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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings. DARA: Delay-Aware Routing Algorithm in a Hybrid Wireless-Optical Broadband Access Network (WOBAN) Suman Sarkar1 , Hong-Hsu Yen2 , Sudhir Dixit3 , and Biswanath Mukherjee1 1 Department of Computer Science, University of California, Davis, CA 95616, USA 2 Department of Information Management, Shih Hsin University, Taiwan 3 Nokia Research Center, Burlington, MA 01083, USA Email: {sarkar, mukherje}@cs.ucdavis.edu, hhyen@cc.shu.edu.tw, sudhir.dixit@nokia.com Abstract— Hybrid wireless-optical broadband access net- i.e., an end user can try to deliver its packet(s) to any onework (WOBAN) is a promising architecture for future of the gateways (from which the packet will find its way tonetwork operations. Recently, the wireless part of WOBAN the rest of the Internet). But in the downstream direction (fromhas been gaining increasing attention and early versions a gateway/ONU to a wireless user), this network is a unicastare being deployed as a municipal access solution to network, i.e., a gateway will send a packet to only its specificeliminate the wired backhaul to every wireless router. This destination (or user).architecture saves on network deployment costs becausefiber (or wiring) does not need to extend to the end user,and it extends the reach of emerging optical access so-lutions, e.g., Passive Optical Network (PON)-based accesssolutions. However, a major research opportunity exists indeveloping an efficient routing algorithm for the wirelessfront end of WOBAN. We propose and investigate the characteristics of “Delay-Aware Routing Algorithm (DARA)” that minimizes theaverage packet delay in the wireless front end of aWOBAN. We model wireless routers as queues and predictwireless link states periodically. Our simulation experi-ments show that DARA achieves better load balancing andless congestion compared to tradional approaches such asminimum-hop routing algorithm (MHRA) and shortest-path routing algorithm (SPRA). In addition to minimizingthe delay, DARA also improves the average hop countcompared to the predictive throughput routing algorithm(PTRA), a popular protocol used in several deployments Fig. 1. SFNet: wireless mesh in San Francisco WOBAN.for the wireless front end of a WOBAN. Note that the wireless links in the front end mesh of a WOBAN may have asymmetric and differential capacities. I. I NTRODUCTION This is because of how a router connects to other routers in A hybrid wireless-optical broadband access network (re- the neighborhood; e.g., if a router is associated with two otherferred to as “WOBAN” here) consists of a multi-hop wireless routers, and the wireless channel is time-division multiplexed,mesh network at the front end, and it is supported by an then on average, each link (associated with that router) willoptical access network, e.g., a passive optical network (PON) get half of the capacity to other routers. Also the effective linkat the back end. At the back end of a WOBAN, Optical Line capacity from router A to router B may be different than thatTerminals (OLT) reside in a Central Office (CO) and feed to from router B to router A, because routers A and B may havemultiple Optical Network Units (ONU). Thus, from ONU to different numbers of neighbors.the OLT/CO, we have a traditional fiber network; and, from In this study, we focus on the packet delay (latency) in theONUs, end users are wirelessly associated. At the front end front end (wireless mesh) of the WOBAN, i.e., the packetof a WOBAN, end users with wireless devices at individual delay from the router to the gateway (attached to ONU) andhomes or business premises are scattered over a geographic vice versa. The packet delay could be significant as the packetarea. Each of them will associate with a nearby wireless may travel through several routers in the mesh before finallyrouter. The collection of routers forms a multi-hop wireless reaching the gateway (in the upstream direction) or to themesh network; and a few of them, called “gateways”, are user (in the downstream direction). The larger the mesh of thestrategically placed over the geographical region of coverage. WOBAN, the higher is the expected delay. Thus, we proposeGateways are attached to ONUs. A ONU can drive multiple “Delay-Aware Routing Algorithm (DARA)” as a proactivegateways [1], [2]. routing scheme where we model each wireless router as an An end user sends a data packet to one of its neighborhood M/M/1 queue and predict the wireless link states (using link-routers. This router then injects the packet into the wireless state prediction or LSP) periodically [6], [7], [8]. Based on themesh of the WOBAN. The packet travels through the mesh, LSP information, we assign link weights to the wireless links.possibly over multiple hops, to one of the gateways/ONUs Links with higher predicted delays are given higher weights.and is finally sent through the optical part of the WOBAN Then we compute the path with the minimum predicted delayto the OLT/CO. In the upstream direction (from a wireless from a router to any gateway and vice versa. While travelinguser to a gateway/ONU), WOBAN is an anycast network, upstream/downstream, a router/gateway will send its packet U.S. Government work not protected by U.S. Copyright

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.along the computed path only if the predicted delay is below not suitable for delay-sensitive services as the correspondinga predetermined threshold, referred to as the delay requirement packets can take longer routes (as long as the route satisfiesfor the mesh; otherwise we will not admit the packet into the the throughput criteria).mesh. We also study how choosing a path from a set of paths There exist several research efforts that address routing(whose delays are below the delay requirement) can alleviate which fits with the front end of a WOBAN. In [10], thecongestion and achieve better load balancing. authors propose a link-activation framework (even-odd link We consider a part of the city of San Francisco, Califor- assignments) for scheduling packets in a wireless network.nia, from approximately (N 37◦ 46 43.39 , W 122◦ 26 19.22 They show that the packet delay for wireline schedulers,(Golden Gate Avenue and Divisadero Street intersection)) to viz., Weighted Fair Queuing (WFQ) and Coordinated Earliest(N 37◦ 46 51.78 , W 122◦ 25 13.27 (Golden Gate Avenue and Deadline First (CEDF), when implemented over the wirelessVan Ness Avenue intersection)) and from (N 37◦ 47 32.57 , multi-hop network, are guaranteed to be approximately twiceW 122◦ 26 28.90 (Divisadero Street and Pacific Avenue in- the delay of the corresponding wireline topology. In [11], thetersection)) to (N 37◦ 47 41.39 , W 122◦ 25 23.71 (Van Ness authors provide admission control schemes for a multihopAvenue and Pacific Avenue intersection)) (see Fig. 1) for our wireless network for packets with QoS requirements. In [12],performance study. This is approximately a one square-mile the authors develop a routing protocol that makes use ofarea in downtown San Francisco with an estimated population Bottleneck Link Capacity (BLC) as the link metric for wirelessof around 15, 000 residents [3], [4], [5]1 . The wireless part of networks. Other interesting research efforts appear in [13],our San Francisco WOBAN (henceforth called “SFNet”, see [14], [15], [16], and [17].Fig. 1) is a mesh that consists of a number of point-to-point Next, we propose our routing algorithm, called DARA (thator point-to-multipoint WiFi routers2 . minimizes the average packet delay and achieves better load The rest of this study is organized as follows. In Section II, balancing), for the wireless front end of a WOBAN.we briefly review the current routing schemes in municipalwireless networks and related research efforts. In Section III,we propose our delay-aware routing algorithm (DARA) and III. D ELAY-AWARE ROUTING A LGORITHM (DARA)analyze the LSP mechanism. Section IV contains performance DARA is a proactive routing algorithm. DARA considersstudies of DARA compared to other routing schemes used the end-to-end delay for packets (here end-to-end means fromin the front-end wireless mesh of WOBAN, and Section V the packet’s source router to a gateway or vice versa in thesummarizes this study. front end of a WOBAN). So, routing in the mesh deals with packets from a router to a gateway (and vice versa). A wireless II. C URRENT A PPROACHES AND R ESEARCH routing path consists of two parts: (1) the associativity of a O PPORTUNITIES user to a nearby wireless router in its footprint, and (2) the The minimum-hop routing algorithm (MHRA) and the path from this (ingress) router to a suitable gateway (throughshortest-path routing algorithm (SPRA) are used in the wire- the wireless mesh).less part of a WOBAN (where the link metric in MHRA is A user needs to decide which router it should associateunity and that in SPRA is inversely proportional to the link with before sending its packets. If there is only one router incapacity). Recent approaches also consider solution providers’ its footprint, the user has to choose that router. If there arepatented routing algorithms. Predictive-Throughput Routing multiple routers, and the nearest router is overloaded, the useralgorithm (PTRA) is one such protocol (where PTRA is sim- can choose the next nearest router, which is not overloaded.ilar to “Predictive Wireless Routing Protocol (PWRP)” [9]). From a router, a packet is injected into the mesh. The packetWe use the name “PTRA” instead of “PWRP” throughout delay due to the single-hop communication between a userthis study. These protocols run inside the wireless routers and and its associated ingress router is unavoidable and is smallgateways in the mesh. compared to the packet delay in the mesh. This is because a MHRA and SPRA work on the shortest-path principle packet could potentially travel through multiple routers in thewithout generally considering other traffic demands on the mesh to get to one of the gateways.network. Therefore, MHRA and SPRA could suffer from The packet delay in the mesh (namely the front end of aseveral routing limitations (viz., increased delay, poor load WOBAN) consists of four components: (1) Propagation delay,balancing, and high congestion in a link or along a segment (2) Transmission delay, (3) Slot synchronization delay, and (4)(consisting of multiple links)). Queuing delay. Unlike MHRA and SPRA, PTRA is not based on the Propagation delay will not be significant assuming routersshortest-path routing principle. PTRA is a link-state based are close to one another. Transmission delay depends on therouting scheme, and it chooses the path (from a set of possible effective link capacity. Higher the link capacity, lower is thepaths between a user-gateway pair) that satisfies the overall transmission delay. Slot synchronization delay comes fromthroughput requirements, as explained below. PTRA takes the time-division-multiplexing (TDM)-based operation of ameasurement samples of link rates periodically across wireless wireless channel, where each router will send packets to itslinks. Given a user-gateway pair, the algorithm computes neighboring routers at the pre-assigned time slots. Queuingavailable paths. Based on the history of samples, PTRA delay depends on the rate of packet arrivals and rate of servicedynamically predicts link condition and then estimates the at a router. Higher the packet arrival rate and slower thethroughput of each path. It chooses the path that gives a higher service rate, higher will be the queuing delay. Queuing delayestimated throughput [9]. Although PTRA is proposed and is cumulative. If a packet traverses multiple routers before itimplemented for only carrying packets in the wireless part reaches a gateway, then in each of these routers it experiencesof a WOBAN, the major problem in PTRA is that the packet queuing delay, which accumulates as the packet travels throughmay end up traveling inside the mesh longer than expected (as the mesh.PTRA does not take into account packet delay). So, PTRA is WOBAN being a municipal network, users with wireless devices have limited or no mobility. They are mostly 1 San Francisco has an area of nearly 47 square-miles with a population of residential and business users. We also know the users’around 745, 000; so the population of SFNet in Fig. 1 is quite representative service level agreements (SLA), the network’s connectivityof San Francisco’s population density. pattern (how routers are associated among themselves), and 2 In greyscale image (of Fig. 1), black squares (five of them) are atached to the locations of routers and gateways or ONUs (which arethe optical part of WOBAN as gateways; others (twenty of them) are routers. attached to the back end of WOBAN) in advance. Also note

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.that the mesh in the front end of WOBAN is “anycast” in the link conditions (see Section III-B) between the intervals toupstream and “unicast” in downstream direction. avoid “stale” information. These link-state predictions (LSP) can also capture the burstiness of data packets in the access Problem Statement network. • Given parameters: In LWA (see Algorithm 1), we assign link weights in such - G(V, E) : directed graph denoting front end mesh of a manner that the links with more delays get more weights WOBAN, and vice versa. where V : set of vertices and E : set of wireless links, Algorithm 1 Delay-Aware Routing Algorithm (DARA) - R : set routers in mesh, - Link-State Advertisement (LSA): - O : set of gateways/ONUs, For each link i, advertise periodically current packet where |V | = |R| + |O|, - λn : rate of packet arrival at router n, n ∈ [1, |R|], intensity (λi ), effective link capacity (Ci ), and time stamp - λj : rate of packet arrival at gateway j, j ∈ [1, |O|], (tn ). - λi : rate of packet arrival at link i, i ∈ [1, |E|], and - Link-State Prediction (LSP): - Ci : capacity of link i, i ∈ [1, |E|]. For each link i, estimate packet intensity (λest ), to be i • Objective: used until next LSA gets advertised (see Section III-B). - Average-packet-delay-optimized routing in front end - Link Weight Assignment (LWA): mesh of WOBAN. Assign weight of each link i as: We will sketch our algorithm next for delay-aware routing. Wi = Qi = µCi + 2µCi + µCi ρi est . 1 1We will model each router inside the mesh as an M/M/1 −λiqueue. A packet’s average packet transfer delay, Q (also - Path Computation:known as “system time”), along a link depends on the trans- 1) Compute K minimum-weight paths (K > 1),mission delay, slot synchronization delay, and queuing delay.Packets arrive at the routers (directed to gateways upstream) i∈Pk Wi , from the source router to the gatewayand gateways (destined to router downstream) in a Poisson or vice versa, where Pk is the k-th path for k ∈distribution (and are denoted by λn and λj , respectively) with [1, K]. We call these paths as K-DARA paths.exponential interarrival time. We know that λi is the average 2) Derive a set of paths, F (called “feasible paths”),packet intensity on link i and follows a Poisson distribution that satisfy the delay requirement of the packet.as well (where λi can be found knowing λn and λj ). The 3) Among F , choose one path.packet lengths are independent and exponentially distributed 1with average packet lengths as µ and the effective link capacity - Admission Control:is Ci . (The independence assumption is being employed as an 1) Admit a new packet in the mesh only ifapproximation for mathematical tractability.) its delay requirement (Treq ) satisfies the The capacity is assigned to each link i in a diffential and minimum delay among the feasible paths F ,asymmetric manner. Consider router A has router B and two M inPk ∈F i∈Pk Wi ≤ Treq .other routers in its vicinity. Similarly, router B attaches torouter A and three other routers. So, router A’s transmitter will 2) Else reject the packet.send packets to three neighboring routers in three consecutivetime slots. So, differential capacity for link i from router A torouter B will be on average one-third of the full capacity C(i.e., CiA→B = C ). Similarly, differential capacity for link i 3 A. Achieving Load Balancingfrom router B to router A will be on average one-fourth of the DARA works on the principle of delay optimization alongfull capacity C (i.e., Ci B→A = C ). Note that the differential 4 paths from a router to a gateway in the front end of WOBAN.capacity assignment is an average-case assignment, because If every packet in the mesh wants the path with minimumtime slots for each TDM frame may not be static. Also, note weight (alternatively, the path with minimum delay), then A→B B→Athat link capacities can be asymmetric (i.e., Ci = Ci ), some links in the mesh may get more packets (overloadbecause routers A and B may have different numbers of situation) compared to the other links. This may adverselyneighbors. affect the throughput of the network as many packets might Therefore, the transfer delay for each link i is Qi = get rejected due to the link congestions in some parts of 1 1 ρi 1 the network (had they chosen some other path they would µCi + 2µCi + µCi −λi , where µCi is the transmission delay have still satisfied their delay requirement). This is why we 1(also known as “service time”) and 2µCi is the slot synchro- compute K minimum-weight paths, instead of only computing ρinization delay, and µCi −λi is the queuing delay, where ρi is the minimum-weight path to leaverage greater flexibility in λi choosing the paths.the link utilization, and ρi = µCi . Delays for K-DARA paths are bounded between the min- Algorithm 1 is our proposed delay-aware routing algorithm imum delay and the maximum delay that satisfies the delay(DARA). requirement of the packet. Let Tpkt denotes the delay of a In LSA (see Algorithm 1), each router/gateway will period- packet whose delay requirement is Treq in the mesh, then Tpktically advertise its link conditions. Smaller the LSA period, is shown to be as follows:less is the possibility of “stale” advertisement (where anadvertisement becomes “stale” when the link state changessignificantly after the last advertised information). However, Tpkt = M inPk ∈F Wi , M axPk ∈F Wi ≤ Treq (1)LSA in smaller intervals leads to the problem of sacrificing a i∈Pk i∈Pksignificant portion of the network’s bandwith in advertisement,which could have otherwise been used for data packets. where Pk is the k-th path with k ∈ [1, K].Therefore, we can increase the LSA intervals suitable for We may achieve better load balancing by choosing pathsWOBAN to preserve the bandwidth for packets and predict described above. DARA will also help us relieve network

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.congestion. Let γ denote the average system arrivals and Tsys that, at low loads (till the normalized load of 0.40, MHRAdenote the average system delay in the mesh, then Tsys can and SPRA perform comparably with DARA. This is expectedbe defined as below (where E denotes the connectivity in the because both MHRA and SPRA work on the shortest-pathmesh): principle. So, at low loads, these two algorithms have higher   probability to find the shortest paths with less delay. But as load increases, DARA’s performance improves significantly 1 λi λi Tsys =  λi Wi + +  (2) compared to MHRA and SPRA. DARA performs much better γ 2µCi µCi − λi than PTRA at all loads. At a very high load of 0.95, the i∈Pk i∈Pk ,i∈E average system delay for DARA improves nearly 30% from (3) its nearest competitor, namely PTRA.where Pk is the k-th path with k ∈ [1, K].B. Analysis of Link-State Predictions Link-State Predictions (LSP) need to be quite accurateto capture the current network conditions and the packetburstiness. We use “weighted moving average (WMA)” toestimate the packet intensity. Let λi (tn ) denote the measuredpacket intensity that gets advertised (through LSA) in the meshat time tn for link i, and let λest (tn−1 ) denote the estimated i(or predicted) packet intensity for the same link at the previoustime instant tn−1 (and used for time interval [tn−1 , tn )). So,LSP will compute the estimated packet intensity for the nexttime instant, tn (and to be used for time interval [tn , tn+1 ))as follows: 3α 1−αλest (tn ) = i ∗ λi (tn ) + λest (tn−1 ) ∗ S 1+α , (4) i Fig. 2. Average delay (system time) vs. load in SFNet. 3α + 1where α is the “decaying index” of WMA and S is the number Figure 3 compares individual path delays among the fourof samples used for predictions. Decaying index has a physical schemes. We choose the furthest origin/gateway pair (1, 25)significance. It captures if a link is highly loaded or not. If a in the mesh (see Fig. 1 for (1, 25) pair in SFNet), becauselink is highly loaded, α = ∞. Then Eqn. (4) estimates the a packet will travel multiple hops and the delay will becurrent intensity based on all previous samples. On the other cumulative in each hop. We find that DARA performs muchhand, if a link is lightly (or moderately) loaded, we set α = 1, better than all the other schemes. The performance improvesand following Eqn. 4, we observe that only 10% of λi (0) at high loads. We also observe that, after a load of 0.50, PTRAremains present in packet intensity computations (or 90% of delay shoots up and overtakes SPRA delay.the past samples are “forgotten” after only eight time periods). IV. P ERFORMANCE S TUDY We compare how delay-aware routing algorithm (DARA)performs vis-a-vis MHRA, SPRA, and PTRA. We took SFNetas our test setting. We envision SFNet as a part of on-goingefforts to deploy the San Francisco municipal network. InSFNet, we distributed 25 wireless routers in one square-milearea. We designated five of these 25 routers as gatewaysto the optical back end of WOBAN and placed them atthe edges of SFNet (see Fig. 1)3 . We generated packets ina Poisson distribution. The packet lengths are independentand exponentially distributed. We assumed a wireless router’scapacity to be 11 Mbps in ideal conditions. In MHRA, we assign all link weights as unity. In SPRA, weassign link weights as the inverse of link capacity. MHRA andSPRA are greedy approaches. In PTRA, we took the measure- Fig. 3. Delay vs. load (for the furthest router/gateway pair (1, 25) in SFNet).ments of wireless links periodically. Then we computed a setof paths between a router and a gateway and chose the path Figure 4 shows the average hop counts of all four schemes.with higher estimated throughput. So, for each path in PTRA, Expectedly, MHRA and SPRA produce the minimum averagewe find the link with the minimum free capacity. We call it number of hops, but DARA performs comparably with themthe “weakest link”. The weakest link will be the bottleneck for (particularly at a low load, till 0.40, DARA performs verypumping packets (and for throughput) in the path. We chose well). DARA performs much better than PTRA for all loads.the path with the best of the “weakest links” (alternatively, we In Fig. 5, we plot the percentage distribution of path lengths forchose the maximum of the minimum of free capacities for a each of these schemes. From the associated table, we observeset of paths.). that DARA performs well, because unlike PTRA, DARA tries Figure 2 shows that DARA outperforms MHRA, SPRA, and to pack many packets in fewer hops (1 − 3 hops). DARA hasPTRA with respect to average system delay. We can observe a maximum of ten hops in this example, but only 0.025% of packets will get routed along the 10-hop paths. 3 We carefully choose the number (as well as distribution) of routers and Figure 6 captures how these schemes perform in termsgateways in SFNet to match the solution provider’s current deployment status, of load balancing and link congestion. We plot the trafficwhere typically 25 − 30 routers are needed to serve one square-mile of area. difference, which is the difference between the maximum

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings. enough so that the total bandwidth consumption due to LSA is low. So, in between the higher LSA periods, LSP will predict link states. Thus, LSP saves WOBAN bandwidth with accurate predictions of link states. Fig. 4. Average hops vs. load in SFNet. Fig. 7. Actual vs. predicted packet intensities at high loads. V. S UMMARY The hybrid wireless-optical broadband access network (WOBAN) is evolving fast as a cost-effective and high- capacity alternate solution to the traditional access networks. The wireless part of a WOBAN is being deployed in many Fig. 5. Hop distributions vs. load in SFNet. communities. The rapid deployment needs efficient routing, control, and management of both the wireless front end and the optical back end of a WOBAN.and the minimum packet intensities for links in the mesh for In this study, we proposed and investigated the character-MHRA, SPRA, DARA, and PTRA paths. Smaller the differ- istics of a “Delay-Aware Routing Algorithm (DARA)” thatence, better will be the load balancing (or less will be the link minimizes the average packet delay in the wireless front endcongestion) and vice versa. In this performance metric also, of a WOBAN. We modeled wireless routers as M/M/1 queuesDARA performs much better than MHRA and SPRA. MHRA and predicted wireless link states periodically. We showedand SPRA find the shortest paths and thereby poorly balance that DARA achieves better load balancing and less congestionthe load. Consequently, they congest a part of the mesh. Both compared to tradional approaches such as minimum-hop rout-DARA and PTRA perform well and are comparable to each ing algorithm (MHRA) and shortest-path routing algorithmother. Till the load of 0.75, DARA performs better than PTRA. (SPRA). In addition to improving delay, DARA also improvesAfter that, PTRA performs better. the average hop count compared to predictive throughput routing algorithm (PTRA), a popular routing algorithm used in the wireless front end of a WOBAN. R EFERENCES [1] S. Sarkar, B. Mukherjee, and S. Dixit, “Optimum Placement of Multiple Optical Network Units (ONUs) In Optical-Wireless Hybrid Access Networks,” Proc., OFC 2006, Anaheim, California, March 2006. [2] S. Sarkar, B. Mukherjee, and S. Dixit, “Towards Global Optization of Multiple ONUs Placment in Hybrid Optical-Wireless Broadband Access Networks,” Proc., COIN 2006, Jeju, South Korea, July 2006. [3] http://en.wikipedia.org/wiki/San francisco. [4] http://quickfacts.census.gov/qfd/states/06/06075.html. [5] http://earth.google.com. [6] L. Kleinrock, Queueing Systems, Vol-I: Theory, John Wiley, 1975. [7] K. Trivedi, Probability and Statistics with Reliability, Queuing and Computer Science Applications, John Wiley, 2002. [8] M. McKusick and G. Neville-Neil, The Design and Implementation of the FreeBSD Fig. 6. Load balancing (or link congestion) vs. load in SFNet. Operating System, Addison Wesley, 2005. [9] Tropos Netwoks, http://tropos.com. [10] G. Narlikar, G. Wilfong, and L. Zhang, “Designing Multihop Wireless Backhaul Networks with Delay Guarantees,” Proc., INFOCOM 2006, Barcelona, Spain, Figure 7 captures the accuracy of our LSP. We plot the April 2006.LSA values for packet intensities in wireless links against [11] S. Lee, G. Narlikar, M. Pal, G. Wilfong, and L. Zhang, “Admission Control for Multihop Wireless Backhaul Networks with QoS Support,” Proc., WCNC 2006,the predicted values by LSP. We observe that, at high loads, Las Vegas, Nevada, April 2006.the predicted values by LSPs are quite accurate. At high [12] T. Liu and W. Liao, “Capacity-Aware Routing with Multi-Channel Multi-Rateloads, predicted values are on average 0.1% off the range Wireless Mesh Networks,” Proc., ICC 2006, Istanbul, Turkey, June 2006. [13] A. H. M. Rad and V. W. S. Wong, “Joint Optimal Channel Assignment andof LSA values. Even at higher LSA intervals, LSPs perform Congestion Control for Multi-channel Wireless Mesh Networks,” Proc., ICC 2006, Istanbul, Turkey, June 2006.well (except during the transient phase where the LSP values [14] M. Kodialam and T. Nandgopal, “Characterizing the Capacity Region in Multi-oscillate before settling down after a certain time period, see radio Multi-channel Wireless Mesh Networks,” Proc., ACM MobiCom 2005,subplots 2 and 3 of the figure). The maximum difference Cologne, Germany, September 2005. [15] M. Alicherry, R. Bhatia, and L. Li, “Joint Channel Assignment and Routing forbetween LSA and LSP values is 15.58%. Similar plot exists Throughput Optimization in Multi-radio Wireless Mesh Networks,” Proc., ACM MobiCom 2005, Cologne, Germany, September 2005.for low loads, where predicted values by LSPs are also quite [16] R. Draves, J. Padhye, and B. Zill, “Routing in Multi-radio, Multi-hop Wire-accurate. (We do not show the plot at low loads to conserve less Mesh Networks,” Proc., ACM MobiCom 2004, Philadelphia, Pennsylvania, September 2004.space.) Also note that the bandwidth consumption for LSAs [17] V. Gambiroza, B. Sadeghi, and E. Knightly, “End-to-end Performance and Fairnessincreases if we decrease the LSA period. For the mesh in in Multihop Wireless Backhaul Networks,” Proc., ACM MobiCom 2004, Philadel- phia, Pennsylvania, September 2004.WOBAN, it is very important to keep the LSA period high

S06 S10 P05

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