Throughput Performance of Multiple Independent Paths in Wireless Multihop Network Yong Shyang Liaw, Arek Dadej, Aruna Jayasuriya Institute for Telecommunications Research, University of South Australia
[email protected],
[email protected],
[email protected] Abstract—In this paper, we investigate the improvement in throughput performance achievable by multiple independent paths in a single-channel wireless multi-hop network. We show that a major limiting factor in multiple path routing is the degree of spatial reuse that can be achieved at the source node; that is, the maximum achievable throughput improvement of multiple paths is determined by the achievable degree of spatial reuse rather than the number of paths used. Hence having more than 2 paths does not significantly improve the performance. We also show that the average throughput improvement resulting from 2 independent paths depends on the probability of finding such independent paths in the network; this probability, although increasing with node density, is not always large enough to guarantee significant improvement in throughput.
significantly improve the performance. We also show that the average throughput improvement from 2 independent paths depends on the probability of finding such independent paths in the network. We briefly investigate the probability of finding independent paths and the resulting average improvement in throughput. The paper is organised as follows. Section II investigates the maximum throughput for single-path, and the maximum improvement offered by multipath routing. Section III presents the simulation results, and section IV presents a discussion and comments on future work. We conclude the paper in Section V. ACHIEVABLE THROUGHPUT AND OPTIMUM WINDOW SIZE
II. I.
INTRODUCTION
Ad-hoc networks are characterized by multi-hop radio broadcast environment and multiple paths available between source and destination. Some recent works [1-7] have shown that routing over multiple paths in ad-hoc networks improves the end-to-end delay and hence throughput performance. These works can be generally categorised according to two approaches to using multiple paths. The first approach [1, 2] uses alternative paths as backup paths and hence improvement results from the availability of alternative paths when the primary paths are broken. The other approach [3-7] involves sending data packets simultaneously over multiple paths to achieve load balancing. However, route coupling (i.e. interference between multiple paths) can limit the effectiveness of load balancing in a single-channel wireless network, even with node-disjoint paths [5, 7]. Hence, independent multiple paths, where transmissions along the different paths do not interfere with each other (except at the end nodes), are highly desirable for multipath routing in ad-hoc networks. Furthermore, the above studies are based on UDP traffic, ignoring the impact of packet losses and packet re-ordering on the performance. When reliable transport such as TCP is used over multipath routing for load balancing in ad-hoc network, its performance is degraded due to out-of-order delivery over different paths [8]. In this paper, we investigate the improvement in throughput performance achievable when multiple independent paths are used in a single-channel wireless multi-hop network. We show that the limiting factor in multiple path routing is spatial reuse at the source node; that is, the maximum achievable throughput improvement of multiple paths is limited by the degree of spatial reuse achievable at the source node rather than by the number of paths used. Hence having more than 2 paths does not
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In this section, we first derive the maximum throughput attainable between a source/destination pair over a single-path (SP) and independent multiple paths (MP) in a multi-hop network, and show that multipath routing has a maximum improvement factor of 50% over a single-path. We also estimate the window size required to achieve optimum TCP performance, and discuss how the improvement from multipath routing can be obtained. We assume that all transmitters have the same transmission range and that the sensing range of network nodes is the same as transmission range. For the rest of the paper, we simply refer to independent multiple paths as multipath. A. Single-path 1
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D
Figure 1. A linear-chain topology
For single-path, a linear-chain topology is considered as shown in Fig. 1. Due to the spatial reuse requirement resulting from contention for the single-channel wireless medium, for a node to transmit successfully, it is required that its neighbouring nodes and 2-hop nodes are not transmitting at the same time, or else the transmission will result in collision. Therefore, when Node #3 is transmitting, Nodes #1, #2, #4 and #5 ought to be silent. Now, we assume that there is a perfect scheduler with perfect knowledge of all nodes in the network, so that it can synchronise transmissions at all nodes for maximum spatial reuse. The maximum spatial reuse is
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achieved when all nodes at 3-hop distance from each other transmit simultaneously. For example, Nodes #1, #4 and #7 transmit simultaneously, then #2, #5 and #8, and so on. The maximum throughput (Tsp) is obtained when one packet is transmitted every 3 hops, and hence if a packet takes an average time of “t” (including queuing, transmission and propagation delays) to be successfully forwarded to next hop node, the Tsp is given by (1), where h is the number of hops.
Tsp =
1 packet
(1)
min (3 × t , h × t )
In the following discussions, the delayed-Ack mechanism is assumed in TCP, and tdata and tack are the respective average transmission times taken to successfully forward a TCP data and Ack packet. When TCP is used, the delayed-Ack mechanism dictates that the TCP receiver will send an Ack for every 2 packets received (assuming the interarrival time between consecutive packets is less than 200 msec threshold). The Ack will then trigger TCP sender to send 2 more packets. Thus after receiving the first packet, TCP receiver will wait for a subsequent packet to arrive 3×tdata later, before it returns an Ack. Assuming that the returning Acks do not interfere with the incoming TCP data packets, for a h-hop path, it takes h×tack for the Ack to return to the sender, and hence the round-triptime (RTT) is (h+3)×tdata + h×tack. The optimum window size is achieved when the source has enough data to transmit over 1 RTT period. Over 1 RTT duration, the sender is able to send at least RTT×Tsp packets, giving an optimum window size as shown in (2), which is similar to the estimate in [9]. When TCP window is increased beyond the optimum window size, it will only increase the RTT and may even degrade the throughput. Fig. 4 shows that the optimum window size computed using (2) for 1500-byte data packet and 40-byte Ack packet (i.e. tdata and tack are1.817 and 0.741msec respectively after taking account of physical link overheads and MAC contention window period) is relatively small, and a small TCP window size may degrade the ability of TCP’s Fast Retransmit and Recovery mechanism to recover losses.
Wopt =
RTT h + 3 h × tack = + 3 × tdata 3 3 × tdata
B. Multiple Paths Multiple paths achieve maximum spatial reuse when the paths are independent from each other; that is, the traffic on one path does not interfere with the traffic on other paths. Consider the 2 independent paths as shown in Fig. 2. Since the intermediate nodes on path 1 and path 2 do not interfere with each other, each path has the potential to deliver the maximum throughput as given by (1). However, using 2 independent paths does not double the achievable throughput. This is because transmission rate at the source node is limited by the contention among the first 2 hops of the paths. For example, in Fig. 2, the source node #1 and nodes #2, #3, #7 and #8 need to take turns to transmit. The source node #1 achieves its maximum transmission rate when it alternately forwards packets between the 2 paths in the transmission pattern as shown in Table 1, where it shows the transmission instances along the 2 paths. Clearly, maximum spatial reuse is achieved by the source node #1 when it transmits after its immediate neighbouring nodes transmit; that is, node #1 alternately transmits simultaneously with nodes #3 and #8. In distributing the load between the 2 paths, the source can transmit 1 packet every 2 hops (i.e. at times t, 3t, 5t, 7t, 9t, 11t), and hence the maximum throughput is given by (3) below. Comparing with (1), this is an improvement (E) of 50%. It is also clear that this is the maximum transmission rate at which the source can transmit packets without making its transmissions collide at the intended next node. Having more than 2 paths cannot increase the throughput beyond this limit, even though it may bring some benefits by distributing the load more evenly.
Tmp =
1 packet
When using TCP over multiple paths, the subsequent data packet will reach the destination on the other path after 2tdata after the first packet arrives, which then triggers an Ack to be sent back, resulting in RTT of (h+2)×tdata + h×tack. Since the maximum throughput of 2 multiple paths is 1 packet/(2×tdata), the optimum window size is RTT/(2×tdata), as shown in (4). Wopt =
(2)
RTT h + 2 h × tack = + 2 × tdata 2 2 × tdata
TABLE I.
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Path 1 (Node) Tx Instance
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(3)
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Path 2 Tx Instance
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(4)
PACKET TRANSMISSIONS ON 2 PATHS MULTIPATH
#1
#2
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#4
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#6
D
t, 5t, 9t #1 3t, 7t, 11t
2t, 6t, 10t #7 4t, 8t, 12t
3t, 7t, 11t #8 5t, 9t, 13t
4t, 8t, 12t #9 6t, 10t, 14t
5t, 9t, 13t #10 7t, 11t, 15t
6t, 10t, 14t #11 8t, 12t, 16t
D
Figure 2. Independent (Non-interfering) multipaths
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C. Overall Performance Improvement Comparing (1) and (3) shows that multipath can enhance the maximum throughput performance by up to 50%. In practice, collisions between transmissions along the paths cannot be avoided, hence the maximum throughput achievable will be lower than the estimates from (1) and (3). Consequently, we shall use (1) and (3) to provide an estimate of the upper bound on the relative improvement (in terms of percentage) from multipath as compared with single-path. Since both single-path and multipath routing are subjected to the same random processes governing contention in IEEE 802.11, the relative performance improvement should be close to that estimated from the equations derived under simplifying assumptions. The overall performance improvement resulting from multipath routing depends on the availability of the alternative independent paths; that is, if the average probability of finding independent alternative paths in a network is Pave, and the throughput is enhanced by a factor E (i.e. 50%), then the overall improvement is Pave × E. In this study, we will briefly investigate (via simulation) the probability of finding independent paths, and give an estimate of average improvement resulting from using multipath routing. III.
SIMULATIONS & RESULTS
There are 2 parts to the simulation experiments. In the first part, we seek to verify our estimates of the 50% upper bound on the improvement offered by multipath and the optimum window size, using OPNET simulation tool. In the second part, we evaluate the probability of finding independent paths in a network, using MATLAB tool. A. Throughput Performance In all simulations, DSR is used as the MANET routing protocol and IEEE 802.11 as wireless MAC protocol, with fixed transmission range of 250 meters. The IEEE 802.11 is operated in DCF mode at 11 Mbps, with the RTS/CTS mechanism disabled. Wireless nodes are placed as in Fig. 1 for single-path and Fig. 2 for multipath, with adjacent node 230m apart. Simulations are performed for path lengths of 2 to 15 hops. An FTP connection is established between Node #1 (client) and Node D (server) to transfer 10-Mbyte file, and its download time is taken to compute the average throughput. The maximum window size of the TCP connection is controlled by setting the advertised window size, which is in multiple MTU size of 1500-byte. The simulation is repeated 3 times and the average download time is taken. In order to minimize the effect of routing, the DSR model is modified to use static routes specified at the start-up of simulation. Additionally, in the case of multipath, a Multipath Transport (MPT) module is inserted between the DSR and TCP model to distribute the outgoing TCP packets alternately between the 2 paths specified, and to re-order incoming out-of-order TCP packets at the destination node. However, a strict re-ordering by MPT at the destination (i.e. out-of-order packets are held till an in-order packet arrives) will incapacitate TCP’s Fast Retransmit and Recovery mechanism and results in TCP timeout whenever a
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packet is lost (i.e. after 7 unsuccessful retransmit attempts by the 802.11 MAC in the scenario considered). Hence, the MPT module at the destination node computes the average packet interarrival time and assumes a packet loss after 6 interarrival periods without successful re-ordering. Then, packets in the reordering queue are passed up to the TCP receiver to send back duplicate Acks and trigger the Fast Retransmit. Simulation Results Fig. 3 shows the optimum TCP throughput for single-path and 2 independent paths, and the percentage improvement of multipath over single-path (note that 2 different y-axis scales are used). It is expected that using 2 independent paths will improve the throughput performance by a maximum of 50% for paths that are 3 or more hops in length, as compared to single-path, and no improvement for 2-hop paths. However, our simulation results show worst performance for 2 and 3-hop paths. This can be explained as follows: for 2- and 3-hop paths, where the optimum window size is 2, the transmission over the last hop to destination node (D) is collision-free in single-path since there is no other node that is transmitting to node D. However in the multipath case, the transmissions from the 2 last-hop nodes to node D can collide with each other, and hence increase the RTT. As the rate of transmissions over the last hop (as compared with overall transmissions) decreases with the increasing path length, the probability of a packet colliding on the last hop decreases. An equivalent view is that the RTT of a longer path is less sensitive to variation introduced by a particular hop (the last hop in our case). Hence, as the path length increases, the multipath starts to outperform the single-path as expected. The improvement increases with the path length and achieves values of around 55%-60% after 9 hops, which is close to our estimate of 50%. The higher level of improvement shown by the simulation can be due to the traffic load being now shared over 2 paths, resulting in less channel contention (and collisions) in the multipath case. Fig. 4 shows the optimum window size (Wopt) estimated from the simulation as compared to the estimates given in (2) and (4). The optimum windows obtained in the simulation are somehow smaller for single-path and larger for multipath as compared with the simplified analytical estimates. However, they still provide reasonably good estimates for the considered path lengths. When the throughput is plotted against the window size in Fig. 5, we observe that the throughput is not significantly affected by the window size increasing beyond the optimum value. This implies that at the optimum window size, the network is already mildly congested (i.e. significant amount of collisions occur between hidden terminals). B. Finding Independent Alternative Paths In this section, the probability of finding an independent alternative path (Palt) for a given shortest path is evaluated via simulation. This is achieved by running a separate MATLAB program with perfect knowledge of the network topology. The program finds all possible shortest paths between a pair of nodes, and corresponding independent alternative paths in a given area with uniformly distributed nodes. Simulations were run for four different uniformly distributed network topologies generated for each given node density, and the average results
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were recorded. The statistics Nsp(h) and Nalt(h, k) are recorded in our MATLAB program to compute Palt, which is the ratio Nalt(h,k)/Nsp(h). Nsp(h)
Total number of shortest paths of h-hop length.
Nalt(h, k) Total number of h-hop shortest paths with a shortest independent path of (h+k)-hop length. Palt(h,k) Probability of finding independent path of (h+k)hop length for h-hop shortest path.
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Opt Throughput (Kbyte/sec)
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Figure 3. TCP Throughput Improvement 12
Optimum Window (packets)
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Fig. 6 shows the probability Palt in a 2km x 2km square area, with transmission range (r) of 250m and 128 nodes, representing node density (d) of 6.3 nodes per cell (i.e. πr2, an area covered by one transmission range). Palt decreases dramatically when the path length (h) exceeds 12 hops since it is bounded by the size of the area. We therefore limit our focus to path lengths of up to 12 hops since the most distant nodes are about 12r apart. It is clear that there is a slim chance (about 3% to 7%) of finding independent path of the same length as the shortest path, and only 10% to 15% chance of finding independent path of up to 2 hops longer than the shortest path for path lengths between 4 and 10. However, when the alternative path’s length is limited as to not exceed the shortest path by one-third (i.e. h/3), the longer paths (i.e. h ≥ 8 hops) have more chance of finding alternative paths. However, that chance is still less than 20%. The above discussion relates to the maximum average probability, since it assumes perfect knowledge of the network. Now, we proceed to find the average probability of finding alternative path up to 1/3 path length longer, Pave, for the 2kmx2km network, and then to obtain an estimate of the maximum average improvement factor (Eave) for the network. Pave and Eave are given by (5), where Fh is the fraction of paths with h-hop length, Ph is its probability of finding an independent path with up to h/3 more hops than the shortest hhop path, and Eh is the resulting improvement factor for h-hop multipath over single-path. For the network considered in the simulation experiments, we are only interested in paths of 3 to 12 hops (i.e. 3 ≤ h ≤ 12); the computed Pave and Eave are 13.7% and 8.2% (we assumed that Eh is a constant of 0.6, the maximum improvement factor obtained in simulation) respectively.
Pave = ∑ Fh × Ph
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Eave = ∑ Fh × Ph × Eh
Estimated (SP) using Eq 2 Simulated (SP)
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Estimated (MP) using Eq 4
(5)
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Figure 4. Optimum TCP window size 120
Throughput (KByte/s)
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However, when the node density is increased to 8.2 nodes per cell, the probability Ph is significantly larger, particularly for longer paths (i.e. h ≥ 5), as shown in Fig. 7. The computed Pave is now 31.3%, and hence Eave is 18.7%. Fig. 8 shows how Pave varies with the maximum path length allowed when Eh assumes a constant value of 0.6 (E=0.6). For example, if we are to limit our interest to paths that are no longer than 7 hops, Eave are reduced to 6.4% and 13% for densities of 6.3 and 8.2 nodes/cell respectively. We therefore conclude that independent alternative paths are worth consideration only in sufficiently dense and large (6 or more hops) networks.
6-hop
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IV.
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6 8 10 Window Size (packet)
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Figure 5. Effect of Window Size on TCP throughput (Single-path)
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DISCUSSION & FUTURE WORK
The results presented above give the maximum average improvement attainable in a given network. In practice, the improvement will be lower since the route discovery algorithms cannot guarantee a discovery of an independent alternative path even if one exists, and hence the probability of finding independent path is lower. Furthermore, the improvement of multipath over single-path will be less than
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60% for shorter hop lengths, as shown in our previous discussion and simulation results. More still, the average overall improvement has to be considered against the additional cost (in terms of extra routing overhead) of finding independent paths. When all these factors are considered, it can be suggested that for small and/or sparse ad-hoc networks, routing strategies involving independent multipath routing does not significantly improve performance. They are only worth considering in evenly distributed and dense networks of medium-to-large sizes. 45% k
