Low-cost and Accurate Intra-flow Contention-based Admission Control for IEEE 802.11 Ad Hoc Networks Abdelouahid Derhab Department of Computer Engineering, CERIST, Rue des 3 fr`eres Aissou, Ben-Aknoun, BP 143 Algiers, 16030 Algeria Abstract. In this paper, we propose a new admission control method for IEEE 802.11 ad hoc networks, called Low-cost and Accurate Admission control (LAAC). The proposed method has two variants: LAACPower and LAAC-CS. LAAC-Power estimates channel bandwidth availability through high power transmissions and LAAC-CS through passive monitoring of the channel. Due to the shared nature of the wireless medium, contention occurs among the nodes along a multi-hop path, which leads to intra-flow contention. LAAC accurately estimates the intra-flow contention. In addition, an analytical study demonstrates that LAAC achieves optimal results in terms of overhead and delay compared to the existing intra-flow contention-based admission control methods. LAAC also utilizes two criteria for accepting flows: one during the route request phase and the other during the route reply phase, which helps to reduce message overhead and avoid flooding route requests in hot spots. Simulation results show that LAAC-CS outperforms LAAC-Power in terms of packet delivery ratio, throughput, message overhead, and energy consumption.
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Introduction
The increasing use of real-time applications such as: teleconferencing and ondemand multimedia retrieval, as well as the adoption of IEEE 802.11 technologies in ad hoc networks raise the issue of how to ensure service guarantee in such environments characterized by unpredictable topology network, shared wireless channel, and which impose different challenges on supporting real-time applications with appropriate QoS. The admitted flows in the network must not exceed the network capacity. To do so, the wireless channel must be kept from reaching the congestion point. This goal is hard to achieve since the channel is not only shared between nodes that can communicate with each other directly, but extends to all nodes within a certain range, called carrier-sensing range (CSR), through channel access contention. This range is typically much larger than the transmission range. Nodes that are within carrier sensing range detect a transmission but may not be able to decode the packet. Nodes within the sender’s transmission range are considered its neighbors, and those which are within the CSR of a sender are called its carrier-sensing neighbors (CSN).
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The admission control must ensure that the network should have sufficient resource before admitting any new flow. Moreover, the flow should not degrade the QoS of existing flows. In IEEE 802.11 MAC protocol, all the CSN of the sender are unable to initiate a packet transmission while the sender is transmitting. Due to the shared nature of the wireless medium, A node’s transmission consumes bandwidth at all nodes within its vicinity (i.e., carrier-sensing range). Let us consider a flow f with a bandwidth requirement, Breq 1 , going through a given route. Multiple nodes on the route may locate within the carrier-sensing range of a given node S, and they all contend for bandwidth. The number of these nodes is called the contention count of the route and is denoted as CC. To make admission control decisions over a multi-hop path, it is not enough to only consider the bandwidth available at a single node, since the effective bandwidth consumed by the flow at node S is: (CC × Breq ). In this paper, our original contributions are the following. First, we propose a new admission control method called LAAC, and which has two variants: LAACPower and LAAC-CS. Second, unlike other intra-flow admission control methods, LAAC guarantees both an accurate estimation of the contention and incurs the lowest cost in terms of message overhead and energy consumption. Using two admission control criteria, the message overhead is reduced. In addition, LAAC does not incur an additional delay over that incurred by regular route discovery to make a multi-hop admission control decision. The rest of the paper is organized as follows: In Section 2, we discuss related works. Section 3 presents a new admission control method. In Section 4, we analyze the performance LAAC as well as other intra-flow contention-based admission control methods. Section 5 compares the performance of LAAC-Power and LAAC-CS. Section 6 concludes the paper.
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Related Work
CACP [8] is the first work to introduce the concept of c-neighborhood available bandwidth, which refers to the available bandwidth at a node’s CSNs. The admission control is integrated with the route discovery procedure of DSR routing protocol [4]. To ensure that all nodes affected by the transmission of the traffic flow have enough available resources to allow the flow to be admitted, CACP proposes two variants: CACP-Power and CACP-CS. In CACP-Power, a node that receives a Route Reply (RREP)packet, broadcasts using a high power transmission an admission request message, which carries the full route of the flow, to its CSNs. Upon reception of the message, nodes calculate their CC using their known CSN and the the identity of the nodes on the route. In CACP-CS, channel availability is estimated through passive monitoring using a threshold called the Neighbor-carrier-sensing Threshold, which is lower than the Carrier-sensing Threshold. A node can then extend its measurement range to enclose the carrier-sensing ranges of all its CSNs. It assumes that any transmission activity in its neighbor-carrier-sensing range consumes bandwidth at all of 1
The equations to derive Breq from the application rate is given in [8]
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its CSNs, which leads that the admission control rejects flows whose bandwidth consumptions are not beyond the capacity of the network. However, CACP has several drawbacks. First, the admission control decision is delayed at each node in order to receive possible rejections before forwarding the reply. Second, CACP operates only on a source routing protocol such as DSR [4] that holds the entire route. Third, it does not propose any strategy to handle mobility and loss of QoS guarantees. Fourth, CACP does not explain how the bandwidth at the node’s CSN is released when the flow is rerouted or terminated. Sanzgiri et al. [7] describe two methods, PRP and RRT, to obtain the CC, in which each node records the duration of the received signal strength corresponding to a packet in a carrier sensing table. Although the packet cannot be decoded, its size can be inferred from its duration. However, PRP and RRT suffer from some drawbacks. A node inside the sender’s carrier-sensing range cannot determine the bandwidth consumption because it does not know the value of Breq . Moreover, the node that is part of the flow cannot make an accurate admission control decision because it ignores the effects of contending flows. Finally, counting sensed packets of a particular duration can produce erroneous results in the case of retransmissions or collisions at the MAC layer. To compute CC, AAC [2] and TAC-AODV [1] consider that the carrier-sense range is more than twice the size of the transmission range. Therefore, every node on the path generally interferes with, at most, two upstream and downstream nodes, which means that the nodes are supposed to have the same transmission range. However, this assumption is not always true since a node can increase or decrease its transmission power depending on its own purposes, and hence the CC calculation as it is proposed by the protocols is not accurate. MACMAN [5] uses the same method described in CACP [8] to calculate CC. It tries to improve the performance of the admission control by maintaining multiple paths to the destination. This allows a source to quickly switch to an alternate path that can support the flow if the current path becomes unusable. To avoid the accumulation of stale routes that no longer can provide the required QoS, MACMAN continuously monitors each alternative route in the cache. To do so, it sends Periodic Route Capacity Query (RCQ) messages along each of the backup paths towards the destination. The disadvantage of this method is that it generates an important overhead on monitoring path that might never be used.
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Low-cost and accurate admission control (LAAC)
Our admission control is integrated with a route discovery procedure of a reactive routing protocol similar to AODV [6]. In LAAC, each node i maintains the flow table F Ti that stores for each flow f circulating in its carrier sensing range: (1) the contention count CCi,f , and (2) the list of the carrier-sensing neighbors which transmit the flow f . The admission control is performed in two phases of route discovery: (1) route request phase and (2) route reply phase. The aim of performing the admission control during the route request phase is to reduce
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the overhead caused by propagating the RREQ in the whole network. If the available bandwidth at a given node is smaller than the bandwidth requirement of the flow, the admission control fails. The Bandwidth reservation is only carried out during the route reply phase. 3.1
Admission control during the route request phase
When a source node wants to send a data flow f to its destination node, it broadcasts a RREQ packet to its neighbors. The RREQ contains the bandwidth requirement Breq,f . Each node that receives the RREQ performs an admission control to check if enough bandwidth is available for the flow. If the admission control fails, the RREQ packet is dropped. If the admission control succeeds, the route RREQ packet can continue its propagation through the network. The question that may arise is how a node i can determine the bandwidth required by the flow f during the request phase without knowing the contention count CCi,f . To deal with this issue, we propose to give the lower bound of CCi,f . This bound is based on the solution proposed in [10].
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In IEEE 802.11, nodes cannot transmit and receive data simultaneously. For any packet transmission, it consumes the same amount of bandwidth resource at all the carrier sensing neighbors, because they should not be able to use that period of time for other transmissions. During route request phase, each node i does not know its carrier sensing neighbors, it only knows the previous node from which it has received the RREQ packet. It also knows its status (i.e., source node, intermediate node or destination node). Based on this knowledge, the lower bound of CCi,f , denoted by LCCi,f can be estimated under the following conditions: – If i is the source node (e.g, node A in Figure 1(a)), it requires Breq,f for sending the data, and another Breq,f is consumed by its next-hop neighbor. So, LCCi,f = 2. – If i is the destination node (e.g, node E in Figure 1(a)), Breq,f is consumed by its previous node. So, LCCi,f = 1.
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– If i is the last intermediate node (e.g, node D in Figure 1(a)), it requires Breq,f for sending the data, and another Breq,f is consumed by its previous node. So, LCCi,f = 2. – If i is not the last intermediate node (e.g, node B and C in Figure 1(a)), it requires Breq,f for sending the data, and another Breq,f is consumed by it previous node and its next-hop neighbor. So, LCCi,f = 3. To admit a new flow f during the request phase, the required bandwidth Breq,f for f must meet the following condition: Bav > LCCi,f × Breq,f The variable Bav in the condition denotes the available bandwidth. In Figure 1(a), node A wants to introduce a new traffic flow 1 to node E requiring ( B7 ) bits/s, such that: B denotes the channel capacity. The route obtained during the route request phase is shown as a sequence of directed links, and the respective minimum bandwidth requirements are shown adjacent to each node of this route. 3.2
Admission control during the route reply phase
When the destination node receives the RREQ packet, it sends a RREP back to its previous node (i.e., the next hop toward the source), denoted by target. If multiple requests arrive at the destination, the destination only sends the RREP along one route. The other routes are cached for a short period of time as backup in case the first RREP does not reach the source due to link breakage or admission failure. In the reply phase, LAAC can use one of the two variants: LAAC-Power or LAAC-CS. In LAAC-Power, reply packets are sent using a larger transmission power level than the transmission power level used for normal data transmission. Using this approach, the reply packets from the sender can reach all of its c-neighbors. In LAAC-CS, channel availability is estimated in the same way as suggested in [8]. LAAC-Power In LAAC-Power, a node that receives the RREP packet, executes the pseudo-code presented in Algorithm 1. If there is enough available bandwidth for the flow f , a soft reservation of bandwidth is set up in the node and a RREP packet is forwarded to its previous node using a high power packet transmission. For example, in Figure 1(b), nodes B, C, E, H, I, J, and L, which are CSN of node D, set their CCi,1 to 1 after receiving a RREP packet from node D. The respective contention counts of the flows are shown adjacent to each node. As the reply packet traverses nodes C, B, and A, each node i that receives the high power RREP packet transmission, increases its CCi,f by 1 (See Figures 1(c), 1(d), 1(e)). In Figure 2, node K wants to introduce a new traffic flow 2 to node M requiring B7 bits/s. After the admission control has succeeded during the route request phase (See Figure 2(a)), node M broadcasts a reply packet with target = K (See Figures 2(b), 2(c), 2(d)). Upon receiving the reply packet, the source node K finds that the total reserved bandwidth is: (2Breq,1 + 3Breq,2 ) = ( 57 )B. So, it broadcasts a reply packet using a high power packet transmission. When node G
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Algorithm 1 LAAC-Power at node i When i receives X a RREP(target) from j 1: if (B −
(CCi,g × Breq,g ) > Breq,f ) then
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if (f exists in the flow table) then 2: CCi,f := CCi,f + 1; 3: 4: else 5: Create a new entry for f in the flow table; 6: CCi,f := 1; 7: end if 8: if (i = target) then 9: if (i = source node) then 10: target := φ; 11: else 12: target := previous node in the route; 13: end if 14: Broadcast RREP(target) using a high power packet transmission 15: end if 16: else if (i = target) then 17: 18: Send ERROR packet toward the destination using a high power packet transmission; 19: else 20: Send Reject to j using a high power packet transmission; 21: end if 22: end if
receives such a message (See Figure 2(e)), it finds that (4Breq,1 +4Breq,2 ) = ( 78 )B. It concludes that flow 2 will hinder the existing flow 1. Then, it sends a Reject packet to K, which will send an Error packet to M . To refresh or release the bandwidth reservation, we suggest to encapsulate two bits in the IP option of every data packet, which are: – Bit M (More), it is set to 1 if the flow contains other packets that need to be transmitted. Otherwise, M is set to 0 if the the packet is the last one of the flow. – Bit HP (High Power ): It is set to 1 if the data packet needs to be transmitted at high power level. After a bandwidth along the route is established, the source node starts sending data packets with (M, HP ) = (1, 0), which indicates that the corresponding flow contains other packets, and the data packet should be sent to the destination node using a normal power packet transmission. To refresh the existing soft-reservation at nodes within the carrier sensing range of the flow, the source node periodically sends a data packet with (M, HP ) = (1, 1), which means that the packet should be sent to the destination node using a high power packet transmission. The last data packet is sent with (M, HP ) = (0, 1). Upon receiv-
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ing this packet, each intermediate node releases the bandwidth associated with the flow f , and sends in turn the data packet using a high power packet transmission. In this manner, the bandwidth reserved at nodes within the carrier sensing range of the flow is also released. LAAC-CS In LAAC-CS, a passive approach is used to obtain c-neighborhood available bandwidth. The node that receives the route reply directly estimates its c-neighborhood available bandwidth using the equation presented in [8] and compares it with the bandwidth consumption of the flow to make admission decisions. 3.3
Node mobility
If the link between two nodes of the flow route fails, e.g, nodes B and C in Figure 3(a), the bandwidth reservation along the partial route [C, E] is released. Moreover, a node decreases its CCi,f by 1 for each node that belongs to both the partial route and the list of the carrier-sensing neighbors which transmit the flow f (See Figure 3(a)). As AODV is not the source routing protocol, node B does not need to notify the source about this event, it locally tries to find an alternative route toward the destination, and the bandwidth reservation is established using the same method explained in Section 3 (See Figure 3(b) and Figure 3(c)). If a node suffers from QoS violation due to the mobility of some nodes, and consequently their flows, in its vicinity, it will send QoS Lost message toward the source node. Upon reception of this message, the source node will interrupt the generation of its flow. After a back-off random time, the source node will generate a new RREQ for the interrupted flow in order to discover a new route to fulfil its request.
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Analytical comparison
In this section, we analyze the performance of the proposed admission control method and compare it with CACP, PRP, RRT, AAC, TAC-AODV, and MACMAN. The performance is studied under the following metrics: the number and size of control packets, the additional delay incurred in making the flow admission control decision, the accuracy of CC calculation, and the energy complexity, which measures the energy required to perform a successful admission control. Note that this performance is for a single flow. The results of comparison are shown in Table 1. In the table, we use the notations given in [7], which are as follows: N and M denote the number of nodes in the network and the number of nodes on the path respectively. Q, P , S, I and J denote the size of RREQ, RREP, RPRM, RREQ tail in RRT, node ID, and short integer respectively. D1 and D2 are constants used in CACP-Power and PRP respectively. We assume that the nodes are randomly distributed in a region of area A. The node density remains constant when the number of nodes increases, and the area A grows with N . Since the expected distance of two uniformly sampled points within a square of size a × a scales with a [3], it is expected √ that the number of hops between two random nodes increases proportional to N . We also assume that the Q, P , and I are proportional to log N . The energy dissipated to transmit K bits using a normal power, and a high power transmission, are proportional to O(K), and (α × K) respectively. If we hold J, T , and α as constants, therefore we get the energy complexities shown in Table 1.
Table 1. Comparison of intra-flow contention-based admission control methods Metrics CACP-Power CACP-CS RREQ sent N N RRRP sent M M Other packet sent M (High Power) 0 RREQ size Q+M ×I Q+M ×I RREP size P +M ×I P +M ×I Other packet size M ×I 0 Extra delay M × D1 0 Energy complexity The accuracy of CC calculation
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A. Derhab
In CACP and MACMAN, RREQ and RREP carry the IDs of the nodes on the route. Thus, the control information piggybacked onto the packets are of the size of M × I. As for PRP, its RREP packet contains the length of the probe packet J sent by the destination. RREQ in RRT carries the lengths of the tails appended by nodes on the path, which causes the packet size to increase by M ×J. Additionally, the RREQ packet carries the tail appended by the last node traversed, which causes a further increase of T in the packet size. Our method, AAC and TAC-AODV, on the other hand, do not piggyback any additional control information onto RREQ or RREP. The forwarding of the RREP in CACP-Power is delayed at each intermediate node by D1 time units. So, the extra delay incurred to make multi-hop admission control decision is M × D1 . As for PRP, the RREP is delayed D2 time units by the destination. CACP-CS, RRT, AAC, TAC-AODV, MACMAN and our LAAC all of which require no additional delay over that incurred by the route discovery procedure. CACP-Power, MACMAN and LAAC-Power can make more accurate admission control decision and CC calculation than the other intra-flow contentionbased admission control methods. For example, AAC, TAC-AODV assume that all nodes have the same transmission and carrier-sensing range and hence each node on the path has, at most, two upstream and downstream c-neighbor nodes. This change is not true because nodes are able to change the size of their transmission range. Therefore, AAC and TAC-AODV cannot give an accurate estimation of CC in case of heterogenous ad-hoc network. RPR and RRT do not give an accurate calculation of CC because of several reasons: First, they ignore the effects of contending flows. Second, in order to make a correct admission control decision, nodes need to know the resources that a flow will consume if admitted, RPR and RRT do not explain how a node can obtain the value of Breq . Third, it is not explained how a node that senses packets can distinguish between MAC control packets that have fixed sizes and other packet, and hence the assumption that each node transmits packets using a unique duration is not true. From this study, we can conclude that among the intra-flow contention-based admission methods presented earlier, LAAC appears to be the one that ensures two properties: (1) it incurs the lowest cost in terms of message overhead, energy consumption, extra delay, and (2) it accurately estimates CC.
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In this section, we study the performance of LAAC-Power and LAAC-CS using GloMoSim simulator [9]. Our simulation environment is characterized by 25 nodes moving in the area of 1000m×1000m, with random initial nodes’ location. Nodes move according to the waypoint mobility model. In this model, a node randomly selects a location and moves toward it with a constant speed uniformly distributed between zero and a maximum speed V max, then it stays stationary during a pause time of 1 second before moving to a new random location. In
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the Glomosim implementation, radio transmission range is set to 376m and the carrier-sensing range is set to 688m. The bandwidth of the channel is 2 Mbps. Six pairs of nodes are randomly chosen to establish connections with a 512B 100 packets/s CBR traffic source. The simulation runs for 900 seconds. We evaluate the performance of LAAC-Power and LAAC-CS using the following four metrics: – Data packet delivery ratio: This is the fraction of data packets sent by a source node that reach the destination. – Message overhead: It measures the number of messages generated by the routing protocol as well as the control admission. – Throughput: Is the amount of data packet received by destination nodes. – Energy consumption: Is the total amount of energy consumed during simulation. Figures 4 shows that LAAC-CS outperforms LAAC-Power in terms of the four metrics. This is due to fact that the c-neighborhood available bandwidth estimation in LAAC-CS is conservative, and hence a few number of flows are accepted. As LAAC-Power accepts more flows than LAAC-CS does, it has to generate more control routing packets to maintain routes, and hence it consumes
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more energy power. LAAC-Power sends some control and data packets using a high transmission power level and may interfere with more nodes than a message at the normal power level. In addition, due to node mobility, interference between two or more accepted flows can occur. This situation leads that network congestion in LAAC-Power occurs more frequently, and hence it incurs low throughput and low data packet delivery ratio than that in LAAC-CS.
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Conclusion
In this paper, we have proposed an admission control method, which can be integrated with any reactive routing protocol. LAAC has the advantage that it does not need to carry information about the entire route like in CACP, PRP, RRT, and MACMAN. It can accurately estimate the contention count without incurring high message overhead, energy consumption, and extra delay. Simulation results have shown that LAAC-CS outperforms LAAC-Power in terms of data packet delivery ratio, throughput, message overhead, and energy consumption.
7. References 1. Carlos Rodrigo Cerveira and Luis Henrique M. K. Costa. A time-based admission control mechanism for ieee 802.11 ad hoc networks. In 8th IFIP/IEEE International Conference on Mobile and Wireless Communication Networks (MWCN’2006), pages 217–228, August 2006. 2. Ronan de Renesse, Mona Ghassemian, Vasilis Friderikos, and A. Hamid Aghvami. Adaptive admission control for ad hoc and sensor networks providing quality of service. Technical report, Center for Telecommunications Research, Kings College, London, UK, May 2005. 3. S. R. Dunbar. The average distance between points in geometric figures. College Mathematics Journal, 28(3):187–197, May 1997. 4. D. B. Jhonson and D. A. Maltz. Dynamic source routing in ad hoc wireless. In Tomasz Imielinski and Hank Korth, editors, Mobile Computing, chapter 5, pages 153–181. Kluwer Academic Publishers, 1996. 5. Anders Lindgren and Elizabeth M. Belding-Royer. Multi-path admission control for mobile ad hoc networks. In 2nd Annual International Conference on Mobile and Ubiquitous Systems (MobiQuitous 2005), pages 407–417, 2005. 6. C. E. Perkins and E. M.Royer. Ad hoc on demand distance vector (aodv) algorithm. In Systems and Applications (WMCSA’99 ), pages 90–100, 1999. 7. Kimaya Sanzgiri, Ian D. Chakeres, and Elizabeth M. Belding-Royer. Pre-reply probe and route request tail: approaches for calculation of intra-flow contention in multihop wireless networks. Mobile Networks and Applications, 11(1):21–35, 2006. 8. Yaling Yang and Member-Robin Kravets. Contention-aware admission control for ad hoc networks. IEEE Transactions on Mobile Computing, 4(4):363–377, 2005. 9. X. Zeng, R. Bagrodia, and M. Gerla. Glomosim: A library for parallel simulation of large-scale wireless networks. In Workshop on Parallel and Distributed Simulation, pages 154–161, 1998. 10. Hua Zhu and Imrich Chlamtac. Admission control and bandwidth reservation in multi-hop ad hoc networks. Computer Networks, 50(11):1653–1674, August 2006.
