A Problem Reduction Approach for the Design of Fault-Tolerant Wireless-Optical Access Networks

Transcription

1 A Problem Reduction Approach for the Design of Fault-Tolerant Wireless-Optical Access Networks N. Correia Center of Electronic, Optoelectronic and Telecommunications (CEOT), Faculty of Science and Technology, University of Algarve, Faro, Portugal G. Schütz Institute of Engineering, University of Algarve, Faro, Portugal Abstract Wireless-optical approaches, leveraging on the strengths of both wireless and optical technologies, are seen as promising approaches for future access networks. For wirelessoptical access networks to provide geographically continuous wireless coverage, fault-tolerance must be integrated in the design of these networks. While at the optical back end different fiber failure impacts must be considered, at the wireless front end the disruption of wireless communication links must be taken into consideration. Here we address the problem of designing a faulttolerant multi-radio wireless-optical access network, a problem that is hard to solve. Our goal here is to extract guidelines for the reduction of such complex problem, which is done through the analysis of wireless and optical failure impacts on network congestion. Two network scenarios, having different risk groups for gateways, are analysed. I. INTRODUCTION Wireless-optical architectures have been recently proposed as flexible and cost-effective access infrastructures where wireless and optical technologies are seen as complementary. The optical fiber, although providing huge amounts of bandwidth, remains expensive for fiber-to-the-home provision. Wireless access networks, on the other hand, can go almost everywhere with a reasonable cost but provide highly bandwidthconstrained transmission channels that are susceptible to a variety of impairments and are spectrum limited. The combined use of both technologies, where fiber is provided as far as possible and then wireless access is provided at the front end, leverages on the strengths of both technologies and clearly emerges as a promising approach [1], [2]. Recent advances in wireless technologies are enabling costeffective and flexible wireless Internet access, and are providing incentives for building efficient multihop wireless networks [1]. Contrarily to wireless adhoc networks, which preclude the use of a wired infrastructure, we focus here on wireless mesh networks (WMNs) that employ multihop communications to forward traffic from/to optical fiber entry points. To enhance network capacity at the wireless section, smart antenna, multiinput multi-output (MIMO), ultra wideband (UWB) and multichannel interface systems are being explored. The use of routers having more than one multi-channel radio interface is a very attractive way of improving network throughput since cost-effective wireless devices are now widely available [3], [4]. Current IEEE b/g and a standards, for example, provide 3 and 12 orthogonal channels, respectively, that can work in the same area with negligible inter-channel interference [5]. Our discussion will assume multi-channel communication at the wireless front end section. For wireless-optical access networks to provide geographically continuous wireless coverage, fault-tolerance must be integrated in the design of these networks. While at the optical back end different fiber failure impacts must be addressed, at the wireless front end the disruption of wireless communication links, which can be a consequence of unlicensed spectrum utilization or radio interface failure, must be considered. In WMNs, although wireless nodes are assumed to have no mobility, other arriving mobile users may activate communication links that will cause interference. With the explosive growth of wireless systems, interferences between co-located systems will increase in a near future [5]. This can be a problem in high-density areas and wireless-optical access networks must be prepared to work under such environments avoiding service breaks. In this article the problem of designing a fault-tolerant multi-radio wireless-optical access network is addressed. This problem can be quite hard to solve since besides network connectivity, flowing of traffic demands and radio/link channel assignment, a large number of wireless and optical failure states must be considered. Our goal here is to extract guidelines for the reduction of such complex problem. The rest of this paper is organized as follows. Section II provides an overview of wireless-optical access architectures, fault-tolerance challenges and state of the art. Section III defines and formalizes the fault-tolerant network design problem being considered. Section IV analyses the impact of wireless and optical failures, and presents a heuristic to determine such impacts. In Section V the computation results are interpreted and guidelines on problem reduction extracted. Section VI concludes the article. II. FAULT TOLERANCE IN WIRELESS-OPTICAL ACCESS ARCHITECTURES Wireless-optical refers to the combined use of conventional wireless and optical technologies. At the back end access section long-range links are provided by optical fibers while at the front end the connection from long-range end-points to c 2011 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. Paper is available online at DOI: /HPSR

2 Fig. 1. Wireless-optical access network architecture. wireless end users is accomplished using radio-frequency (RF) wireless technology [2]. The back end dominant technology in wireless-optical access networks is the passive optical network (PON), illustrated in Figure 1, consisting of optical line terminals (OLTs), at the service provider s central office (CO), and optical network units (ONUs) near end users. An ONU can serve multiple gateways. Regarding the wireless infrastructure, standard WiFi or WiMAX technology can be used for wireless mesh connectivity. Wireless-optical access network architectures are primarily envisioned for residential, business or public environments where wireless devices have limited or no mobility [2]. That is, the location of wireless mesh routers is known in advance allowing traffic flow and radio channel assignment to be carefully planned in advance. Any wireless user, scattered over such geographical area and requiring for Internet access, can associate with a nearby wireless mesh router that has access to gateway routers through multiple paths. Wirelessoptical access solutions are expected in many cities around the world in a near future. A yet to be explored research issue in these architectures is how service breaks can be avoided in these propitious to failure environments or, in other words, how can fault-tolerance be provided whenever either foreign mobile users activate communication links, causing interference, or a fiber fails. This issue can become more challenging, when compared with single optical or wireless network deployments, because of the interplay between these two different technologies. A. Optical Back End For fault-tolerance to be provided in wireless-optical architectures, different fiber cut impacts must be considered according to the location of the fiber. These include: ONU: Whenever one of the splitter s fiber branch fails, the ONU connected to that branch may be considered as being inoperable. From the wireless point of view, one or multiple gateways will be affected thus becoming also inoperable. In this case traffic must be redirected to gateways connected to alive ONUs; OLT: Whenever a fiber directly connected to an OLT fails, all ONUs (and gateways) connected to that OLT will become inoperable. In this case traffic must be redirected to gateways connected to alive ONUs and alive OLTs; More severe failures lead to larger portions of traffic being rerouted. The risk groups (RGs) must be known when designing the network. Two gateways in the network share a risk group if they share a common fiber (main fiber or fiber branch according to the level of optical fault-tolerance being considered). This implies that if one gateway fails, other gateways included in the risk group will fail too. In case of an optical failure, a flat 1 single-radio wireless mesh front end provides inherent risk awareness characteristics since traffic can be redirected to other gateways/onus. When multiple radio interfaces are used for capacity increase, the impact of an optical failure can be more significant since the wireless induced mesh topology, resulting from the assignment of channels to radios, may not provide an alternative route to alive gateways/onus if not carefully planned. B. Wireless Front End Radio interfaces can operate on any of the available orthogonal channels using time division for transmission and reception. A wireless router u can transmit to another wireless router v only if the distance between u and v, denoted by d u,v, is smaller than the transmission range of router u, denoted by T u. That is, a feasible transmission link from u to v exists if and only if d u,v T u. To generalize this to multi-radio wireless mesh routers we assume that all radio interfaces are identical. We also assume that if router u is at the transmission range of router v then router v is also at the transmission range of router u, allowing communication in both directions. While the transmission range of a router, T u, defines the maximum physical range of radio signals, the interference range determines the area where other routers cannot use the same channel at the same time 2. In the following discussion a feasible transmission link or feasible link refers to a potential transmission link while a true transmission link, with a channel already assigned to it, is called transmission link or link. At the wireless front end the wireless link failures are basically a consequence of radio failure or interference (e.g. use of unlicensed spectrum by wireless devices). If, under normal conditions, the traffic is flowing using route (u v GW 1 ), whereuandv are wireless mesh routers andgw 1 is a gateway router, and then a wireless link failure occurs, for example, between router v and gateway GW 1, affecting traffic in both directions, then another route between router v and any alive gateway must be established, say (u v w GW 2 ), for example. Here we assume upstream and downstream traffic to take the same routes since devices are able to transmit and receive using time division on a specific channel. 1 By flat we mean the use of the same channel in all radio interfaces. 2 A common interference model is considered.

3 When flat single-radio channel assignment is used, wireless front end failures/interferences may lead to the disruption of all communications in some interfering area. When multiple channels and/or radios are present, the network may become either disconnected or may have an unacceptable alternative route (e.g. many hops) if not carefully planned. C. State of the Art Recent research efforts in wireless-optical architectures mainly address routing and optimal placement of ONUs assuming single-radio routers [2], [6], [7], [8]. Wireless-optical fault-tolerance has been addressed in [9], [10]. In [9] an alternative path is provided to alive gateways after failure and no integrated reliability (both wireless and optical failures being considered) is performed. The only work considering such integration is [10] that provides an approach for a joint wireless and optical reliability planning. Here we go further by addopting a problem reduction approach to the design of such fault-tolerant wireless-optical access networks. III. FAULT-TOLERANT DESIGN PROBLEM The problem of designing a network taking into account failures is generally referred to as reliability or fault-tolerance design problem. In such problems the link failures are taken into account assuming failure scenarios (states) in which one or more links become unavailable. The goal is to determine demand flow and required link capacities to carry the demand volumes. In the context of wireless-optical access networks the goal is to design the wireless access section considering that either optical or wireless related failure states can occur. A. Definitions and Assumptions Let us consider a wireless-optical network represented by graph G = (V,L), where V is the set of nodes (routers), each equipped with one or more radios (interface cards), and L is the set of feasible wireless links. The set of wireless mesh nodes aggregating local user traffic is denoted by V A V while the set of nodes acting as gateways, and attached to an ONU, is denoted by V G V. In the following discussion a directed graph is considered. This assumption will enable a clearer understanding of the problem formulation and further analysis. It is clear, however, that planning a route starting in a wireless mesh router and directed toward a gateway, corresponds to finding an undirected route for upstream and downstream direction since devices are able to transmit and receive on that assigned frequency, as previously mentioned. For network reliable design it becomes necessary to summarize dependence among wireless feasible links. For this purpose we define a matrix I, having L lines and L columns, where I[l,l ] = 1 if l L and l L cannot transmit/receive simultaneously on the same channel (not independent) because they are at the interference range of each other. If wireless feasible links interfere then time division must be used during transmission. We also define a matrix I r for router interference, meaning that I r [u,v] = 1 if router u V interferes with router v V. We denote by RG the set of existing risk groups, which are known in advance, and by RG i a specific risk group i. It is assumed that risk groups form a partition of V G, namely i {g RG i} = V G RG i RG j =, i,j : i j. A total number of R radio interfaces are available at the network, each radio having a set of available orthogonal channels denoted by C. Routers can have a different number of radios but, for simplicity, the set C is the same for all radios. For reliability to be provided at least 2 V A + V G radios must exist in the network. That is, wireless mesh nodes require at least an alternative radio while gateways may require a single radio if traffic to/from that gateway can be redirected to an alternative gateway in case of failure. The local upstream/downstream traffic demand is denoted by D u, u V A. B. Failure States Let us denote the set of failure states, optical or wireless, as F. The subset of optical failures is denoted by F O F while the subset of wireless failures is denoted by F W F. Optical failure: An optical failure state f F O is defined for every risk group RG i RG. Considering a specific risk group RG i, the set of wireless feasible links associated with an optical failure state f F O is given by L f = {l L g RG i,s(l) = g d(l) = g}, where s(l) and d(l) are the source and destination nodes of l L. Whenever an optical failure f F O occurs, all transmission links matching L f and working on any channel c C are affected. Wireless failure: A wireless failure state f is defined for every feasible wireless link l L. When defining the set of wireless feasible links associated with a wireless failure state f F W, L f, one of the following possibilities can be assumed: i) L f = {l L l = l}; or ii) L f = {l L I[l,l] = 1}. That is, a wireless failure may affect a single wireless link or many wireless links. In the first case only l is included in L f while in the second case all links in the interference range of l are included in L f. Whenever a wireless failure f F W occurs on a specific channel c C, all transmission links matching L f within the following range {l L l = l} L f {l L I[l,l] = 1}, (1) and communicating using channel c C, will be affected. C. Fault-Tolerant Network Design Problem Formulation We now formulate the fault-tolerant network design problem taking into account possible optical and wireless failure states. For any failure, the set of transmission links that were not affected must be dimensioned to support the extra flow of demands. The following notation is used for variables: v,l,c ρ c u Under a failure state f F affecting channel c C, this is the flow allocation for demands sent from node v V A, toward any gateway, on the transmission link matching l L and working on channel c C. One if the node u V transmits or receives through channel c C; zero otherwise.

4 Objective Function: To handle traffic growing the traffic must be distributed accross the network. This is achieved when minimizing the load of the most congested interference area: χ = Minimize max f F,c C,l L,c C { v V A l L:I[l,l]=1 v,l,c }. (2) This takes into account that time-division is used to allocate traffic transmissions whenever nearby communication links are at the interference area of each other and using the same channel. Communication links, at the interference area of each other, will use the same channel if no extra channels and/or radios are available. Routing Flow Conservation Law: = { l L:s(l)=uc C v,l,c l L:d(l)=uc C v,l,c = D v, if u = v 0, otherwise, v,u V A, f F, c C (3) g V G l L:d(l)=g c C v V A v,l,c = D v, v V A, f F, c C Wireless Reliability: v,l,c = 0, f F W, c C (5) l L f Optical Reliability: v V A l L f c C c C Assignment of Radios to Nodes: ρ c u v V A l L:s(l)=u d(l)=u ωf,c v,l,c v V A D v L (4) v,l,c = 0, f F O (6), u V,, f F, c,c C (7) ρ c u R (8) u V c C Binary and Non-Negative Assignments: ρ c u {0,1}; v,l,c 0. (9) Note that the flowing of traffic demands is not conditioned to take a single particular route. Constraints (3) and (4) ensure flow conservation for the delivery of demands. For a specific wireless or optical failure, constraints (5) and (6) force traffic flow to be zero at the affected links. Therefore, together with the flow conservation constraints, these force the set of transmission links, not affected by a specific failure, to be dimensioned in order to support all the demands. Constraints (7) will make the assignment of radios (operating at a specific channel) to nodes, according to the flow variables used to carry demands, and constraint (8) limits the total number of radios. Computing expression (2) can be arbitrarily complicated since the network connectivity, flowing of traffic demands, radio and channel assignment, and wireless and optical failure states are part of its definition. We analyse next the impact of wireless and optical failures on network congestion. This will allow problem reduction guidelines to be obtained. IV. IMPACT OF WIRELESS AND OPTICAL FAILURES To proceed with this analysis we will assume that the flowing of traffic demands at the wireless section is done using a set of precomputed primary routes, working under normal conditions, and using a set of precomputed backup routes activated in case of wireless failure. More specifically, we denote by P the set of precomputed primary routes and by B p the set of precomputed backup routes protecting a specific primary route p P. That is, backup routes are failure dependent, meaning that a backup route is activated for a specific link failure of the primary route it protects. The gateway router of a backup route can not be at the same risk group as the gateway router of the primary route it protects. A specific primary route included in P is denoted by p while a backup route included in B p is denoted by b. Every route p P or b B p can be defined as a connected series of links, written as p : s(p) V A... d(p) V G and b : s(b) V A... d(b) V G. We define E p and E p b as the set of feasible links used by primary route p and backup route b, respectively. In addition we define E p,u and E p b,u as the set of feasible links used by primary route p and backup route b, respectively, having node u V as its source or destination. The set E includes all feasible links used by primary and backup routes. The variables include ρ c u, previously defined, and: One if channel c C is assigned to primary route τ p c,l c,l p P, at link l E p ; zero otherwise. One if channel c C is assigned to link l E p b used by backup route b B p protecting primary route p P against the failure of link l E p : s(l ) = s(b); zero otherwise. A wireless-optical network, using precomputed routes, provides fault-tolerance to wireless and optical failures only if: i) the gateway of a backup route is not at the same risk group as the gateway of the primary route it protects (ensured by precomputed routes); and ii) a transmission link used by a primary route does not simultaneously go down with the transmission links included in the backup route protecting it. A. Impact Analysis As previously stated, the impact of interference at the wireless front end can go from the disruption of a single wireless connection to the disruption of a set of interfering wireless connections. Thus, it is realistic to assume that the congestion in a wireless-optical network will be lower bounded by the impact of a single wireless link failure and upper bounded by the highest value between the impact of an optical failure and the impact of a set of interfering wireless links going down. To measure such impacts, let us define the following traffic

5 load variables related to a wireless link l E operating in channel c C: No Failure: In the absence of failures the traffic flowing through primary routes at the interference range of link l E, and operating on channel c, is accounted by: α l,c = τ p c,l D s(p) (10) p P l E p :I[l,l]=1 Wireless Link Failures: The largest amount of traffic that can be forwarded at a time to the interference range of a transmission link matching l E, and operating using channel c C, due to a single wireless link failure is accounted by or β l,c = max c C,l E ( l E p b :s(b)=s(l ) I[l,l]=1 φ l,c = max c C,l E ( p P:τ p c,l =1 c,l D s(p) ) (11) p P: l E p I[l,l ]=1 τ p c,l =1 l E p b :s(b)=s(l ) I[l,l]=1 c,l D s(p) ) (12) according to the discussion in Section III-B and condition (1). Optical Failure: The largest amount of traffic that can be forwarded at a time to the interference range of a transmission link matching l E, and operating using channel c C, due to an optical failure is accounted by γ l,c = max RG i RG ( l E:d(l ) RG i c C p P:τ p c,l =1 l E p b :I[l,l]=1 c,l D s(p) ). (13) When examining expressions (11), (12) and (13) we can clearly establish that β l,c φ l,c and β l,c γ l,c. Furthermore, when capturing the network congestion using functions f 1 = max l E,c C (α l,c +β l,c ) (14) f 2 = max l E,c C (α l,c +φ l,c ) (15) f 3 = max l E,c C (α l,c +γ l,c ) (16) we also assume that, in general, f 1 f 2,f 1 f 3. Using this information we wish now to minimize the lowest and highest expected impact and analyse its components in order to extract guidelines on problem reduction. The lowest and highest impacts can be obtained by solving the problem and LI = min f 1 (17) HI = min {max{f 2,f 3 }} (18) respectively, both subject to c C l E p b :I[l,l]=1 ρ c u p P τ p c,l = 1, p P, l Ep (19) c C c,l = 1, p P, b B p, l E p b (20) c,l (1 τ p c,l ) Ep b, p P, c C,, l E p E p b, b Bp : s(b) = s(l) (21) l E p,u τp c,l + p P b B p l E p c,l b,u p P Ep,u + p P b B p Ep b,u,, c C, u V (22) ρ u c R (23) u V c C τ p c,l,σp,b c,l,ρc u {0,1};α l,c,β l,c,φ l,c,γ l,c 0. (24) Constraints (19) and (20) assign a channel to each link used by primary and backup routes, respectively. Constraints (21) ensure that a link channel used by a primary route will not interfere with link channels included in the correponding backup routes, meaning that primary and backup routes will not fail simultaneously. Constraints (22) force ρ c u to be one if at least one primary or backup route uses channel c, at some link starting or ending at node u. Constraint (23) limits the total number of available radios to R. Constraints (24) identify binary and float variables. B. Computation of Impact In order to find a solution for the previously defined problem, we develop a heuristic that explores some of its properties. 1) Problem Properties: Let us consider single radio gateway routers, denoted by g i, dual-radio mesh routers, denoted by u or v, and any set of precomputed primary and backup routes. Under these assumptions the following propositions can be enunciated. Proofs are omitted due to lack of space. Proposition 1: If gateway routers g i1 and g i2 interfere, I r [g i1,g i2 ] = 1, then they must have their receivers tuned to different channels. Mesh routers simultaneously adjacent to g i1 and g i2 must have their radios assigned to those two different channels. Proposition 2: If two adjacent mesh routers, u and v, are also adjacent to a gateway, g i, then ρ c u = ρ c v, c C. As a consequence of these two propositions we conclude that: if gateway routers g i1 and g i2 interfere, router u is adjacent to g i1 and router v is adjacent simultaneously to g i1 and g i2, then router u must have the same channel assignment of router v.

6 Proposition 3: If gateway routers g i1 and g i2 interfere, router u is adjacent to g i1, router v is adjacent to g i2 and router u and v are adjacent, then either both gateway channels are assigned to routers u and v, or routers u and v have at least a common channel different from the two gateways channels. When gateways have 2 or 3 radios, proposition 3 still holds. Proposition 4: If gateway routers g i1, g i2 and g i3 interfere, a router u is adjacent to two of them and no more than two links join u to the other gateway then there is no feasible solution for 2 V A + V G. Clearly, this result still holds when a router is adjacent to three (or more) gateways. 2) Failure Impact Heuristic (FIH): As previously mentioned, we develop a heuristic to find the lowest and highest failure impacts. The approach used in our heuristic (FIH) is based on Greedy Randomized Adaptive Search Procedures (GRASP). GRASP were first proposed by Feo and Resende, [11], and have been used several times to solve hard combinatorial optimization problems [12]. GRASP combine a greedy randomized constructive algorithm with local search in an iterative procedure composed by independent iterations. A minimization basic GRASP can be described as: 1 f(s ) + (s is the incumbent solution and f is the objective function) 2 for i = 1 to r do 3 Apply a greedy randomized procedure (GRP) to construct a solution s; 4 Perform a local search on s and obtain a solution s ; 5 if f(s ) < f(s ) then 6 s s ; 7 end 8 end After obtaining the minimum feasible number of radios, R F, applying proposition 4, FIH performs its steps as follows: - In step 2, r is initialized to the number of feasible channel assignments to one radio gateways, determined applying proposition 1. - In step 3, the GRP is applied for R F radios available in the network. It starts with the i-th feasible assignment to gateway routers (determined by proposition 1) and reduces the number of free variables applying propositions 1, 2 and 3. In each of the GRP iterations, for available channels at unassigned primary and backup links, the traffic flowing in its interference range is computed, and a list with the best assignments (lowest congestion values) is maintained. Then, one assignment from this list is randomly chosen and assignments done to corresponding routers according to expression (22). - In step 4, the local search is performed by adding one extra radio, per iteration, until R radios are reached (that is, from R F to R). During this local search a substantial number of feasible solutions is explored since each iteration consists in: i) finding the end routers (denoted here by u and v) of the most overloaded link, included in the best solution obtained by that time; ii) obtaining a set of new feasible solutions, each one produced by temporarily inserting an extra radio at each Fig. 2. San Francisco s wireless optical access network. neighbour router of u or v (denoted by w), and reassigning channels at the neighbourhood of w; iii) retaining the best solution produced in ii). V. COMPUTATIONAL RESULTS AND PROBLEM REDUCTION ANALYSIS In this section we analyse the impact of wireless and optical failures on network congestion and extract guidelines on complexity problem reduction. Results were obtained for the SFNet, a wireless-optical network in San Francisco discussed in [2]. The network graph of SFNet, shown in Figure 2, includes 25 routers, 5 of which are gateways: V G = {5,13,16,22,25}. We study two network scenarios having different RGs for gateways: - Scenario I: RG1={5}, RG2={13}, RG3={16}, RG4={22} and RG5={25}. That is, gateways belong to different risk groups. - Scenario II: RG1={5,13}, RG2={16,22}, RG3={25}. That is, gateways 5 and 13 are connected to the same OLT. The same happens for gateways 16 and 22. The transmission and interference ranges are considered to be the same for all radios inside a specific node. The available number of independent channels in a router, C, was set to 3 and the maximum total number of radios available in the network, R, was set to 55. The local traffic demand is set to D u = 0.5, u V A, assuming that the maximum channel transmission rate is normalized to a unit constant. All precomputed primary routes and link failure dependent backup routes take the shortest path, so that no unacceptable long routes are computed. Choosing the shortest routes also indirectly leads to a network that is able to support more traffic due to the reduced number of hops and, therefore, reduced use of resources per route. The gateway router of a backup route cannot be at the same risk group as the gateway router of the primary route it protects. Whenever a wireless mesh router becomes aware of a failure/interference in any channel,

7 TABLE I f 1, f 2 AND f 3 VALUES FOR SCENARIOS I AND II Number of Radios I f ,5 5, ,5 4,5 4 4 f 2 11, f II f 1 6 5, f 2 8 6,5 6, f , Fig. 3. LI and HI heuristic solutions for Scenario I. Fig. 4. LI and HI heuristic solutions for Scenario II. it activates the backup routes of the affected primary routes for upstream/downstream transmission to proceed. The heuristic results for the LI and HI problems, indicating the load of the most overloaded wireless link at the network, are plotted in Figure 3 and 4 for Scenarios I and II, respectively. We can say that, in these scenarios, 2 extra radios beyond the lower bound 2 V A + V G, 47 radios in total, provide the most significant improvements on network congestion. This is so because, although the LI solution presents a small extra decrease on congestion when more than 47 radios are available, the HI solution stops decreasing after 47 radios in both scenarios. A more significant reduction on HI, when compared with LI, for radios also allows us to conclude that two extra radios are enough to provide the capacity required for fault-tolerance. Although the network capacity required, when 45 and 46 radios are available, is higher for Scenario I than for Scenario II when HI is computed, the difference between these scenarios is small. This HI related observation, together with the observation that Scenario I and II are very similar when computing LI, allows us to conclude that the network capacities required for these scenarios are not so different, meaning that the capacity required for protection is not strongly dependent on the RGs. That is, the extra capacity required to consider RGs with more than one gateway is not much, when analysing the highest and lowest failure impacts. Note that, when compared with the use of dedicate resources for fault-tolerance provision, the approach under study can be much more bandwidth effective because backup routes, not activated simultaneously by any failure, can share the extra capacity reserved for backup, thus allowing a better spectrum reutilization. The use of dedicate resources implies that at least 50 radios are necessary, 2 radios per node (gateways included), while with our approach reliability can be provided using a smaller number of radios since gateways are allowed to have a single radio. As shown in Table I, f 1 f 2 and f 1 f 3, as assumed previously (see expressions 14, 15 and 16). We have observed that the α values (contribution of primary routes to the most overloaded link channel) vary from 1.5 to 3.5 and no significant differences exist between network scenarios and measured failure impacts. The α values increase when the other components (β, φ and γ) decrease, a consequence of the nature of the problem being solved (minimizing the highest congested area means that an upper bound is being minimized and oscillations between parameters might exist when seeking for the optimal). Still in Table I, since f 2 = f 3 in Scenario I, except for 45 radios, and f 2 < f 3 in Scenario II, then the minimization of f 3 could be enough to plan a faulttolerant wireless-optical network for any scenario, while the minimization of f 2 would be enough to plan a fault-tolerant wireless-optical network when gateways are singly affected by an optical failure. That is, when gateways are singly affected, optical failure states can be ignored for network design, when using our approach. Figures 5 and 6 plot the β, φ and γ components obtained when solving the LI and HI problems, so that an easier comparison between variables can be done. These figures exhibit the expected relation β φ and β γ. In fact we have always β < φ and β < γ, except in one case (46 radios in Scenario II) where β = φ. While in Scenario II we always have γ > φ, in Scenario I this only happens when 52 or more radios are available and with a small difference between them. This confirms that the impact of a severe wireless failure,

8 enough to plan a reliable wireless-optical network when one or more gateways are affected by an optical failure, meaning that wireless failure states can be ignored when solving this design problem. When RGs include a single gateway, the minimization of f 2 is enough to plan a fault-tolerant wirelessoptical network and optical failure states can be ignored. This is so because the impact of a severe wireless failure, involving a set of interfering links, is the most demanding when gateway are singly affected, and it is comparable to the impact of an optical failure, while the impact of an optical failure is the most demanding when multiple gateways are affected by an optical back-end failure. Fig. 5. β, φ and γ components when solving the LI and HI problems for Scenario I. Fig. 6. β, φ and γ components when solving the LI and HI problems for Scenario II. involving a set of interfering links, is the most demanding when gateway are singly affected, and it is comparable to the impact of an optical failure, while the impact of an optical failure is the most demanding in Scenario II due to optical back-end severe failures affecting more than one gateway. VI. CONCLUSION In this article we address the problem of designing a faulttolerant multi-radio wireless-optical access network. Due to its complexity, we have analyzed the impact of wireless and optical failures on network congestion in order to extract guidelines on complexity problem reduction. The results allowed us to conclude that, in terms of network topology planning, a small increase in the number of total radios available, beyond the lower bound 2 V A + V G, is enough for fault-tolerance provisioning. Also, the network capacity required to provide fault-tolerance is not strongly dependent on the risk groups (RGs) defined or, in other words, the extra capacity required to consider RGs with multiple gateways is not much. In terms of problem reduction, the minimization of f 3 is ACKNOWLEDGMENT This work was supported by the Foundation for Science and Technology from Portugal within CEOT (Center for Electronic, Optoelectronic and Telecommunications). REFERENCES [1] N. Ghazisaidi, M. Maier, and C. M. Assi, Fiber-Wireless (FiWi) Access Networks: A Survey, IEEE Communications Magazine, vol. 47, no. 2, pp , [2] S. Sarkar, H.-H. Yen, D. Dixit, and B. Mukherjee, A Novel Delay- Aware Routing Algorithm (DARA) for a Hybrid Wireless-Optical Broadband Access Network (WOBAN), IEEE Network, vol. 22, no. 3, pp , [3] S. Avallone and I. Akyildiz, A Channel Assignment Algorithm for Multi-Radio Wireless Mesh Networks, in IEEE ICCCN, August 2007, pp [4] J. Zhang, H. Wu, Q. Zhang, and B. Li, Joint Routing and Scheduling in Multi-Radio Multi-Channel Multi-Hop Wireless Networks, in International Conference on Broadband Networks, October 2005, pp [5] K. Ramachandran, E. Belding, K. Almeroth, and M. Buddhikot, Interference-Aware Channel Assignment in Multi-Radio Wireless Mesh Networks, in IEEE INFOCOM, April 2006, pp [6] W.-T. Shawand and et al., Hybrid Architecture and Integrated Routing in Scalable Optical-Wireless Access Network, IEEE JLT, vol. 25, no. 11, pp , [7] S. Sarkar, H.-H. Yen, D. Dixit, and B. Mukherjee, Hybrid Wireless- Optical Broadband-Access Network (WOBAN): Network Planning and Setup, IEEE JLT, vol. 26, no. 6, pp , [8], Hybrid Wireless-Optical Broadband Access Network (WOBAN): Network Planning Using Lagrangean Relaxation, IEEE/ACM Transactions on Networking, vol. 17, no. 4, pp , [9], RADAR: Risk-and-Delay Aware Routing Algorithm in a Hybrid Wireless-Optical Broadband Access Network (WOBAN), in IEEE/OSA OFC, March 2007, p. OThM4. [10] N. Correia, J. Coimbra, and G. Schütz, Fault-Tolerance Planning in Multi-Radio Hybrid Wireless-Optical Broadband Access Networks, IEEE/OSA JOCN, vol. 1, no. 7, pp , [11] T. Feo and M. Resende, Greedy Randomized Adaptive Search Procedures, J. Global Optimization, vol. 6, pp , [12] P. Festa and M. Resende, An annotated bibliography of GRASP, Part II: Applications, Int. Tr. in Operational Research, vol. 16, pp , 2009.