA slots and show that the allocation sequence in a flow is critical for reducing the multihop packet transmission delay in an environment where a node allocates a different slot to each flow in a link.
5.2.1 Delay effect produced by an allocation sequence
Proof
□
5.2.2 MSA process
To efficiently describe the proposed MSA process, we show two types of examples using an algorithm and a figure. To carry out the proposed MSA process, three packets are used: a map request (MA P_{REQ}) packet, a map response (MAP_{REP}) packet, and a slot allocation (SA) packet. The MAP_{REQ}and MAP_{REP}packets are used by a node to request the frame map of its neighbors and to respond to the request, respectively. The SA packet is employed for transferring the information on the allocated slot index to the next node. The followings are some terminologies used for describing the proposed MSA process.

forward/reverse path: path to the destination/source node.

TN/RN: a transmitting node and a corresponding receiving node in an allocated slot.

Allocated Slot Index: the slot index allocated.

next node: a neighbor peer node to the destination node in a forward path.

MAC_{NEXT}: medium access control (MAC) address of a next node.

MAC_{SOURCE}: MAC address of a source node.

MAC_{DESTINATION}: MAC address of a destination node.
Field size of packets used for the proposed MSA process
Fields  Size (bits) 

MAP_{REQ} ID  8 
MAP_{REP} ID  8 
SA ID  8 
MAC_{NEXT}  48 
Allocated Slot Index  16 
Algorithm 1 shows the proposed MSA process initiated by a source node. Further, Algorithm 2 shows the proposed MSA process when either an intermediate node or a destination node receives an SA packet from node p_{ k }(1≤k<q,q≥2) in a forward path. An intermediate node or a destination node invokes Algorithm 2 whenever it receives an SA packet wherein MAC_{NEXT}is equal to its MAC address. In Algorithm 2, when an intermediate node allocates the slot(s) as a TN, it is very important for the intermediate node to reserve the righthand side slot for comparison with the Allocated Slot Index within the SA packet received, such that multihop links can be scheduled sequentially on a path.
Algorithm 1
MSA in a source node
1: if k=1then
2: p_{1}first obtains frame maps of its onehop neighbors by exchanging MAP_{REQ}and MAP_{REP}packets.
3: p_{1}allocates the commonly available slot(s) for both p_{1}and p_{2}as a TN.
4: p_{1}transfers the SA packet with Allocated Slot Index to p_{2}.
5: end if
Algorithm 2
MSA in an intermediate/a destination node
1: if 1<k<q then
2: Based on the received Allocated Slot Index, p_{ k }allocates the slot(s) for both p_{k−1}and p_{ k }as anRN.
3: Then, p_{ k }obtains the frame map of its onehop neighbors by exchanging MAP_{REQ}and MAP_{REP}packets.
4: p_{ k }allocates the commonly available slot(s) for both p_{ k }and p_{k + 1}as a TN.
5: p_{ k }transfers the SA packet with Allocated Slot Index to p_{k + 1}.
6: else if k=q then
7: Based on the received Allocated Slot Index, p_{ q }allocates the slot(s) for both p_{q−1}and p_{ q }as anRN.
8: end if
In each frame in Figure 6, the gray slots are those that have already been allocated by other flows. First, p_{1} obtains the map information of its neighbors by exchanging MAP_{REQ}and MAP_{REP}. Then, p_{1} assigns the 2^{nd} slot as a TN and then sends SA {MAC_{NEXT},Allocated Slot Index}to p_{2}. When p_{2} receives SA {p_{2},2} from p_{1}, it assigns the same 2^{nd} slot as an RN. Second, for communication between p_{2}and p_{3}, p_{2} assigns the 3^{rd}slot as a TN after it obtains the map information from its onehop neighbors. Then, p_{2} sends SA {p_{3},3} to p_{3}. Next, for communication between p_{3}and p_{4}, p_{3} first assigns the 5th slot as a TN after it obtains the map information from its onehop neighbors. After finishing the slot allocation, p_{3} sends SA {p_{4},5} to p_{4}. Finally, the destination node p_{4}assigns the 5th slot as an RN. After the proposed MSA process is completed, the map status of p_{1}, p_{2}, p_{3}, and p_{4} beomes ‘11000’, ‘01100’, ‘00111’, and ‘00001’, respectively.
5.3 Global frame length synchronization: GFLS
In this study, all the nodes undergoing the proposed MSA process employ the initial frame length L_{init}. L_{init} is calculated as the upper bound of the affordable frame length. After the proposed MSA process is completed, the frame length of all the nodes may be less than L_{init} because of slot reuse in the TDMA system [22]. Therefore, L_{init}needs to be reduced for efficiency. In the proposed MSA process, the slots are always allocated from each sourcenode side in a flow. Therefore, the slot index allocated by the destination node is the highest one in the flow. After the proposed MSA process is completed, all the destination nodes broadcast that slot index. If a destination node is related to multiple flows, the highest slot index among the slot indices allocated by the destination is broadcast. If a node hears a higher slot index than the one it currently knows, it rebroadcasts the new index. After some predetermined dissemination time, all the nodes calculate the global frame length on the basis of the highest slot index they learns, i.e., the global frame length L_{proposed}=the highest slot index. Subsequently, all the nodes adjust their frame length to L_{proposed}.
6 Performance analysis
6.1 Overhead analysis
In this section, we evaluate the overhead of the proposed MSA process in terms of the power consumed for the scheduling by all the nodes in the network. The proposed scheme gets the map information of its onehop neighbors in each hop on the path before transferring the SA packet to the next node. Considering all the possible combinations, we find that the total power consumed for scheduling, P_{total}, consists of the following two components.

P_{MAP}: power consumed for exchanging map information by all the nodes.

P_{SA}: power consumed for transferring SA packets by all the nodes.
In Equation (5), N denotes the total number of nodes; h(i), the total number of hops obtained by the i th source node to transfer its packet to its destination node; δ, the onehop degree in a node which means the number of onehop neighbors; l_{REQ}, the length of the MAP_{REQ} packet; l_{MAC + PHY}, the sum of the overhead in MAC and physical (PHY) layers; l_{total−REQ}, the sum of l_{REQ}and l_{MAC} + PHY; and l_{ACK}, the length of the acknowledgement (ACK) packet. Further, p_{tx}denotes the energy spent in transmitting a bit over a distance of 1meter, and p_{rx} denotes the energy spent in receiving a bit.
where l_{REP} denotes the length of the MAP_{REP}packet and l_{total−REP} is the sum of l_{REP}and l_{MAC} + PHY.
6.2 Analysis of multihop packet transmission delay
In this section, we derive the average multihop packet transmission delay of the proposed scheduling scheme.
where ρ=λ·T_{ M }. If we consider a deterministic packet arrival and a deterministic service time, then W_{ q } is equal to zero [15, 23].
7 Performance evaluation
In this study, we compare the delay performance of the proposed scheme with that of the conventional scheme that uses distance2 graph coloring. Distance1 graph coloring causes the wellknown hidden node problem [9, 21]. Therefore, it is excluded in this article.
7.1 Simulation scenarios
For the performance evaluation, two scenarios are considered. In Scenario # 1, we simulate five grid networks to evaluate the delay effect produced by the secondary queuing delay. In Scenario # 2, a grid network and a random network are simulated for the performance comparison of both the proposed scheduling scheme and the conventional graph coloring. In Scenario # 2, as a consideration of primary queuing delay, we also consider both a deterministic packet arrival (DPA) and a nondeterministic packet arrival (NONDPA) having exponential distribution. These two cases are considered for observing the behavior for both nonconstant and constant packet interarrival characteristics.
7.1.1 Scenario #1
This article simulates X by X grid networks, where X is set to 3, 4, 5, 6, and 7 to observe the queuing behavior of distance2 graph coloring when only one packet is transferred from each source node. In this network, the vertical and horizontal distances between two adjacent nodes are 30 m, and the communication range of each node is 30 m. After each node allocates slots by distance2 graph coloring, each source node transfers one packet in its allocated slot. If any intermediate nodes receive packets from the previous node on the path, they transmit the received packet in the allocated slot. This study considers ten different seeds for this scenario, and their simulation results are averaged.
7.1.2 Scenario #2
To compare the performance of the proposed scheduling scheme with that of the conventional scheme using distance2 graph coloring as carried out in [15], this study simulates two TDMA networks with different topologies. One is the X by X grid network, where X is set as 7. In the grid network, the vertical and horizontal distances between two adjacent nodes are 30 m. The other is the network with 100 nodes randomly distributed in a square area of 200 × 200 m. In both networks, the communication range of each node is 30 m. As soon as all the source nodes complete the proposed MSA process successfully, they generate packets before transmitting them in the allocated slot. If intermediate nodes receive packets from the previous node on the path, they transmit the received packets in the allocated slot for each flow. For the grid network, this study considers five different seeds. In case of random topologies, this study considers ten different random topologies and their simulation results are averaged.
Some preliminary results
Grid network  Random network  

unit slot time  (N=49)0.001 s  (N=100)0.001 s 
L _{coloring}  21  88 
L _{init}  196  440 
L _{proposed}  75  200 
onehop degree  3.35  7.5 
twohop degree  5.67  11.9 
h  4  4.4 
7.2 Numerical and simulation results and discussions
In this section, we first discuss the results of overhead analysis. Next, the simulation results from Scenario # 1 are discussed. Finally, the simulation results from Scenario # 2and the related analysis results are discussed.
7.2.1 Results from the overhead evaluation
Parameter for overhead calculation
Parameters  Value (bits) 

l_{MAC} + PHY  496 
l _{ACK}  496 
l _{REQ}  8 
l _{REP}  8 + L_{proposed} 
l _{SA}  8 + 48 + 8 
l_{total}−REQ  l_{MAC} + PHY + l_{REQ} 
l_{total}−REP  l_{MAC} + PHY + l_{REP} 
l_{total}−SA  l_{MAC} + PHY + l_{SA} 
MSA overhead: power consumption
49 nodes (Joules)  100 nodes (Joules)  

P_{MAP}−REQ  0.1120  1.2474 
P_{MAP}−REP  0.1203  1.4967 
P _{SA}  0.0356  0.1769 
P _{total}  0.2679  2.9210 
7.2.2 Results from scenario #1
Some preliminary results in graph coloring
# of nodes  9  16  25  36  49 

L _{coloring}  6  7  18  21  22 
h  1.44  2.13  2.72  3.22  4.10 
frame delay  2.2  3.5  5.7  7.5  9.4 
7.2.3 Results from scenario #2
In case of DPA, both scheduling schemes show a stable performance except in the intolerable cases. However, the proposed scheduling scheme shows a shorter multihop packet transmission delay, even though it starts the packet transmission with slightly greater frame length than that in case of graph coloring. As mentioned before, graph coloring shares slots (resources) for multiple flows in a link [9]. Therefore, an increase in the frame delay caused by the secondary queuing delay causes an increase in the multihop packet transmission delay. For the NONDPA case, the proposed scheme shows slightly longer multihop packet transmission delay. The proposed scheduling scheme is more efficient when there is only one packet waiting for the packet transmission at the beginning of each frame. If there are more than two packets at the beginning of each frame, then all packets but one packet to be transferred in the current frame experience a long delay because of long frame length. When considering the NONDPA case in the source node, each source node has the chance to see more than two packets; that is, the primary queuing delay may occur. Therefore, the proposed scheduling scheme shows a slightly lower delay performance for the NONDPA case. However, the proposed scheme is more tolerable for a high packet interarrival rate than graph coloring.
8 Conclusions
This article proposed a new delayefficient TDMAbased distributed scheduling scheme to eliminate the secondary queuing delay, which may occur in the conventional minimum length scheduling schemes. We derived the multihop packet transmission delay of the proposed scheduling scheme and validated it through a simulation. Finally, we compared the performance of the proposed scheme with that of the conventional minimum length scheduling scheme that employs distance2 graph coloring. The important contributions of this study are as follows:

An intuitive method for eliminating the secondary queuing delay.

Analysis of the delay effect caused by an allocation sequence of the TDMA slots.

A distributed method to sequentially allocate slots on a path.

Analysis of the proposed scheme and its simulation.
According to the simulation and analysis results, for the DPA case, the proposed scheme works well irrespective of the packet interarrival rate and outperforms the conventional graph coloring. However, in case of NONDPA, the multihop packet transmission delay of the proposed scheme is slightly longer than that of the conventional graph coloring because the probability that each node has more than two packets increases at the beginning of the frame. However, the proposed scheduling scheme is more tolerant for a high packet interarrival rate.
9 Future study
In the future studies, first, we intent to extend the proposed scheduling scheme to an autonomous environment where either new nodes can efficiently assign time slots or existing nodes can release their slots on a path in a distributed manner. Second, the proposed scheme has the characteristics that each node allocates a different slot to each flow in a link. Therefore, it needs lots of slots; however, the distance2 coloring leads to slightly smaller frame length because each node allocates one common slot for multiple flows in a link. This study have considered a situation wherein each node has only one flow. However, it is somewhat unrealistic. If two flows are considered per node, the frame length of the proposed scheme is up to two times greater than that when considering one flow per node. Accordingly, we are also interested in reducing the frame size and in concurrently reducing the network load by using conventional network coding (NC) schemes.
Declarations
Acknowledgements
“This research was supported by the Ministry of Knowledge Economy (MKE), Korea, under the Information Technology Research Center (ITRC) support program supervised by the National IT Industry Promotion Agency (NIPA)” (NIPA2012(C109012210011)), “This study had been supported by National GNSS Research Center program of Defense Acquisition Program Administration and Agency for Defense Development”.
Authors’ Affiliations
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