Spatially Limited Contention for Multi-Hop Wireless Networks

Transcription

1 Spatially Limited Contention for Multi-Hop Wireless Networks Fikret Sivrikaya, Sahin Albayrak DAI-Labor / TU Berlin, Germany Bülent Yener Rensselaer Polytechnic Institute, NY, USA Abstract With rapid developments in the community mesh networks and wireless sensor networks research, the need for more efficient channel access techniques for multi-hop wireless networks has become eminent. In this work, we propose a novel hybrid channel access scheme that spatially limits the contention in the network such that 2-hop neighbors access the channel contention-free among each other whereas only the immediate neighbors may contend among each other. The contention among neighbors can be handled much more efficiently by a basic CSMA protocol as if operating in a single-hop network. We provide a general framework for the scheme and compare its performance to the conventional RTS/CTS-based collision avoidance scheme. By a case study using the IEEE 82. protocol as the underlying CSMA protocol, the proposed scheme pleads itself as a more efficient alternative to the RTS/CTS based collision avoidance scheme for large and dense multi-hop ad hoc networks with stationary nodes, such as wireless mesh and sensor networks. I. INTRODUCTION Medium Access Control (MAC) protocols determine how nodes in a wireless network access the shared wireless medium and they play a crucial role on the overall throughput and energy utilization in the network. MAC protocols can be broadly classified as contention-based and contention-free schemes. In general, contention-based MAC protocols have good throughput and delay performance under light load conditions, but their performance degrades as the load increases because of the increased collisions, retransmissions, and control message overhead. In contrast, contention-free MAC protocols perform better when the load is high since they can better utilize the channel with less control message overhead and collision-free media access. Their drawback is increased latency under light load conditions due to the reserved access policy. Limited contention MAC protocols aim at combining the advantages of both access mechanisms while eliminating their weaknesses []. A limited contention-protocol utilizes reservation-based channel access as in contention-free protocols, but the reservation is mostly not exclusive to a single node, allowing a controlled level of contention. In multi-hop wireless networks, a node contends with not only its immediate neighbors, but also its 2-hop neighbors due to the hidden terminal problem. Carrier Sense Multiple Access (CSMA) protocols, designed mainly for single-hop networks, are known to perform poorly in multi-hop wireless networks. Indeed, an analysis by Tobagi and Kleinrock [] shows that the performance of CSMA protocols degrades to that of the Aloha protocol in the existence of hidden terminals. Corresponding author fikret.sivrikaya@dai-labor.de The IEEE 82. MAC protocol and many of its variants use a collision avoidance technique, the Request-To- Send/Clear-To-Send (RTS/CTS) scheme, to overcome the hidden terminal problem and reduce the cost of collisions in CSMA. RTS/CTS is a 4-way handshake mechanism introducing extra overhead in resource-constrained wireless networks. The overhead of collision avoidance is particularly high when the data payloads are small as is typical for sensor network applications. The default packet size in TinyOS is only 29 bytes [8]. Moreover, it is shown in [2] that the collision avoidance scheme can accommodate much fewer competing nodes within a region in a network infested with hidden terminals than in a fully-connected network, which raises a scalability issue for dense networks spanning over a large area. In this paper we propose a new approach based on spatially limiting the contention in the network; the 2-hop neighbors access the channel contention-free among each other, and a node may contend with its immediate neighbors only. Hence the contention region of a node is effectively reduced from a circular area of radius 2r to an area of radius r, where r is the common transmission radius. This media access scheme, which we name Spatially-Limited-Contention (), provides an alternative to the RTS/CTS type of handshake mechanism for collision avoidance in large multi-hop networks with stationary nodes. By eliminating the hidden terminals, the contention among neighbors can be handled much more efficiently by a CSMA-based protocol as if operating in a single-hop network. A. Related Work There is considerable work on MAC protocols for wireless ad hoc and sensor networks. Most of the initial attempts are based on the CSMA technique or are variations of the IEEE 82. protocol, trying to improve their power-saving characteristic by occasionally turning off the radio transceivers of sensor nodes. S-MAC [] is the first among those, introducing the low-duty-cycle operation in sensor networks by letting nodes periodically sleep, i.e. turn off their radio. The T- MAC protocol [2] attempts to improve on S-MAC protocol s energy conservation by using variable duty-cycles as opposed to the fixed, pre-defined duty cycles in S-MAC. Polastre et al. proposed B-MAC in [3]. B-MAC is a light-weight protocol that provides an interface to the applications to implement their own MAC. By using a small amount of information from the applications, B-MAC minimizes idle listening to provide increased energy savings. B-MAC is shown to have

2 2 higher throughput and better energy efficiency than S-MAC and T-MAC, and is used as the default MAC for Mica2 motes [4]. All these protocols focus on the receiver to save energy by limiting the idle listening of the radio. On the transmitter side, having CSMA/CA as their underlying access technology, they still suffer from the mentioned inefficiencies of the RTS/CTS mechanism. Our work addresses the efficiency at the transmitter and can be thought of as a complementary tool to the mentioned work based on duty-cycling. Z-MAC [5] is a hybrid protocol combining TDMA and CSMA. The communication is slotted as in TDMA protocols and each node is assigned a time slot, however nodes may also transmit during other slots in Z-MAC with less priorities than the slot owners. Z-MAC is claimed to behave like CSMA under low contention and like TDMA under high contention. It utilizes the distributed slot assignment algorithm DRAND [6] to assign a slot to each node that is unique in its twoneighborhood, which may require arbitrarily large frame sizes at nodes depending on the network density. We show that a small constant frame size is sufficient to eliminate hidden terminals in the scheme, regardless of the network size and density. Since nodes are allowed to transmit in slots they don t own in Z-MAC, TDMA slot do not eliminate the hidden terminal problem. Instead, Z-MAC uses explicit contention notification (ECN) messages between two-hop neighbors to reduce the effect of hidden terminals when contention is high; hence it introduces an extra overhead as in the RTS/CTS method. B. Model and Assumptions We consider large multi-hop wireless networks of stationary nodes, where each node has the same transmission range r, determining the set of nodes it can communicate directly. Without loss of generality, we treat the transmission range as normalized to a unit, i.e. r =. Such a network is generally abstracted by a unit disk graph G = (V, E), where each vertex v V represents a node in the network, and each edge e E represents the existence of a direct wireless link between two nodes in the network. In general, a limited-contention MAC protocol divides the channel in some domain (such as time, frequency or code) and grants access to a subset of nodes in each portion of the channel (e.g. at a specific time or frequency). We use the time domain framework in most of this paper in order to present our results, but the ideas can be generalized to other domains without much effort. Where appropriate, we refer to the time slot/frequency/code assigned to a node in our scheme as the node s color, attributing to the graph theory analogy of the channel assignment problem, which we will later come back to. Within the time domain framework, we assume only a local synchronization among nodes in the network, which can be maintained using a lightweight synchronization protocol such as [4] or [5]. II. SPATIALLY LIMITED CONTENTION () SCHEME The scheme in its broadest sense defines a restricted class of MAC protocols that satisfy a simple criterion: Two nodes u and v are allowed to contend for the channel only if they are direct neighbors, or else if they have no common neighbor. A MAC protocol of which channel access schedule satisfies this criterion is said to implement or apply the scheme. In the graph theoretical framework, the channel allocation in an ad hoc network corresponds to solving a (maximal) independent set problem at every time step (e.g. time frame or time slot) on a graph that represents the given network. Then at each time step, nodes that are in the independent set are allowed to access/contend for the channel. We now provide a formal definition of the scheme within this graph theoretical framework. Definition 2. ( Media Access Scheme): Let G be the graph representing a given network topology and M a given MAC protocol. Further, let S t denote a subset of nodes in G that are granted permission by M to contend for the channel at time t. Then M is said to implement the scheme if and only if S t is an independent set in G 2 G for any time instant t. Note that any graph H = G 2 G has edges between every (and only) pair of vertices that are exactly two hops away in G. Hence an independent set in H is equivalent the scheme criterion described earlier. Any reservation-based access scheme employs either a static or a dynamic channel allocation technique. Dynamic channel allocation works online by gathering information from nodes in order to reserve the channel to active nodes only. This provides better utilization of the channel as it avoids the channel being wasted by nodes that have nothing to send. However, it also introduces a significant control overhead and consumes a portion of the channel. Static channel allocation works offline by making the reservation in advance of actual network operation. Thereafter, the need for control signalling is eliminated and the channel is used only for data communication, but the utilization may drop due to inactive nodes acquiring the channel. This effect may be severe in the case of pure contention-free channel access, but in limited-contention protocols since a single node does not acquire the channel exclusively the likelihood of the channel being wasted due to inactive nodes is much less. The static allocation has the additional benefit of less energy dissipation, which is crucial for small battery-powered devices as in wireless sensor networks. As a result, the static channel allocation stands as a favorable choice for limitedcontention channel access in resource-constrained ad hoc networks, provided that the nodes are stationary and some level of local synchronization is present in the network. Static channel allocation can be viewed as a dynamic allocation scheme which repeats a fixed set of allocation choices in a periodic fashion. In graph theoretical terms, it can be represented by a fixed set of independent sets, which in turn represents a vertex coloring scheme where each independent set corresponds to the vertices of a unique color. Therefore in the domain of static channel allocation, the scheme corresponds to a coloring of G 2 G for a given graph G representing an ad hoc network. We restrict our attention to the static allocation case in the rest of this paper.

3 3 In the media access scheme, the length of each slot may typically be larger than that of a contention-free protocol; allowing multiple packets to be transmitted successfully by multiple stations in a single slot. In each slot σ, the nodes assigned to σ contend for the channel by a regular CSMA protocol. At the end of the slot, all involved nodes pause their operation, storing the current values of their local CSMArelated information (such as CW min, CW max, NAV, backoff timers, if applicable), until the next occurrence (instance) of slot σ, in which they resume their operation from the stored state. In effect, if all instances of slot σ were to be adjoined, removing all other slots from the time line, there would be a set of independent groups of nodes executing a regular CSMA protocol in a single-hop network (i.e. no hidden terminals). Hence the whole network behaves as a set of independent channels, where each channel is operated with a CSMA protocol with no hidden terminals. We use the term slot allocation (or coloring) for the process of assigning a time slot (color) for each node in the network such that the criterion is satisfied. Fig. demonstrates an output of greedy coloring on a random unit disk graph with nodes, where 3 colors are used. In the media access scheme, nodes assigned to a specific color are activated for channel access in the corresponding slot. We observe that clusters of nodes naturally emerge as a result of the coloring. Each of these clusters can operate with CSMA as if there are no hidden terminals..8.6 A. Scalability of the Scheme As common in TDMA-based protocols, the number of available time slots, i.e. the number of colors used to color G 2 G, is called the frame size, which we denote by f. Hence time is divided into frames, each consisting of f recurring slots and each node is assigned a slot σ [, f] satisfying the scheme criterion, in which it contends for the channel. The chromatic number of the graph G 2 G is one of the key issues to be addressed in understanding the applicability and performance of the scheme, where G is a given network graph. For a static channel allocation protocol applying the scheme, the chromatic number of G 2 G corresponds to the minimum frame size that can be used for slot allocation. The frame size, in turn, is an important parameter of channel allocation protocols, directly affecting the delay and throughput performance. This issue is well addressed in the context of STDMA protocols. While it is known that finding the chromatic number is NP-hard even for the restricted class of unit disk graphs [7], the main objective of a distributed STDMA slot assignment algorithm is to minimize the frame size in order to reduce delay and increase throughput. In this section, we study the the minimum possible frame size for the scheme, i.e. the chromatic number of G 2 G, for any given network graph G. The main result will be that the chromatic number of a graph G 2 G is bounded above by a small constant when G is a unit disk graph. In doing so, we first introduce a new class of geometric graphs, Unit Ring Graphs, which will serve as the basis of our analysis. Definition 2.2 (Unit Ring Graphs): Consider an undirected geometric graph G, and let d(u, v) denote the Euclidean distance between vertices u and v in G. Then G is called a unit ring graph if, for every edge (u, v) G, we have < d(u, v) Fig.. Sample output of greedy coloring on a network of nodes, where the transmission radius is set to. for all nodes. The color bar at the bottom represents all colors used in the greedy coloring as slots in a time frame. In the next section, we investigate the characteristics of SLI- CON slot allocation. In particular, we show that a small and constant number of slots is sufficient for assigning slots to all nodes in an arbitrarily large or arbitrarily dense network. Greedy coloring refers to applying a greedy coloring algorithm on G 2 G for a given graph G. Fig. 2. Unit ring graphs; each node has a surrounding ring (annulus) of identical size and is connected to every other node within its ring. The edges of two nodes are shown only, for a clear demonstration. As the name implies, each node in G effectively has a surrounding ring (annulus) with inner radius of unit size and outer radius of 2 units, and is connected to every other node within its ring, as depicted in Fig. 2. We note the natural analogy of this definition to that of unit disk graphs. We will first try to assess the special structure and (bounds on) the chromatic number of unit ring graphs, and then show that this family of graphs are a super set of the graphs of the form G 2 G, when G is a unit disk graph. This allows us to utilize the results on unit ring graphs for the analysis of the scheme.

4 4 Lemma 2.: The clique number of any unit ring graph is at most 5. Proof: The proof is similar to Khuller et al. s proof for the maximum independent set size in the neighborhood of a vertex in unit disk graphs [3]. Since the distance between any two connected vertices in a unit ring graph is at most 2 units, all vertices in a clique must reside within a circle of unit radius, as shown in Fig. 3. u x v Fig. 5. Coloring a unit ring graph with 2 colors. Regardless of the size of the graph and the degrees of vertices, the entire graph can be tiled using the marked structure of 2 hexagons (colors). Fig. 3. The maximum clique size in a unit graph is at most 5. Suppose there is a clockwise ordering of vertices in this circle, and consider any two adjacent vertices, u and v, in this ordering. Label the center of the circle as x. We have xu and xv. Since u and v are connected in the unit ring graph, we have uv >. Then uv is the largest edge in ûxv and hence x > π/3. Therefore, the number of mutually connected vertices in the circle can be at most 5. Lemma 2.2: The chromatic number of any unit ring graph is at most 2. Proof: The proof is by construction. We present a coloring scheme that uses at most 2 colors on any given unit ring graph. We first place a hexagonal grid, i.e. a tessellation of regular hexagons, on top of the entire graph. Each side of the hexagons is of length /2, ensuring that all nodes within the same hexagonal area are at most a unit distance apart (see Fig. 4). Hence there is no edge among those nodes, allowing one to use a single color for all nodes within each hexagon. /2 /2 Fig. 4. The regular hexagons used to tessellate the entire graph for the proof of Lemma 2.2. The same color can be used for vertices within the two shaded hexagons. On the other hand, the hexagons that are far enough from each other can use the same color. This allows one to tile the entire graph using a structure of 2 colors as depicted in Fig. 5. Lemma 2.3: Given a unit disk graph G, let H = G 2 G. Then for any such H, there exists a unit ring graph G R such that H G R. Proof: Given G = (V, E), construct a geometric graph G R = (V, E R ), preserving the vertex locations in G. The edge set E R is then determined using unit rings for each vertex instead of the unit disks in G. Consider an edge (u, v) in H; we have (i) d(u, v) > and (ii) there exists a vertex w such that d(u, w) and d(w, v), where d(u, v) is the /2 Euclidean distance between vertices u and v. From (i) and (ii) we have that < d(u, v) 2, which implies (u, v) E R. Hence H G R. We now state the main result of this section, which follows from Lemma 2.2 and Lemma 2.3. Theorem 2.4: A constant frame size f, where f 2, is sufficient for assigning time slots to all nodes in a network using the scheme, regardless of the network size and density. Theorem 2.4 emphasizes the scalability of the scheme as it allows a constant frame size regardless of the network size and density. B. Performance Analysis In this section we use an OPNET Modeler [9] implementation of the media access scheme to study its performance in terms of throughput and media access delay. Note however that our aim is not to provide a comprehensive comparison of the scheme with the RTS/CTS-based collision avoidance scheme. Rather, we aim to obtain some insights by a case study that uses the IEEE 82. MAC protocol s basic access mode for the scheme and its RTS/CTS mode for the collision avoidance scheme. For the scheme, we use a constant frame size of 2 slots, following the coloring scheme given in the proof of Lemma 2.2. In obtaining the results here, Direct Sequence Spread Spectrum (DSSS) is used as the 82. physical layer, for which the slot size is 2 µs and the minimum and maximum contention window sizes are CW min = 32 and CW max = 24, respectively. We use Mbps as the data rate and the sizes of RTS, CTS, and ACK packets are the defaults defined in the standard [7]. As we use the same underlying CSMA protocol for both and collision avoidance schemes, the results trend are not much affected by the values of 82. parameters. Due to limited space, we present only a small representative set of results in this section. In order to simulate a multi-hop network with a desired density, we place N nodes in a circle of 5m, which is set as the transmission range for all nodes. Then we place 3N nodes within an annulus of inner radius 5m and outer radius 3m. Finally we place 5N nodes within an annulus of inner radius 3m and outer radius 45m. This is depicted in Figure

5 5 Data generation rate, g Node throughput, S (bits/sec) Mean packet interarrival time (sec) Fig. 6. The topology used to simulate a large multi-hop network, where the simulation results are collected for the center node. 6 for N = 2. We collect the statistics for the center node. The nodes further than the outermost circle have minimal effect on the performance of the node at the center; hence this topology enables us to simulate a node within a large multi-hop network. We repeat each simulation with 2 different random seeds, recording the statistics for the center node at each time. Fig. 7 demonstrates the throughput and delay comparison between the collision avoidance scheme and the scheme for a small packet size and a varying traffic load. Since the overhead of RTS/CTS becomes much more significant when the data size is small, one may wonder the (without RTS/CTS handshake) performance in case of small packet sizes; hence, we include it in the simulation results. In moderately high data loads, we observe that the scheme throughput is superior to both other schemes, while it performs comparable to the collision avoidance scheme in terms of media access delay. Higher delay for the scheme at lowest traffic levels is unavoidable due to the scheduled access scheme, but it should be noted that this drawback is significantly reduced in the scheme compared to traditional scheduled access schemes such as TDMA, where the frame size and hence delay is proportional to the 2-neighborhood size. Fig. 8 shows the amount of data and control traffic sent for each access scheme for the same simulation set. As expected, the overhead of control traffic is significant in the collision avoidance scheme, whereas frequent collisions and retransmissions in a dense network causes a high overhead of data traffic in the basic CSMA scheme. On the other hand, scheme achieves the lower bounds for data and control traffic of both access schemes, suggesting a much lower energy dissipation at the transmitter of a node. Fig. 9 presents the capacity, i.e. saturation throughput, for each access scheme using different packet sizes. As the packet size increases, the throughput initially increases for all access schemes, but large frame sizes in a dense network cause higher costs for collided packets and retransmissions. Since the RTS/CTS handshake of 82. does not provide perfect collision avoidance [2], its throughput degrades as the packet Media access delay, D (sec) Data generation rate, g Mean packet interarrival time (sec) Fig. 7. Throughput and media access delay for different access schemes versus traffic load, for a small data size of 4 bits. Fig. 8. Data traffic sent (bits/sec) x 4 3 Data generation rate, g x Mean packet interarrival time (sec) Data and control traffic overhead for each access scheme. size increases over a threshold. The scheme, on the other hand, eliminates the hidden terminals and reduces the number of contenders, thus significantly reduces collisions and retransmissions, thereby increasing the capacity of the network. Due to space considerations, we have presented limited results in this paper. For an analytical framework for performance comparisons and more results, please refer to [8]. III. COLOR ASSIGNMENT In this paper, we focus on the definition and generic analysis of the scheme. An implementation of the Control traffic sent (bits/sec)

6 6 Node throughput, S (bits/sec) Packet size, L (τ) data Packet size (bits) Fig. 9. Capacity analysis for different access schemes with different data packet sizes. scheme clearly requires an assignment of colors (slot/frequency/code) to all nodes in the network. We provided a coloring algorithm based on the geographical positions of nodes and based our analysis on this coloring scheme. We do not address the distributed coloring in detail in this paper, but we provide a brief discussion here on different approaches for various scenarios. For wireless mesh networks, the geographical slot assignment presented in Section II-A can be easily applied in practice; since these networks are not expected to be completely self configuring, a mesh router can be configured to use a specific color at the time of deployment based on its exact geographical location and a virtual hexagonal tessellation. In [6] the authors consider the greedy graph coloring problem in a distributed network, and they propose a new distributed algorithm, which is shown to color a graph in an expected time of O( log n log ) rounds, where is the maximum vertex degree in the graph. Propagating the coloring information to the 2-neighborhood rather than the neighbors of a node, this algorithm can be generalized for the coloring of G 2 G rather than G. We have applied the greedy coloring algorithm for coloring of random unit disk graphs and observed that the greedy coloring performs surprisingly well. In most cases, the number of colors used is very close to the constant bound obtained by hexagonal grid coloring; hence a distributed implementation of the greedy coloring algorithm seems suitable for color assignment. An output instance of the SLI- CON coloring on a network of nodes was demonstrated in Fig.. IV. SUMMARY AND CONCLUSION We have proposed a new hybrid channel access scheme for stationary multi-hop wireless networks, which uses the novel idea of contracting the contention area of a node and thus eliminating contention among hidden terminals. We have shown that a very small frame size is sufficient to assign each node a color (slot/frequency/code) such that no 2-hop neighbors in the network are assigned the same color. All nodes assigned to the same color contend for the channel using a basic CSMA protocol as if operating in a singlehop network (no hidden terminals). The reduced number of contending nodes and the elimination of hidden terminals yield superior overall CSMA performance, even though each node is allowed to contend for the channel only in a portion of the channel. The proposed scheme could be used as a standalone channel access scheme for multi-hop mesh networks or with duty-cycling based channel access schemes for wireless sensor networks for additional energy savings at the transmitter of a node. We have briefly discussed the distributed color assignment issue, but this deserves a separate study of its own. The implementation of a detailed MAC protocol along with a distributed color assignment is reserved as a future work. REFERENCES [] F. A. Tobagi and L. Kleinrock, Packet switching in radio channels: Part II the hidden terminal problem in carrier sense multiple-access modes and the busy-tone solution, IEEE Transactions on Communications, 23(2) pp , December 975. [2] Y. Wang and J. J. Garcia-Luna-Aceves, Modeling of collision avoidance protocols in single-channel multihop wireless networks, Wireless Networks, Volume, Issue 5, pp , September 24. [3] S. Banerjee and S. 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