Fair TDMA scheduling in wireless multihop networks - Amazon Web ...

Telecommun Syst DOI 10.1007/s11235-010-9397-9

Fair TDMA scheduling in wireless multihop networks Dimitrios J. Vergados · Aggeliki Sgora · Dimitrios D. Vergados · Demosthenes Vouyioukas · Ioannis Anagnostopoulos

© Springer Science+Business Media, LLC 2010

Abstract In wireless multihop networks, communication between two end-nodes is carried out by hopping over multiple wireless links. However, the fact that each node has to transmit not only its own traffic, but also traffic on behalf of other nodes, leads to unfairness among the communication rates of the nodes. Traditional Carrier Sense Multiple Access/Collision Avoidance (CSMA/CA) based media access control does not work satisfactory in a multi-

D.J. Vergados School of Electrical and Computer Engineering, National Technical University of Athens, 7, Iroon Polytexneiou St., Zografou, 157 73 Athens, Greece e-mail: [email protected] A. Sgora · D.D. Vergados · D. Vouyioukas · I. Anagnostopoulos Department of Information and Communication Systems Engineering, University of the Aegean, 832 00 Karlovassi, Samos, Greece A. Sgora e-mail: [email protected] D.D. Vergados e-mail: [email protected] D. Vouyioukas e-mail: [email protected] I. Anagnostopoulos e-mail: [email protected] D.D. Vergados () Department of Informatics, University of Piraeus, 80, Karaoli & Dimitriou St., 185 34 Piraeus, Greece e-mail: [email protected] I. Anagnostopoulos Department of Computer Science and Biomedical Informatics, University of Central Greece, 2-4, Papasiopoulou St., 35100 Lamia, Greece e-mail: [email protected]

hop scenario, since an intended target of a communication may be subject to mutual interference imposed by concurrent transmissions from nodes, which cannot directly sense each other, thus causing unfair throughput allocation. Although Time Division Multiple Access (TDMA) seems to be a more promising solution, careful transmission scheduling is needed in order to achieve error-free communication and fairness. Several algorithms may be found in the literature for scheduling TDMA transmissions in wireless multihop networks. Their main goal is to determine the optimal scheduling, in order to increase the capacity and reduce the delay for a given network topology, though they do not consider the traffic requirements of the active flows of the multihop network or fairness issues. In this paper, we propose a joint TDMA scheduling/load balancing algorithm, called Load-Balanced-Fair Flow Vector Scheduling Algorithm (LB-FFVSA). This algorithm schedules the transmissions in a fair manner, in terms of throughput per connection, taking into account the communication requirements of the active flows of the network. Simulation results show that the proposed algorithm achieves improved performance compared to other solutions, not only in terms of fairness, but also in terms of throughput. Moreover, it was proved that when a load balancing technique is used, the performance of the scheduling algorithm is further improved. Keywords Wireless multihop network · Fairness · Load balancing · TDMA scheduling 1 Introduction Wireless multihop networks are formed by a set of nodes, where communication between two-end nodes is carried out by hopping over multiple short wireless links. In such a network, each node has to send/receive packets to/from adja-

D.J. Vergados et al.

cent nodes. Nodes also forward packets on behalf of other nodes, acting as a router. However, since a node has not only to transmit its own generated traffic but also the relayed one, unfairness may be observed, especially for transmissions among nodes that are more than one-hop away. The first reason responsible for this unfairness is the network topology. The multihop nature of the network results in diverse distances among the sources and the destinations. Therefore, a small number of flows require one transmission from source to destination, while other flows require multiple retransmissions, causing increased delays. Consequently, some flows present longer delay times than others, resulting in unfairness. The second unfairness factor is related to the medium access control protocols. The medium access protocols, which are currently used in multihop networks, were initially designed for single-hop networks. Therefore, their primary goal is to define the order of transmissions that will occur when a number of wireless stations compete for channel access. The result of this procedure is an equally shared timeslot, where each competing wireless station has the same transmission probability. However, a packet that requires several retransmissions from source to destination will be involved in multiple channel access contentions. The great number of contentions may result in increased delays or even higher packet loss and therefore unfairness is introduced, especially for lengthier flows that require more retransmissions. Thus, the end-to-end delay times and the packet loss probabilities are significantly larger than the other ones that require fewer retransmissions. The third reason that generates unfairness in multihop networks is the spatial-temporal variation of the congestion levels in the network. As stated earlier, in single hop networks, each wireless station competes to every other one for access to the channel and as long as there is only one channel available, two simultaneous transmissions are not possible. Thus, the traffic, which is generated by all nodes in the single hop network, influences the performance of each station. This means that a single congestion level is perceived throughout the network. However in wireless multihop networks, simultaneous transmissions in different parts of the network are possible. Therefore, some traffic flows will perceive the network to be highly congested, whereas at the same time, other traffic flows will perceive it to be noncongested. Consequently, the latter traffic flows yield lower delay times, decreased packet loss and more available bandwidth in comparison with the former ones, increasing the unfairness. The fourth reason that may cause unfairness is the physical layer capture, i.e. the phenomenon where, when a collision occurs, the hardware is capable of detecting and decoding the packet with a stronger strength signal [1]. Since this effect occurs consistently and frequently in wireless multi-

hop networks, it causes severe unfairness since traffic from weaker signal senders requires more retransmissions. In this paper, our study is focused on the medium access control protocols. We propose Fair Flow Vector Scheduling Algorithm (FFVSA), which is an algorithm that schedules the transmissions in a fair manner, taking into consideration the communication requirements of the active flows of the network. Moreover, a load-balancing algorithm called Load Balanced—Fair Flow Vector Scheduling Algorithm (LB-FFVSA) is proposed, in order to further improve the throughput and decrease the frame length in the network. The remainder of the paper is organized as follows: Sect. 2 presents the related work concerning TDMA Scheduling and fairness in wireless multihop networks. Section 3 describes our network model, while Sect. 4 outlines the proposed joint scheduling and the load-balancing algorithm, while the following two sections present the performance analysis of the proposed algorithm, as well as, the simulation results. Finally, Sect. 7 concludes this paper.

2 Related work 2.1 TDMA scheduling algorithms Since, the most popular medium access control scheme for wireless multihop networks is the IEEE 802.11 Distributed Coordination Function (IEEE 802.11 DCF) [2], which uses the CSMA algorithm, most of the research works on wireless multihop networks adopt it as the MAC protocol. However, the DCF operation suffers from the fairness problem, which is caused by the existence of hidden terminals and exacerbated by the adopted binary exponential backoff algorithm to resolve contention [3, 4]. Furthermore, the IEEE 802.11 DCF has numerous disadvantages, such as, high overhead, increased access delay, high jitter and limited QoS capabilities. Therefore TDMA seems to be a more promising solution, since it can overcome all these issues. However, a solution for the NP complete Broadcast Scheduling Problem (BSP) [5] is needed for using TDMA in a wireless multihop environment. Several TDMA scheduling algorithms for wireless multihop networks may be found in the literature [5–21]. These algorithms may be classified in two main categories: link (or point-to point) and broadcast (or node) scheduling (or activation) [5]. In a broadcast schedule, the scheduled entities are the stations themselves and therefore each node’s transmission must be received collision-free by all of its neighbors. On the other hand, in a link schedule, the links between the stations are scheduled. The transmission of a node is intended for a particular neighbor, and it is required that there is no collision at this receiver [7]. However, since the success link scheduling is straightly affected by the conditions of the physical layer and in

Fair TDMA scheduling in wireless multihop networks

such case an optimal scheduling solution is difficult to be achieved, in this paper we focus on broadcast scheduling. The main goal of the TDMA broadcast scheduling algorithm is to determine the timeslots used from each node when its packets are transmitted, ensuring collision avoidance, and to minimize at the same time the delay that each node experiences, maximizing the total network capacity. Several TDMA broadcast scheduling algorithms can be found in the literature [5–21]. These algorithms use several heuristic approaches, including “greedy” algorithms [5], mean field annealing [8], “tabu” search [9], genetic algorithms [10, 11, 14], neural networks [12–15, 18], graph coloring [17] and mathematical theories [19–21], in order to solve the Broadcast Scheduling Problem (BSP). In all the previous algorithms the optimum frame length is obtained, as well as the network throughput maximization is achieved. Thus, maximizing the overall network throughput can lead to an extremely unfair allocation of resources to users [22]. However, there might be a tradeoff between fairness and slot utilization since the schedule that guarantees fairness may not necessarily be the one that maximizes the slot throughput [23]. Therefore, He et al. [26] proposed a new MAC protocol, the Extended Hybrid Asynchronous Time Division Multiple Access (EHATDMA) to deal with the severe unfairness caused by the lack of synchronization problem, the double contention areas problem and the lack of coordination problem. Hsieh et al. [29] proposed an ideal per-flow-fairness based MAC protocol that incorporates priorities to the nodes proportional to the number of flows that traverse each node.

contention resolution algorithm. Mo and Warland [33] proposed a fair end-to-end window-based congestion control mechanism using a multiclass closed fluid model. Luo et al. [28] proposed a fair queueing scheme, the enhanced maximize-local-minimum fair queueing (EMLM), in which a flow is scheduled to transmit based on its rank in the sender as well as the rank in the receiver. Jun et al. [32] showed that per-flow queueing at the network layer can ensure fairness in wireless multi-hop networks at the expense of bandwidth efficiency. The authors also showed that per-flow queues at the network layer with MAC-layer QoS support may provide differentiated services in wireless multi-hop networks. He et al. [26] proposed a new MAC protocol, the extended hybrid asynchronous time division multiple access (EHATDMA) to deal with the severe unfairness caused by the lack of synchronization problem, the double contention areas problem and the lack of coordination problem. Hsieh et al. [29] proposed an ideal per-flow-fairness based MAC protocol that incorporates priorities to the nodes proportional to the number of flows that traverse each node. To the best of our knowledge no paper has addressed the problem of fair node slot assignment-scheduling using TDMA. Thus, in this paper, we introduce an algorithm that achieves both efficiency and fairness by scheduling the transmission opportunity, taking into consideration the communication requirements of the active flows of a wireless multihop network.

3 The network model 2.2 Fairness Fairness is one of the key factors in order to evaluate the performance of a wireless network, since it ensures that wellbehaved users will not be penalized because of the excessive resource demands of aggressive users. However, in multihop networks, since a user node has to transmit not only its own traffic but also the relayed traffic, fairness is a property that is difficult to be achieved. For that reason several research articles may be found in the literature that propose mechanisms to alleviate unfairness in wireless multi-hop networks. A common approach to enhance fairness is fair queueing scheduling. These proposals invariably emulate fair queueing operations (i.e., assign start and finish tags for each packet) in a distributed manner by exploiting the broadcast nature of a wireless channel [26]. More specifically, Vaidya et al. [27] presented a distributed fair scheduling algorithm for wireless LAN that emulates Self-Clocked Fair Queuing in a distributed manner and chooses a backoff interval that is proportional to the finish tag of the packet to be transmitted. Nandagopal et al. [31] proposed a mechanism that can translate any given fairness requirement into a matching

We consider a wireless multihop network with a set of N nodes, a set of L logical links, and a set of F flows, i.e., assignments of bandwidth traffic to each link in L. Every transmission of a node is broadcasted over the wireless channel, and all nodes located close to the transmitting node receive the transmission, whereas far away nodes cannot receive the transmission. Nodes that can transmit with each other are called neighboring nodes. Furthermore, the receiving nodes can only receive one transmission at a time without errors, and nodes cannot transmit and receive packets at the same time. Also, all network nodes are assumed to have the same traffic characteristics, and the same traffic generation rate. The network is represented by a graph G = (V , E), where V is the set of nodes (|V | = N ), and E is the set of undirected edges (|E| = L). The existence of an edge between two nodes means that these two nodes are neighbors. Consequently, we consider the one-hop neighboring table A, where 1, if node i and j are neighbors, or i = j , Ai,j = (1) 0, otherwise.


We assume that the multiple access scheme in the wireless channel is achieved by TDMA. All nodes in the wireless multihop network must have at least as many transmission opportunities as the number of packets that has to transmit on behalf of the flows that traverse them within each TDMA frame. The TDMA frame (denoted as M in the following of the paper) consists of a number of TDMA timeslots. More than one wireless multihop nodes may transmit in every TDMA timeslot without collision, if they do not have any common neighbors. The topologies that are examined include static topologies, with fixed node positions and random topologies. The static topologies that are studied have been commonly used in other relevant research papers, which publish their produced schedules on these topologies. This allows a direct comparison among the scheduling algorithms, without implementing all of them. However, since these topologies may not be considered very realistic, we have examined our proposed algorithms on random topologies, with varying characteristics. Thus, the performance of our algorithms may be examined on more realistic topologies.

4 The proposed algorithm 4.1 The overall framework The main goal of the algorithm is to determine the optimal slot assignment in terms of overall performance and fairness per flow. This is achieved through the combination of a scheduling algorithm that assigns the appropriate transmission slots to each node, and a load balancing technique, that improves the scheduling performance by limiting the required frame length. The operation of the proposed algorithm relies on four phases, namely the information discovery, routing, scheduling and load balancing (Fig. 1). When a flow is created, an information discovery phase is initiated, similarly to any on-demand routing algorithm, which helps the source node to retrieve information concerning the network topology. Then, a routing algorithm is applied in order to determine the optimal path for the specific network flow, according to a cost value which has been calculated during the establishment of the previous flows. At the next phase, the scheduling algorithm is performed. The scheduling algorithm is based on an interference vector that in our previous work [30] it was shown to produce smaller execution time than the ones using graph coloring, and decreasing degree ordering results to the best frame length. However, regardless of the scheduling algorithm, the lower and upper bounds of the frame length, which in turn determine the throughput for each flow, have been proved to be determined by the maximum sum of timeslots needed by any set of neighbors.

Fig. 1 The phases of the proposed algorithm

Thus, the load balancing phase is introduced, which causes the routes to avoid these congested neighborhoods, and consequently improves the performance bounds. This is realized through a cost function that assigns higher cost values to nodes which belong in such neighborhoods. By applying this technique, the number of times that each node has to transmit during a frame is normalized. 4.2 The scheduling algorithm—FFVSA We represent the set of nodes transmitting during timeslot k as Sk . Also, we consider the collision avoidance vector C, which helps to determine if a node i may collide with node j that is already scheduled to transmit in timeslot k, where Ci = Ai,j . (2) j ∈Sk

If node m ∈ / Sk and there is at least one node l ∈ Sk , where m and l have z as a common neighbor, then Az,l = Az,m = 1. Therefore, Cz ≥ 1 and Am · C > 0. On the contrary, if Am · C = 0,

(3)


there is no l ∈ Sk that has a common neighbor with node m and consequently node m can be added to the timeslot. This technique provides an easy test to determine if a node collides with a node in the TDMA frame, and it reduces the complexity of the algorithm. Moreover, it is shown that the greedy collision vector algorithm shows equivalent or better performance than other more complicated schemes like Genetic Algorithms and Mean Field Annealing, for unit disk graph topologies [19]. Also it has been shown that the greedy colouring algorithm is 3-optimal [34]. Thus the greedy algorithm is chosen due its lower complexity and good performance. We also consider the flow-path table X, where 1, if link (i, j ) is used by flow f , f (4) Xi,j = 0, otherwise.

Create Nodelist = {i ∈ N|Wi > 0} slot = 0; do { Sslot := ∅; // Initialize a new Slot sort the Nodelist in descending Wi ; C := 0; for each m ∈ Nodelist { //Start to fill up the slot if (Am · C == 0) then { //Check for collision Sslot := Sslot ∪ {m}// Add node m C = C + Am //Update vector C Wm − −; } } slot++; } while (WNodelist.first() > 0);

Obviously, the set of nodes in every timeslot is determined by the order by which the nodes are tested. Since the objective of the algorithm is fairness we created a weight vec , where tor W

Input: Set of source-destination pairs (si , di )

Wi =

T N

f

Xi,j ,

(5)

f =1 j =1

and T denotes the number of active flows in the network (|F | = T ). In order to create each timeslot, the nodes are ordered based on the following rule: ◦ If Wm > Wj then bm > bj , where bi denotes the order of node i. This rule means that nodes that transmit in many timeslots should be checked first, because nodes that participate in fewer flows have a greater chance of transmitting in a following timeslot. Then, the ordered nodes are tested one by one. If (3) is true for the tested node i, then the node is added to the timeslot and the vector C is updated; otherwise it is not added and the next node is tested. When all nodes in the network are tested, then the first timeslot is produced. After each timeslot is created, the values in W are updated and the nodes are re-ordered. If a timeslot has been assigned to node i then Wi is reduced by 1, meaning that now it requires one less timeslot to fulfill its transmission requirements. Similarly, the next timeslots are created until all nodes have fulfilled their transmission requirements based on the Wi . Figure 2 depicts the pseudocode of the proposed scheduling algorithm. 4.3 The load-balancing algorithm—LB-FFVSA The proposed algorithm, called Load Balanced-Fair Flow Vector Scheduling Algorithm (LB-FFVSA), tries to avoid nodes that take part in other transmissions, as well as, their

Fig. 2 The proposed scheduling algorithm

Output: Set of Node Routes for (si , di ) Algorithm: R=∅ Set initial cost For every set of source-destination pairs (si , di ) { Find the shortest path to obtain route ri using the current costs Update costs based on load-balancing policy (6) Insert ri in R } Fig. 3 The proposed load balancing algorithm-LB-FFVSA

neighbors. Therefore, after each node assignment the cost value of all nodes are updated, based on the following rule: L(i) =

N

Aij Wj + 1.

(6)

j =1

Initially, we set the cost value of each node equal to 1. When a flow is generated this cost value for each node is recalculated according to the number of transmissions in each node’s neighborhood. More specifically, for every node i, the cost is equal to the number of transmissions the routing protocol chooses a path, which has the minimum cost. Figure 3 depicts the pseudocode of the LB_FFVSA. Since always LB-FFVSA selects routes with the lowest, it avoids nodes with increased Wi , i.e. nodes with many transmissions, resulting in increased throughput and in smaller frame length.


5 Performance analysis 5.1 Complexity analysis

Mmax =

max

i∈{1,...,N }

N

Kij Wj .

(9)

j =1

This is taken into account during node ordering. In order to produce the TDMA transmission schedule according to the proposed algorithm, all nodes have to be tested once (in the worst case) for every TDMA timeslot. During each test, there is a vector multiplication that requires up to N multiplications (since determining that the product is not zero usually requires fewer multiplications). Also the maximum number of timeslots required for every node to transmit until all N nodes have fulfilled their transmission requirements based on the Wi is N ∗ max{Wi }. Therefore, the worst case complexity is at N 3 ∗ max{Wi }. The complexity in most cases is expected to be significantly smaller. If Ci > 0, ∀i, then no other node can be added to the timeslot, so the remaining nodes don’t have to be tested. Also, in most cases the produced frame length is significantly smaller than the number of nodes in the network, and the average Wi max{Wi }. 5.2 Performance metrics Frame length The frame length produced by the algorithm is the number of timeslots required for all nodes to fulfill their transmission requirements. The frame length is desired to be as small as possible, because the access delay increases proportionally to the frame length. The frame length can be reduced by placing as many nodes as possible in every timeslot, without having collisions. For every node i the assigned timeslots are different from the ones assigned to its every neighbor. In addition, in all one-hop neighbor of this node different timeslots are assigned among them, since they have a common neighbor, e.g. node j . The minimum frame length is defined by the node where the sum of its timeslots and its neighbors has the maximum value. Therefore the minimum frame length is equal to N Aij Wj . (7) Mmin = max i∈{1,...,N }

j =1

Moreover, in order to compute the maximum frame length we consider the two-hop neighbor matrix K, where 1, if Ai · Aj > 0, (8) Ki,j = 0, if Ai · Aj = 0, since the latest possible timeslot for every node is determined by its two-hop neighbors. In the worst case, in all its two-hop neighbors different timeslots are assigned among them. If this happens, the lat est timeslot for node i is limited by N j =1 Kij Wj . Thus, the maximum frame length is equals to

Throughput Assuming that every node shares its transmissions nodes fairly among the forwarded flows and uses only 1 timeslot on every transmission, the throughput of flow i is given by: 1 (10) Th_Fi = . M End-to-end delay Let Pf denotes the order of nodes that have to transmit on behalf of flow f . Then, the delay between two consequent transmissions (e.g. the transmissions of nodes i and j ) on behalf of flow f is given by: t − k, if t > k, df (i, j ) = (11) M + t − k, otherwise, where t and k denote the timeslots assigned for nodes j and i to transmit, respectively. Therefore the end-to end delay for flow f is given by: df (i, j ). (12) Df = (i,j )∈Pf

Fairness index As stated previously our goal is to propose a joint TDMA scheduling/load balancing algorithm that schedules the transmissions in a fair manner, in terms of throughput per connection, taking into account the communication requirements of the active flows of the network. For that reason the notion of per-flow fairness where the access to the channel is in proportion to the number of flows that traverse them and act as relays is considered [29]. In order to compute the effective fairness gain for the network several fairness indices have been proposed [31, 35]. In this paper, the fairness of the algorithms were evaluated using the Jain’s Fairness Index [36], that is given by ( ni=1 xi )2 , (13) findex = n n i=1 xi2 where xi and n are the amount of allocated resource to the user (or to the flow) i and the total number of users (flows), respectively. Absolute fairness is achieved when findex = 1 and absolute unfairness is achieved when findex = n1 . It should be noted that in our paper xi denotes the flow throughput. Therefore, if all flows have the same throughput, then absolute fairness is achieved, while in the case of flows with different throughput the fairness decreases.

6 Simulation results In order to evaluate the proposed algorithms a simulation tool has been created. The simulation tool has the ability of emulating the TDMA scheduling and routing functions

Fair TDMA scheduling in wireless multihop networks Fig. 4 The network topologies used in the simulation studies: (a) Topology 1: a 15-nodes network, (b) Topology 2: a 30-nodes network, and (c) Topology 3: a 40-nodes network

in a wireless multihop network topology. It was designed in such a way as to permit multiple runs to be repeatedly executed and performance metrics to be gathered. Due to the inability to implement the other scheduling algorithms,

given that not all details concerning their implementation were available, the comparison in reference with their performance was made on the basis of the three common reference topologies: a 15-nodes network (Fig. 4a), a 30-nodes


Fig. 5 The frame length obtained for different topologies: (a) Topology 1: a 15-nodes network, (b) Topology 2: a 30-nodes network, and (c) Topology 3: a 40-nodes network


Fig. 6 The throughput vs. the number of connections for each topology: (a) Topology 1: a 15-nodes network, (b) Topology 2: a 30-nodes network, and (c) Topology 3: a 40-nodes network


Fig. 7 Fairness vs. the number of connections for each topology: (a) Topology 1: a 15-nodes network, (b) Topology 2: a 30-nodes network, and (c) Topology 3: a 40-nodes network


Fig. 8 The frame length improvement obtained by applying the load-balancing algorithm in the different topologies: (a) Topology 1: a 15-nodes network, (b) Topology 2: a 30-nodes network, and (c) Topology 3: a 40-nodes network


Fig. 9 Throughput improvement obtained by applying the load-balancing algorithm in the different topologies: (a) Topology 1: a 15-nodes network, (b) Topology 2: a 30-nodes network, and (c) Topology 3: a 40-nodes network

Fair TDMA scheduling in wireless multihop networks Fig. 10 The random topology used in the simulation

network (Fig. 4b) and a 15-nodes network (Fig. 4c) that are also used in [8, 10, 13, 14, 18]. Figures 4a, 4b, 4c illustrate these topologies, where scheduling results were available for the MFA, the HNN-GA, the SVC, the Fuzzy, the Factor, and the Ephremides’ scheme, and for the Lyui’s scheme [24, 25], that provided the implementation details. The other relevant algorithms, i.e. [9, 10, 12] and [18], are correspondingly similar to the compared ones and show similar performance, since they produce a topology dependent, traffic independent schedule, with a fixed frame length.

and the fairness index of the network (Fig. 7). Therefore, we test our algorithm (denoted as FFVSA in the following figures) in terms of frame length, throughput and fairness in comparison with MFA, HNN-GA, SVC, Fuzzy, Factor, Ephremides’s algorithms, since all algorithms use the same network topologies. Finally, we compare FFVSA with Lyui’s scheduling algorithm as described in [24, 25] where a scheduling algorithm with variable frame length is presented. From the above mentioned figures we came up to the following conclusions:

6.1 Comparison of the existing TDMA scheduling algorithms

• As it was expected, MFA, HNN-GA, SVC, Fuzzy, Factor, and Ephremides’ algorithms have a constant frame length for each topology, whereas FFVSA’s frame length increases as the number of concurrent connections increases. This difference is apparent in all three topologies (Fig. 5). In addition, regarding Lyui’s algorithm, which produces different frame lengths for each node, we depicted the average frame length among all nodes. This average frame length, as Fig. 5 depicts, is larger than the ones obtained from the other algorithms. • The average throughput of FFVSA is much larger than the other seven algorithms, especially at lower loads. This occurs due to the fact that the TDMA frame length is adapted to the communication requirements, making the scheduling more efficient. As the number of concurrent connections increases, the throughput is reduced, approaching the throughput of the other seven schemes (Fig. 6).

In each topology, we randomly select nodes to be used as sources for the connections, and other nodes to be used as destinations. For these topologies different simulation runs were executed for the eight scheduling schemes. Each simulation run consisted of nine iterations, each having an increasing number of concurrent connections. A connection generator was implemented, generating 1000 connections for each iteration. After each generated or ended connection, the average throughput, as well as the fairness among all active connections was recalculated. It should be noticed that for each iteration, the frame length, throughput and fairness values were the average values of each recalculation. The obtained results for the three topologies are depicted in Figs. 5, 6, and 7. More specifically, our interest is focused on the frame length (Fig. 5), the throughput (Fig. 6)

D.J. Vergados et al. Fig. 11 The improvement obtained by applying the load-balancing algorithm in the random topology in terms of frame length (a) and throughput (b)

• FFVSA has absolute fairness, regarding throughput. On the other hand, the fairness of the remaining seven schemes is reduced as the number of the concurrent connections increases (Fig. 7). • FFVSA offers superior performance, in terms of frame length and throughput, especially when the number of connections is small (Figs. 5 and 6). Although, in heavy load conditions, the size of the frame length is increased (in order to keep the fairness factor equal to 1), the proposed algorithm’s performance in terms of throughput is better than the other seven algorithms. In topologies where many alternative paths exist, such as topology 2 (Fig. 5b), the obtained size for the frame length is satisfactory enough. All the above observations, lead us to the conclusion that the proposed scheme provides better throughput to the system users, while at the same time, maintains the fairness of the network in very high levels. Thus, the proposed scheme

is suitable for creating the transmission schedules in a more efficient way than the other relevant techniques. 6.2 The advantage of the load-balancing algorithms Different simulations runs for the same three topologies (Fig. 4) were also performed over the proposed scheduling algorithm, with and without the load-balancing technique (denoted as FFVSA and LB-FFVSA respectively in the following figures). The obtained results are shown in Figs. 8 and 9. Considering these results, we may summarize the following: • The load algorithm decreases the size of the frame length and increases the network throughput, without affecting the fairness (the fairness obtained in each scenario is equal to 1). • Since the number of nodes in topologies 1 and 2 is rather small (Figs. 4a and 4b respectively), the performance of LB_FFVSA is quite identical. However, in topology 3,

Fair TDMA scheduling in wireless multihop networks Fig. 12 The random topology used in the simulation

where alternative paths exist (Fig. 4c), the performance scheduling algorithm is better when the load balancing technique is applied. • The use of load balancing algorithm affects mainly the size of frame length. More specifically, by applying the load balancing algorithm the size of the frame length decreases by 2–7 timeslots, (Fig. 8). This effect becomes more obvious in topologies 2 and 3 (Figs. 4b and 4c), where in the first case, there are more alternative connections between a specific path whereas in the second one, due to the large number of neighbors, there are more alternative paths. In order to show the benefits of using the joint loadbalancing-scheduling technique, we apply the loadbalancing algorithm into a random topology (Fig. 10). This random topology was generated by placing 200 nodes on square area of dimension 1000 meters, following a twodimensional uniform distribution. The transmission and interference ranges were equal to range 200 meters. The simulation results, depicted in Fig. 11, showed that by avoiding both the nodes that take part in other transmissions as well as their neighbors, the throughput was further improved and the size of the frame length was minimized. In addition, a similar scenario was performed on realistic topology, which was generated using the NPART tool [37] (Fig. 12). For the demand pattern a Poisson distribution is applied for the arrival process, and setting the distribution of the connection duration as exponential. The number

of nodes was 275 and the transmission/interference range 250 meters. The results are depicted in Fig. 13, and are qualitatively similar regardless of the topology. Finally, an improvement on the network capacity is accomplished by applying the LB-FFVSA, as it is depicted in Fig. 14.

7 Conclusions A wireless multihop network is a network where the communication between two end nodes is carried out by hopping over multiple short wireless links. In such a network, each node apart from sending/receiving packets to/from adjacent nodes, also acts as a router and forwards packets on behalf of other nodes. Thus, in this kind of networks, fairness is limited. The topologies of wireless multihop networks, in addition to the medium access control protocols that have been designed for single-hop networks, in relation to the spatialtemporal congestion variation and the physical capture phenomenon responsible for the severe unfairness experienced in these kind of networks. In this paper, we proposed a TDMA scheduling algorithm, called FFVSA, which is capable of scheduling the transmissions in a fair manner, taking into consideration the communication requirements of the active flows of the network. Simulation results showed that the proposed algorithm exhibits improved performance compared to other

D.J. Vergados et al. Fig. 13 The improvement obtained by applying the load-balancing algorithm in the random topology in terms of frame length (a) and throughput (b)

Fig. 14 The improvement on the network capacity by applying the load-balancing algorithm in the random topology

solutions, not only in terms of fairness, but also in terms of throughput. Moreover, in order to further improve the obtained results, a load-balancing algorithm (LB-FFVSA),

was also proposed. Simulation results showed that, when applying load-balancing policy in the FFVSA, the performance of the algorithm can be further improved. Thus, the


LB_FFVSA can be used for creating the transmission schedules in a more efficient way, than other relevant techniques.

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D.J. Vergados et al. 35. Lodi, A., Malaguti, E., & Stier-Moses, N. E. (2010). Efficient and fair routing for mesh networks. Mathematical Programming Series B, 124(1–2), 285–316. 36. Jain, R. (1991). The art of computer systems performance analysis: techniques for experimental design, measurement, simulation, and modeling. New York: Wiley. 37. Milic, B., & Malek, M. (2009). NPART—node placement algorithm for realistic topologies in wireless multihop network simulation. In Proceedings of the international conference on simulation tools and techniques for communications, networks and systems & workshops, Rome, Italy, 2–6 March 2009. Dimitrios J. Vergados was born in Ioannina, Greece, in 1980. He received his Diploma in Electrical and Computer Engineering from the National Technical University of Athens (NTUA) in 2003, and his Ph.D. from the School of Electrical and Computer Engineering of the National Technical University of Athens (NTUA) in 2009. His research interests include wireless networks, scheduling algorithms, and multi-hop networks.

Aggeliki Sgora received her B.Sc. in Mathematics and her M.Sc. in Technologies and Management of Information and Communication Systems, as well as, her Ph.D. in Computer Networks from the University of the Aegean. Her research interests are in the area of Communication Networks, mainly in Wireless Networks (Cellular, WLAN, Ad hoc Networks, Multihop and Mesh Networks).

Dimitrios D. Vergados is a Lecturer in the Department of Informatics, University of Piraeus. He had also held a position as a Lecturer in the Department of Information and Communication Systems Engineering, University of the Aegean. He received his B.Sc. from the University of Ioannina and his Ph.D. from the National Technical University of Athens, Department of Electrical and Computer Engineering. His research interests are in the area of Communication Networks (Wireless Broadband Networks, Wireless Sensor Networks, Ad-hoc Networks, WLANs, IMS, Mesh Networks), Neural Networks, GRID Technologies, and Computer Vision. He has participated in several projects funded by EU and National Agencies and has several publications in journals, books and conference pro-

ceedings. He has served in technical program committees of several conferences. He is also a guest editor and a reviewer in several journals. Demosthenes Vouyioukas received the Diploma in Electrical and Computer Engineering from the National Technical University of Athens, Greece, in 1996 and the Ph.D. degree in Wireless Communications from the School of Electrical and Computer Engineering in National Technical University of Athens, in 2003. He also received a Joint Engineering-Economics M.Sc. from the National Technical University of Athens. He is currently an Assistant Professor at the Department of Information and Communication Systems Engineering, University of the Aegean, Greece, where he had been an adjunct lecturer and researcher since 2004. His areas of expertise are wireless communications systems, analog and digital communication systems, Wireless Sensors and Broadband Networks, Digital Video Broadcasting (DVB), Satellite Systems, DVB-RCS, UMTS, HSPA, LTE, LTE-A and WiMAX systems and applications along with Femto and MIMO techniques. Within these topics he has published more than 50 journals, book chapters and international conferences and he is also reviewer in several scientific journals. He is a member of IEEE since 1997, a member of the Communication Society of the Greek Section of IEEE and also a member of the Technical Chamber of Greece since 1997. Ioannis Anagnostopoulos was born in Athens, Greece in 1975. He received his diploma from the Department of Electrical Engineering and Computer Technology, University of Patras, Greece, in 1998 and his Ph.D. from the School of Electrical and Computer Engineering, National Technical University of Athens (NTUA), Greece, in 2004. Currently he is an Assistant Professor with the University of Central Greece at the Department of Computer Science and Biomedical Informatics. From 2003 until the mid of 2010 was with the University of the Aegean at the Department of Information and Communication Systems Engineering, serving as a Lecturer. His research interests include Internet technologies and services, web search and retrieval software methodologies, E-commerce, Telecommunication Networks and Intelligent Multimedia Systems. As far as his teaching activity is concerned, he teaches Internet Communications, Internet/Web Programming, Computer Networks, and Multimedia Systems. Dr. Anagnostopoulos is a full member in the Technical Chamber of Greece, IEEE, IEE, and ACM. He has more than 20 articles in international journals as well as more than 50 papers in international refereed conferences, while he participated in more than 10 European and National funded Research Projects. He speaks English and French fluently.