The reliability of wireless backhaul mesh networks

Transcription

1 The eliability of wieless backhaul mesh netwoks Gei Egeland 1, Paal E. Engelstad 2 1 Depatment of Electical and Compute Engineeing, Univesity of Stavange, 4036 Stavange Noway 1 gei.egeland@gmail.com 2 Teleno Reseach and Innovation 1331 Fonebu, Noway 2 paal.engelstad@teleno.com Abstact When planning the stuctue of a backhaul mesh netwok fo public access, it is common to intoduce edundant nodes in the mesh netwok. These ae called edundant, because they do not incease the netwok capacity unde nomal opeation, due to the shotest-path metic of the outing potocol. Instead, thei sole pupose is to incease the netwok eliability by poviding failove links when a link in the shotest-path fails. This pape shows how to estimate the additional netwok eliability that esults fom intoducing a edundant node. The best location of a edundant node, i.e. whee to locate the node in ode to maximise the additional netwok eliability, can also be found. I. INTRODUCTION The popula IEEE standad [1] is widely used fo wieless local aea netwoks (WLAN) and is deployed in a wide ange of diffeent devices. At the moment, IEEE is developing a new extension to the standad, IEEE s [2], in ode to use the technology also fo wieless mesh netwoking. A wieless mesh netwok (heeafte efeed to as a mesh netwok o a mesh) is an ad hoc netwok composed of a goup of self-configued and self-oganised nodes inteconnected via wieless links. A node is also efeed to as a mesh point () o a oute. An is efeed to as a mesh access point () if it includes the functionality of access points allowing egula stations (s) to connect to the mesh infastuctue as clients. Futhemoe, an is efeed to as a Mesh Potal (P) if it has additional functionality fo connecting the mesh netwok to othe netwok infastuctues. Mesh netwoking is elated to mobile ad hoc netwok (MANET) technology. While the MANET effot is mainly focusing on the outing aspects of ad hoc netwoks, s standadises all necessay functionality fo a fully opeational netwok, including netwok discovey and negotiation of netwoking paametes, authentication and secuity, inte-woking with othe netwoks and outing. Fo outing, Radio-Metic AODV o Radio-Awae OLSR can be used. These ae the adio-awae vesions of the outing potocols AODV [3] and OLSR [4] that wee oiginally developed fo MANETs. Thee ae many pomising applications of mesh technology. A lage goup of applications takes advantage of the fact that a mesh netwok can be set up in an ad hoc fashion. Mesh technology can theefoe povide a self-fomed tempoay communication infastuctue fo disaste ecovey opeations, fo communication at confeences o conventions and in tactical militay opeations. Anothe goup of applications appeas as a consequence of the high costs associated with inteconnecting the s (i.e. outes) with wied links. With mesh technology it is possible to extend the each of the wied backbone though a wieless backhaul mesh of s in a cost-efficient manne. Cuently, thee ae a lage numbe of commecial deployments of such solutions fo public access in uban aeas, whee the nodes ae often placed on oof-tops. Such backhaul mesh netwoks ae nomally not fomed in an ad hoc manne. Instead, the location and placement of each, P and is caefully planned (netwok planning). Since the eliability of such mesh netwoks often is poo and a consideable hudle fo wide deployment, it is common to intoduce edundant s in the netwok in ode to impove netwok eliability. Figue 1. Redundant P Wied infastuctue : Mesh Point P: Mesh Potal : Mesh Access Point : Station A backhaul mesh netwok with a edundant node. Figue 1 illustates the intoduction of a edundant node in a backhaul mesh netwok. In nomal opeation, each is connected to a, and the s taffic is fowaded along the shotest path between the and the P. Howeve, if a link in the shotest path becomes unavailable, the outing potocol ensues that a new path between the and the P is fomed via the edundant node. Note that due to the shotest-path featue of the outing potocol, thee is no load-shaing on the netwok. This means that the intoduction of the edundant node does not incease 1

2 the oveall thoughput of the netwok. Its main function is to impove the netwok eliability. Thus, in ou study, we ae solely concened with the connectivity measues of a wieless mesh netwok, while othe netwok pefomance metics, such as thoughput and delay, ae not elevant hee. Fo many mesh netwoks, including commecial backhaul mesh netwoks in uban aeas (e.g. oof-top mesh netwoks), thee is a high site-acquisition cost associated with each node, and it is not economically feasible to intoduce too many edundant nodes. Instead, one needs caeful netwok planning in ode to estimate the optimal numbe of edundant nodes. The netwok planning should include a cost-benefit analysis, whee the additional netwok eliability of adding a edundant is weighted against the additional costs (including equipment cost, installation cost, site-acquisition cost and opeational cost) of adding the node. While the cost of adding a edundant node is nomally easy to foecast, it is moe difficult to foecast the additional eliability of adding the node. The main eason is that little have been published about netwok eliability fo mesh netwoks. Thus, the benefit in tems of impoved eliability of adding a edundant node is unknown fo the netwok planne. One component of netwok planning is to also find a good location fo nodes, including the edundant nodes. Applying common sense, it is clea that thee ae cetain mesh topologies that ae less favouable than othes with egads to eliability. The main pupose of this pape is to analyse the eliability of mesh netwoks, poviding esults that can be useful fo netwok planning. By using the methodology pesented hee, a simila analysis can easily be applied to othe mesh topologies. The est of the pape is oganised as follows: In Section II we descibe some elated wok. Section III povides some backgound on mesh netwok and the eliability of these. Reliability and availability metics fo a mesh netwok ae pesented in Section IV. In Section V we evaluate the effect of edundant s in a backhaul mesh netwok. In Section VI we descibe how to obtain the mean time to failue fo a backhaul mesh and finally, Section VII concludes the pape. II. RELATED WORK Thee has been seveal studies on two-teminal eliability fo wied netwoks [5][6][7]. The esults fom most wok on netwok eliability of fixed netwoks ae not geneally applicable to wieless netwoks. The main eason is that in fixed netwoks the pobability of a link failue is so low compaed to the pobability of a node failue, that in the analysis it is common to conside the link as invulneable to failue. In wieless netwoks, on the othe hand, link failues occu fequently due to the inheent chaacteistics of the adio channel, such as adio fading, signal attenuation, adio intefeence and backgound noise. The link failue fequency is nomally so much highe than the node failue fequency that it is natual to model the nodes as invulneable to failue, and only focus only on the link failues in the analysis. In [7], howeve, link failues in fixed ing o double ing netwok stuctues ae analysed. The wok focuses on the design of a physical netwok topology that meets a high level of eliability using uneliable netwok elements. It is shown that fo independent link failues, netwok design should be optimised with espect to eliability unde high stess, as eliability unde low stess is less sensitive to netwok topology. Thee ae seveal othe easons why fixed netwok analyses ae not applicable to wieless netwoks. Fo example, in fixed netwoks a link monitoing mechanism, o a Link Integity Test opeation is often used to identify if a link has failed, while thee is no equivalent to this in wieless netwoks. Thee is, howeve, only a limited numbe of studies on netwok eliability of wieless netwoks. The ealy wok in [8], analyses adio boadcast netwoks showing that computing the two-teminal poblem fo these netwoks ae computational difficult. The wok in [9] deals with the poblems of computing a measue fo the eliability of distibuted senso netwok and fo the expected and the maximum message delay between data souces. The two-teminal eliability of ad hoc netwoks is computed in [10]. This wok focuses on the eliability of nodes and on the effects of node mobility, while the effects of link eliability in static topologies - which we investigate in this pape - ae not consideed. III. BACKGROUND A. The eliability of the links in the mesh Diffeent layes of the netwoking stack intoduce epai mechanisms that ty to emedy and hide the effects of loss of signal o loss of packets due to vaious adio effects. Such epai mechanisms include modulation and coding techniques at the physical laye and the use of two-way (DATA-ACK) and fou-way (RTS-CTS-DATA-ACK) handshakes at the MAC laye, as well as etansmission of lost MAC fames (until the ety counte expies). Fuhemoe, often the outing module exchanges peiodically HELLO-packets with the immediate neighbous to detect link failues (e.g. OLSR), but hides the effects of the uneliable delivey of HELLO-packets by not consideing the link as failed befoe a numbe of consecutive HELLO-packets (typically thee packets) ae lost. The outing module also deals with failues of othe links in the netwok (e.g. by the TC-messages of OLSR). The outing potocol hides the effects of a link failue by tying to find an altenative oute. Howeve, if the link failue disconnects the mesh netwoks, it might not be possible to epai the failue. In othe wods, the mesh netwok does not fail to povide connectivity between two nodes, befoe the mesh netwok is consideed as disconnected. In the next subsection, we will investigate eliability metics fo mesh netwoks, with this outing pespective in mind. B. The eliability of a mesh netwok The wieless mesh netwok is composed of the nodes v j S, and is modelled as an undiected gaph G whee the nodes v j seve as vetices. Any of two distinct nodes v j and v i ceate an edge ɛ i,j if thee is a link between them.

3 The visibility gaph is defined as a gaph whee thee is an edge between two nodes, if the two nodes ae within adio tansmission ange of each othe. The connectivity gaph is defined as a gaph whee thee is an edge between two nodes, if the two nodes ae within adio tansmission ange of each othe and if the communication link between the two nodes has not failed. A minimal set of edges in the gaph whose emoval disconnects the gaph is an edge cutset. The minimum cadinality of an edge cutset is the edge connectivity o cohesion β(g). A (minimal) set of nodes that has the same popety is a node cutset, and the minimum cadinality of this is the node connectivity χ(g). To povide an adequate measue of netwok eliability, one has to use pobabilistic eliability metics and a pobabilistic gaph. This is an undiectional gaph whee each node has an associated pobability of being in an opeational state, and likewise fo each edge. A stating point fo the analysis of netwok eliability in this pape is the all-teminal and two-teminal eliability of a netwok. These measues ae each a specialised vesion of the k-teminal eliability, which is defined as the pobability that a path exists and connects k nodes in a netwok (k = n o k = 2). IV. THE RELIABILITY AND AVAILABILITY OF BACKHAUL MESH NETWORKS A. All-teminal and two-teminal eliabilities As discussed ealie, fo ou analysis of mesh netwoks we assume that the nodes v j S in the topology ae invulneable to failue. Futhemoe, we assume that a link ɛ s,d connecting two nodes v s and v d fail independent fom ɛ i,j S\{v s, v d }. The all-teminal eliability, P c (G, p), is the pobability that all the nodes v j S in the netwok have opeating paths between them. It is given by: P c (G, p) = A i (1 p) i p ɛ i (1) i=n 1 = 1 C i p i (1 p) ɛ i (2) whee A i denotes the numbe of connected subgaph with i edges, and C i denotes the numbe of edge cutsets of cadinality i. The two-teminal eliability, on the othe hand, is the pobability that a given pai of nodes, v s and v d, have an opeating path between them: Pc sd (G, p) = A sd i (1 p) i p ɛ i (3) i=w sd = 1 Ci sd p i (1 p) ɛ i (4) i=α sd whee w sd is the shotest path length between nodes v s and v d, A sd i is the numbe of subgaphs with i edges that connect nodes v s and v d, α sd is the minimum numbe of edge failues equied to disconnect nodes v s and v d. Ci sd is the numbe of cutsets with espect to nodes v s and v d of cadinality i. B. The netwok availability The netwok eliability [11] is defined as the pobability that a netwok G is disconnected at a time t = t a, given that it was not disconnected at the time t = 0, and incopoates the tansient behaviou of the netwok. The netwok availability, on the othe hand, is the steady-state pobability that the netwok is not disconnected as t. Fo a netwok planne, the netwok availability is an impotant eliability measue because it says how big shae of the time the netwok is opeational. Let us assume that link failues on an opeational link ɛ ae Poisson distibuted with an failue ate paamete λ. We also assume that a failed link, ɛ, can be epaied, and that the epais ae Poisson distibuted with a epai ate paamete µ. Then, the link can be modelled by a two-state Makov diagam, whee one state epesents the link being up, while the othe epesents the link being down (Figue 2) Figue 2. q u λ µ q d A simple two state Makov model of the eliability of a link At steady-state, the state pobabilities ae: q u = µ µ + λ, q d = λ (5) µ + λ C. The eliability and availability of a backhaul mesh netwok Conside a mesh netwok, G, that woks as a backhaul mesh netwok and includes k 1 diffeent distibution nodes d i in D, D = (d 1, d 2,..., d k 1 ), and one oot node. Accoding to ou pevious teminology of IEEE s, a distibution node coesponds to a in an IEEE s netwok, while the oot node coesponds to an P (Figue 1). Unde nomal netwok opeation, tansit taffic in the netwok is diected along the shotest path between the oot node and each distibution node, d i in D. If any distibution node is disconnected fom the oot node, the netwok has failed, as it is not opeating as intended. Thus, the netwok planne should conside the netwok as fully opeational only if thee is an opeational path between the oot node and each of the distibution nodes. This is tue if, and only if, k nodes, consisting of the oot node and the k 1 distibution nodes ae all connected. Thus, the netwok planne should analyse the eliability of the netwok using the k-teminal eliability. When consideing the eliability, the netwok availability is of highest inteest. Using the expessions above, we can now find the k-teminal availability as: P,,,d k 1 c (G) = 1 C,,,d k 1 i (q d ) i (1 q d ) ɛ i (6)

4 With cuent IEEE s equipment, it is possible to let the s connect to the s at one fequency band (e.g. using b o g) and use anothe fequency band fo the communications between the s in the backhaul mesh netwok. Since the exta equipment cost of such a configuation is nomally minimal compaed to othe costs, such as site-acquisition costs, it is anticipated that many commecial mesh netwoks will implement a at each in the netwok. With such a configuation, one has to conside the all-teminal availability of the netwok. The (all-teminal) netwok availability is the pobability of a netwok G being connected at steady state. It can now be expessed using Eq. 25 as: P c (G) = 1 C i (q d ) i (1 q d ) ɛ i (7) Finally, since some s might be of highe impotance than othe s, the netwok planne might instead pefe to use a weighted aveage of the diffeent two-teminal availabilities: The availability of a backhaul mesh netwok, P c (G, D, ), can then be defined as a combination of diffeent two-teminal availabilities: P c (G, D, ) = W 1 P, c whee W k is a weighting facto. + W 2 Pc,d2,, W k 1 P,d k 1 c (8) V. EVALUATION In this section we evaluate the availability fo a topology (Figue 3) whee two s ae distibuted and connected to a P. With espect to netwok planning, we ae inteested in finding the availability fo the sevice povided by the s, thus one has to detemine the steady-state condition of the thee-teminal eliability Pc,,d6. add negligible impovement to the availability, since at this point, all the nodes in the backhaul has at least two links on which thei sevice can be eached. Adding d 12, does not change the numbe of links connecting the backhaul, and can theefoe be emoved fom the netwok without any noticeable loss in availability. Availability (P,,d6 No edundancy With d7 With d7, d8 With d7,, d9 With d7,, 0 With d7,, 1 With d7,, Pobability of link failue (p) (a) Availability {, d 5, d 6 } Figue 4. Availability (P,,d p = p = p = Numbe of edundant s (b) Effect of edundant s Sevice availability when adding edundant s We can also deduce fom Figue 4 that the effect of adding edundant s is geatest fo a pobability of link failues in the appoximate ange p {0.1, 0.5}. In Figue 4 b) we show the incease in availability as we add edundant s, poviding a cleae pictue of how they impove the availability. d6 d4 d2 P (a) Initial topology Figue 5. d6 d4 d2 P 0 d8 d7 d9 1 (b) With edundant s An altenate deployment of edundant s d6 d4 d2 P (a) Initial topology d6 0 d4 d8 2 d2 d7 d9 1 P (b) With edundant s An altenate configuation fo the edundant s, is to deploy them geogaphically close to the backhaul mesh as illustated in Figue 5. Assuming the edundant s have equivalent tansmission ange as the ones in Figue 3, positioning the s close to the backhaul mesh nodes, will incease the numbe of links fom the edundant s to the backhaul. Figue 6 shows the impoved eliability by adding edundant s accoding to the topology in Figue 5. Figue 3. Topology with and without edundant s In the netwok planning phase, a cost-benefit analysis needs to be pefomed in ode to detemine cost vesus the added eliability intoduced by a edundant. Ignoing the cost facto of adding edundant s, we plot the availability and the effect when an exta is added to the netwok (Figue 4). The edundant s ae added in a paticula ode, d 7,, d 12 (Figue 3). Fom Figue 4 a), we see that the availability is inceasing as we add the edundant nodes. Howeve, adding d 12 only Availability (P,,d6 No edundancy With d7 With d7, d8 With d7,, d9 With d7,, 0 With d7,, Pobability of link failue (p) (a) Availability {, d 5, d 6 } Figue 6. Availability (P,,d p = p = p = Numbe of edundant s (b) Effect of edundant s Sevice availability when adding edundant s

5 VI. TRANSIENT NETWORK RELIABILITY While the netwok availability is a useful eliability measue, it does not povide a full pictue of the netwok eliability, since it is a steady-state measue. Fo example, it gives the shae of time the netwok is up, but it does not povide insight into the mean time to failue (MTTF) given that the netwok is connected at time t = 0 o the mean time between failues (MTBF). To estimate such time-dependent measues, one needs to study the tansient behaviou of the k-teminal eliability. Analysis of tansient behaviou nomally becomes vey complex when consideing link failues with epai. Thus, when studying tansient eliability, it is not uncommon to simplify the analysis by consideing link failues without epai. We will do the same in this section. Howeve, assuming that links that fail have infinite epai time is not vey ealistic. We theefoe intend to continue ou analysis to conside link failues with epai, and plan to addess this topic in follow-on eseach. A. The tansient all-teminal eliability without link epai In this section we investigate the all-teminal eliability fo abitay mesh topologies. We assume that netwoks stats out with all links between two nodes within adio ange of each othe is fully opeational, so that the connectivity gaph is equal to the visibility gaph. We futhe assume that link failues ae Poisson distibuted with paamete λ and that when a link ɛ fail, it can not be epaied. The pobability of a topology G being disconnected is then given by P d (G, t < T ) = C i (1 e λt ) i (e λt ) ɛ i (9) It is easy to show that the mean time fo when the topology will fail, is equal to Eq. 10, whee B(x, y) is the complete Beta function. E(T d ) = 1 λ ( ) ɛ ( 1) n+1 ɛ 1 C i B(i + 1, ɛ i) (10) n n n=1 B. The tansient k-teminal eliability without link epai Similaly, we can show that the expected time that k-nodes will be disconnected, is given by: E(T vi,,v k d ) = 1 λ ( ) ɛ ( 1) n+1 ɛ 1 n n n=1 i B(i + 1, ɛ i) (11) C vi,,v k Using Eq. 11, we can find the MTFF fo the topologies in Section V. This esults ae shown in Figue 7. Pecentage incease in MTFF [%] Numbe of edundant s (a) Topology in Figue 3 Pecentage incease in MTFF [%] Numbe of edundant s (b) Topology in Figue 5 Figue 7. Relatively vaiation in MTFF as the numbe of edundant s is inceased (λ = 1) VII. CONCLUSION AND FUTURE WORK This pape investigates the eliability and availability of backhaul mesh netwoking, moe specifically finding the benefit of adding edundant nodes in such netwoks. To the best of ou knowledge, this has not been studied in pevious woks. Ou esults show how edundant nodes impove netwok eliability. Although analyses and esults depend on the actual topology, the same analyses as pesented hee can be applied to any specific backhaul mesh topology of inteest. Fo futue wok we want to analyze the OLSR ad hoc outing potocol and use a Makov model to descibe the onehop neighbou discovey mechanism as a pobability function fo whethe the link is intepeted as up o down. Also, we want to analyse the MAC- and physical- laye behaviou and deive a moe adequate pobability distibution fo link failues in mesh netwoks. In a wieless envionment, a link failue is often coelated with link eos in othe pats of the netwok, thus we also want to include link failue dependencies in the analysis. REFERENCES [1] Wieless LAN Medium Access Contol (MAC) and Physical Laye (PHY) Specification, IEEE Std , [2] LAN/MAN Specific Requiements - Pat 11: Wieless Medium Access Contol (MAC) and physical laye (PHY) specifications: Amendment: ESS Mesh Netwoking, IEEE Std s Daft 2.0, [3] C. Pekins, E. Belding-Roye, and S. Das, Ad hoc on-demand distance vecto (aodv) outing, IETF, July [4] T. Clausen and P. Jacquet, Optimized link state outing potocol (ols), IETF, Octobe [5] C. J. Colboun, Reliability issues in telecommunications netwok planning, in Telecommunications netwok planning, B. S. P. Soiano, Ed. Kluwe Academic Publishes, 1999, ch. 9, pp [6], The Combinatoics of Netwok Reliability. Oxfod Univ. Pess, [7] G. Weichenbeg, V. Chan, and M. Medad, High-eliability topological achitectues fo netwoks unde stess, Selected Aeas in Communications, IEEE Jounal on, vol. 22, no. 9, pp , Nov [8] H. AboElFotoh and C. J. Colboun, Computing 2-teminal eliability fo adio-boadcast netwoks, Reliability, IEEE Tansactions on, vol. 38, no. 5, pp , Dec [9] H. AboElFotoh, S. Lyenga, and K. Chakabaty, Computing eliability and message delay fo coopeative wieless distibuted senso netwoks subject to andom failues, Reliability, IEEE Tansactions on, vol. 54, no. 1, pp , Mach [10] S. Khabash and W. Wang, Computing two-teminal eliability in mobile ad hoc netwoks, Wieless Communications and Netwoking Confeence, 2007.WCNC IEEE, Mach [11] M. L. Shooman, Reliability of Compute Systems and Netwoks: Fault Toleance, Analysis, and Design. John Wiley and Sons, Inc, 2002.