Internatonal Journal of Hybrd Informaton Technology Vol., No., Aprl, 009 Routng n Degree-constraned FSO Mesh Networks Zpng Hu, Pramode Verma, and James Sluss Jr. School of Electrcal & Computer Engneerng The Unversty of Oklahoma, Schusterman Center 450 E. 41 st Street, Tulsa, OK 74135-51, USA {zpng.hu, pverma, sluss}@ou.edu Abstract Ths paper addresses the routng problem n packet swtchng free-space optcal (FSO) mesh networks. FSO mesh networks are emergng as broadband communcaton networks because of ther hgh bandwdth (up to Gbps), low cost, and easy nstallaton. Physcal layer topology desgn of degree-constraned FSO mesh networks has been studed n a recent communcaton [1]. In ths paper, we propose four dfferent routng algorthms, and evaluate ther performances through smulatons for a number of FSO mesh networks wth dfferent topologes and nodal degrees. The performance parameter aganst whch we evaluate these algorthms s the mean end-to-end delay. Our proposed least cost path (LCP) routng algorthm, whch s based on mnmzng the end-to-end delay, s consdered as the bench mark. The performance of each of other three proposed algorthms s evaluated aganst the bench mark. Our proposed mnmum hop count wth load-balancng (MHLB) routng algorthm s based on the number of hops between the source and the destnaton node to route the traffc. Smulatons show that the MHLB routng algorthm performs best n most cases compared wth the other two. It results n mnmum average delay and least blocked traffc. 1. Introducton FSO networks are emergng as broadband communcaton networks because of ther hgh bandwdth (up to Gbps), low cost, and easy nstallaton. An FSO network conssts of a set of geographcally dstrbuted FSO nodes and FSO lnks nterconnectng the nodes. Each FSO node can carry a router and several transcevers. An FSO node can carry only lmted number of transcevers due to sze, weght and power ssues. Each transcever operates both n transmttng and recevng modes. FSO lnks that form the communcaton channels of FSO networks are pont-to-pont drectonal lght beams. To mprove the performance of FSO networks through network desgn, the two major ssues are topology desgn and routng. Tradtonally, for wred communcaton networks such as fber-optc networks, a fxed physcal layer topology s formed based on external traffc flow requrements and/or other requrements. Routng s then a task of fndng optmal logcal connectons that can be mapped on the physcal layer topology n order to acheve low delay, hgh throughput, or reduced congeston. Research n [] presents a delay-constraned mnmum hop (DCMH) dstrbuted routng algorthm for real tme communcaton applcatons. An optmal dverse routng algorthm s proposed n [3] to fnd the shortest par of physcally-dsjont paths n order to mprove the relablty of fber optcal networks. Reference [4] presents an algorthm that computes the shortest path from a gven source to a destnaton for any number of hops for QoS routng. Research n [5] extends the work n [4], 71
Internatonal Journal of Hybrd Informaton Technology Vol., No., Aprl, 009 and proposes an All Hops Shortest Paths (AHSP) algorthm to compute the shortest path wth hop count lmtaton n order to fnd a feasble path. A load-balanced routng scheme s proposed n [6] to randomly dstrbute the traffc load over all avalable paths to the destnaton for real tme applcatons. A survey s presented n [7] that ntroduce several approaches to solve mult-constraned paths problem for QoS routng. All the above mentoned routng approaches assume a gven physcal layer topology. However, for FSO networks, current approaches [8-11] have combned both topology desgn and routng problems nto one makng use of the auto-trackng functon of FSO nodes. In these approaches, logcal topologes are frst calculated at upper layer. Physcal layer topologes are then gradually formed based on the calculated logcal topologes. Snce the mappng of physcal layer topology to logcal topology nvolves a number of rounds of mechancal movements of transcevers n FSO nodes, and each movement of a transcever takes about 500ms for algnment purpose only [8]; these approaches are not, n general, practcal for FSO communcaton networks. Our work approaches the problem n a way that s smlar to wred networks. In our prevous work [1], we constructed a hghly relable physcal layer topology for an FSO mesh network through topology desgn. Now, based on gven physcal layer topology, and external traffc demands, our objectve n ths paper s fndng optmal logcal topology that can be mapped onto the physcal layer topology n order to acheve low average packet delay. Four dfferent routng algorthms are proposed n ths paper. Through extensve smulatons, we show that the proposed mnmum hop count wth load balancng (MHLB) routng algorthm leads to the best overall performance. In ths paper, Secton defnes all the notatons used n our work. Secton 3 presents the problem that needs to be solved. A queung system model s ntroduced n Secton 4. Secton 5 presents the mathematcal background. The four proposed routng algorthms are presented n Secton 6. Secton 7 shows the smulaton results. Secton 8 concludes our work.. Notatons We treat a degree-constraned FSO mesh network as a graph G(N,L) wth N representng the set of nodes and L representng the set of lnks. The followng notatons are used n our work. A=[γ jk ] denotes the N x N traffc matrx, where γ jk : external traffc flow enterng node j, and destned to node k B=[ ] denotes the N x N lnk utlzaton matrx, where st st : utlzaton of lnk between node s and node t. μ : departure rate λ : traffc load on lnk λ: total nternal traffc load γ: total external traffc demand T: average delay for a packet travelng through the network 3. Problem Statement Three factors can affect the delay performance of FSO networks: physcal layer topology, external traffc demands, and routng strategy. In our work, we assume that the physcal layer topology and external traffc demands are gven. To smplfy the problem, we also assume that all lnk capactes are the same. The problem becomes fndng an optmal routng strategy 7
Internatonal Journal of Hybrd Informaton Technology Vol., No., Aprl, 009 that mnmzes the average delay T; therefore t s a flow assgnment (FA) problem [1]. The FA problem can be stated as follows. Gven: network topology and external traffc flows Mnmze: T Wth respect to: {λ }, =1,,, L 4. System Model To solve the FA problem, a packet swtchng FSO network s modeled as a network of queues. Each FSO node (or lnk) s modeled as a queue and a server, and treated as an ndependent M/M/1 model [1-13]. For example, gven the physcal layer topology of a fve node network shown n Fgure 1, external traffc flow, and the routng strategy of the traffc, the network can be modeled as a network of queues shown n Fgure. Fgure 1. Physcal layer topology of a L fne node 5. Mathematcal Background Fgure. Network of queues Assume for an FSO network wth N nodes and L lnks, the external traffc flow requrement from a source node j to a destnaton node k s jk, then the total external traffc flow (n packets per second) that s offered to the network can be expressed as N N = j1 k 1 jk (1) Snce a packet may travel multple hops from source to destnaton, the total nternal traffc flow n the network wll be hgher than the external offered traffc. The total nternal traffc load n the network s therefore gven as L = () 1 We can see that the total nternal traffc flow depends on not only the external offered traffc, but also the actual paths taken by packets through the network. The total traffc load 73
Internatonal Journal of Hybrd Informaton Technology Vol., No., Aprl, 009 on each ndvdual lnk s determned by both the offered traffc flows, and the routng algorthm. Snce each FSO lnk s actually a drectonal lght beam, an FSO lght sgnal propagates at lght speed. Wth lmted FSO lnk length (up to 4 km), the propagaton delay can be neglected; therefore when a packet travels along ts mult-hop path, t s served at a node, and then goes drectly to the next node on ts path. Let Tr denote the resdence tme of a packet at lnk. The average delay T can be defned as T = 1 L T r (3) By applyng the M/M/1 model, 1 T = 1 L 1 = 1 L = 1 L 1 1 ( ) 1 1 (4) Because of the separatblty [1] of each component at the rght hand sde of equaton (4), the senstvty of the average delay T to the utlzaton of lnk can be expressed as T 1, = 1,,, L (5) (1 ) Further, T (1 ) = 3, =1,,, L (6) Snce the utlzaton of lnk, =, always satsfes that 0 < 1 to keep the T network n a stable state; therefore, we have > 0 for all under lnk utlzaton constrant. We conclude that T s a convex functon of lnk utlzaton. It shows that wth the ncrease of lnk utlzaton, the growth of T becomes faster. Therefore, an optmal routng strategy should keep lnk utlzaton of each lnk mnmal n order to mnmze the average delay T. The total nternal traffc flow n the network also affects the average delay T; therefore, gven external traffc flow requrements and physcal layer topology of a network, an optmal routng algorthm should be able to mnmze the total nternal traffc flow of the network n order to mnmze the average delay T. Based on above analyss, we specfy the propertes of an optmal routng algorthm: For all lnks n the network, the lnk utlzaton constrant has to be satsfed,.e., 0 < 1, =1,,, L. The lnk utlzaton of each lnk has to be kept as low as possble, whch means that lnks wth low utlzaton should have hgher prorty of beng chosen to route gven traffc demand. Gven physcal layer topology and external traffc flow requrements, the total nternal traffc should be kept as low as possble through routng n order to decrease the average delay. 74
Internatonal Journal of Hybrd Informaton Technology Vol., No., Aprl, 009 6. Proposed Routng Algorthms We frst ntalze traffc matrx A, and lnk utlzaton matrx B. Each entry of the traffc matrx conssts of source node j, destnaton node k, and requred traffc flow jk, where j = 1,,, N, k = 1,,, N. If j = k, then jk =0. Each entry of the lnk utlzaton matrx conssts of node s, node t, and lnk utlzaton st, where s = 1,,, N, t = 1,,, N. If there s no drect lnk between node s and node t, or s = t, then st = 1. Otherwse, t sets to 0. For practcal reasons and for smplfcaton, we set the mum lnk utlzaton of each lnk as 0.8. Because of ths lnk utlzaton constrant, all traffc that can't be routed s regarded as blocked traffc. We propose four dfferent routng algorthms as follows. 6.1 Least Cost Path routng algorthm (LCP) * Assume the exstng traffc load on lnk s, or the exstng lnk utlzaton of lnk * * s. Usng equaton (5), we compute the cost (the ncrease of average delay) of routng traffc flow jk through lnk as T jk 1 jk Cost() = = (7) (1 * * ) Therefore, the total cost of routng traffc jk through a path of m lnks scost( ). In order to mnmze the average delay T, each traffc demand has to be routed through the least cost path. Our proposed least cost path routng algorthm s as follows. 1. Set =0.8. Route all one hop count traffcs under the constrant that. Update traffc matrx and lnk utlzaton matrx.. Arrange all traffc demands n the decreasng order. If the mum traffc demand s 0, then stop. 3. Startng from the heavest traffc demand, fnd the least cost path to route the traffc under the constrant that < for any lnk on the path. Because of the upper bound of lnk utlzaton, the part of traffc that can't be routed through the path remans unrouted. Update traffc matrx and lnk utlzaton matrx. If no such path exsts, consder next traffc demand. Repeat Step 3 untl all traffc demands are consdered. Go to Step. Varatons of Djkstra s or Bellman-Ford algorthm are the most wdely used algorthms n least cost routng n packet-swtchng networks. In our LCP routng algorthm, because of lnk utlzaton constrant, we use a modfed Djkastra algorthm to fnd the least cost path at step 3 n order to route a gven external traffc demand. Lnk cost s computed accordng to equaton (7). 6. Mnmum Hop Count Path Routng Algorthm (MHP) Proposed mnmum hop count path routng algorthm s used to route each traffc demand through the mnmum hop count path n order to mnmze the total nternal traffc load on the m 1 75
Internatonal Journal of Hybrd Informaton Technology Vol., No., Aprl, 009 network. In ths way, t's expected to acheve low average packet delay. The proposed mnmum hop count path routng algorthm s presented as: 1. Set =0.8. Route all one hop count traffcs under the constrant that. Update traffc matrx and lnk utlzaton matrx.. Arrange all traffc demands n the decreasng order. If the mum traffc demand s 0, then stop. 3. Startng from the heavest traffc demand, fnd the mnmum hop count path to route the traffc under the constrant that < for any lnk on the path. If more than one mnmum hop count path exsts, choose the one wth the mnmum mum lnk utlzaton. Because of the upper bound of lnk utlzaton, the part of traffc that can't be routed through the path remans unrouted. Update traffc matrx and lnk utlzaton matrx. If no such path exsts, consder next traffc demand. Repeat Step 3 untl all traffc demands are consdered. Go to Step. At step 3, by settng the cost of each lnk to be the same, a modfed Djkastra s algorthm s used to fnd the mnmum hop count path for a gven traffc demand under lnk utlzaton constrant. For a path wth m lnks, the mum lnk utlzaton of the path s defned as: {, =1,,, m}. Ths concept s also used n the followng routng algorthms. 6.3 Mnmum Hop Count wth Load Balancng Routng Algorthm (MHLB) The MHLB routng algorthm s used to route all traffc demands based on the hop count of the paths. All one hop count traffc are routed frst, then two hop count traffc, next three hop count traffc, and so on. The mum lnk utlzaton of a lnk s set at 0.6 frst, whch s ncreased up to 0.8 n the subsequent rounds. The steps are as follows. 1. Set =0.6. Route all one hop count traffcs under the constrant that Update traffc matrx and lnk utlzaton matrx. Set counter = 1... Arrange all traffc demands n the decreasng order. If the mum traffc demand s 0, then stop. Otherwse ncrease counter by 1 (or counter++), let = +, 0 0. (the actual value of selected s determned by searchng the optmal value from a small set). If > 0.8, then set =0.8. 3. Startng from the heavest traffc demand, fnd the path wth total hop count less or equal to counter to route the traffc under the constrant that < for any lnk on the path. If more than one such path exsts, choose the one wth the mnmum mum lnk utlzaton. Update traffc matrx and lnk utlzaton matrx. If no such path exsts, consder next traffc demand. Repeat Step 3 untl all traffc demands are consdered. Go to Step. At step 3, a modfed Bellman-Ford algorthm s used to fnd the path wth total hop count less or equal to counter to route a gven traffc demand. Traffc load balancng s acheved through ncreasng the upper bound of lnk utlzaton from 0.6 to 0.8 step by step. The MHLB s expected to acheve low average delay, low total nternal traffc, and least blocked traffc. 6.4 Mnmum Hop Count Routng Algorthm (MH) Proposed MH routng algorthm s used to route all traffc demands based on the hop count of the paths smlar to MHLB. All one hop count traffc are routed frst, then two hop count 76
Internatonal Journal of Hybrd Informaton Technology Vol., No., Aprl, 009 traffc, next three hop count traffc, and so on. However for MH algorthm, the upper bound of lnk utlzaton always remans as 0.8 durng the whole process. 1. Set =0.8. Route all one hop count traffc under the constrant that. Update traffc matrx and lnk utlzaton matrx. Set counter = 1.. Arrange all traffc demands n the decreasng order. If the mum traffc demand s 0, then stop. Otherwse ncrease counter by 1 (or counter++). 3. Startng from the heavest traffc demand, fnd the mnmum hop count path wth total hop count less or equal to counter to route the traffc under the constrant that < for any lnk on the path. If more than one such path exsts, choose the one wth the mnmum mum lnk utlzaton. Update traffc matrx and lnk utlzaton matrx. If no such path exsts, consder next traffc demand. Repeat Step 3 untl all traffc demands are consdered. Go to Step. At step 3, a modfed Bellman-Ford algorthm s used to fnd the path wth total hop countless or equal to counter to route a gven traffc demand. Through MH routng the total nternal traffc s expected to be the least. 7. Smulatons and analyss Case1: Gven a physcal layer network topology of degree 3 wth 10 nodes and 15 lnks, we set the departure rate μ as 130 unts. (a) Lght external traffc demands: For a 10 nodes network, there are 10 9 dstnct source-destnaton node pars. Therefore 90 external traffc demands are generated randomly from 0 to 9 unts correspondng to the 90 dfferent source-destnaton node pars. Smulatons are done over 10 dfferent topologes wth proposed four dfferent routng algorthms to route the traffc. Under lght external traffc demands, the total blocked traffc s 0. The average delay s shown n Table 1. Table 1. Average delay (ms) 1 18.64 18.6 18.6 18.6 1.73 1.87 1.69 1.69 3 18.66 18.64 18.61 18.61 4 19.13 19.14 19.17 19.17 5.76.79.8.8 6.9.48.66.66 7 18.6 18.58 18.61 18.61 8 18.8 18.8 18.45 18.45 9 3.19 3.19 3.19 3.19 10 1.4 1.11 1.06 1.06 (b) Heavy traffc demands: 90 external traffc demands are generated randomly from 0 to 19 unts correspondng to the 90 dfferent source-destnaton node pars. Smulatons are done over the same 10 dfferent topologes wth proposed four dfferent routng algorthms to route the traffc. The average delay under heavy traffc load s shown n Table.1. The total blocked traffc n dfferent scenaros s shown n Table.. 77
Internatonal Journal of Hybrd Informaton Technology Vol., No., Aprl, 009 Table.1. Average delay (ms) 1 8.17 8.4 7.55 7.59 40.85 4.6 39.95 39.95 3 7.4 7.65 7.1 7.1 4 30.39 30.81 9.89 30.8 5 4.88 43.3 40.88 40.88 6 39.44 38.45 37.86 37.9 7 7.69 7.83 7.87 8.0 8 7.16 7.8 7.39 7.4 9 51.87 49.45 47.65 48.03 10 4.48 40.77 39. 39.4 Table. Total blocked traffc (unts) 1 0 0 0 0 5 5 5 5 3 0 0 0 0 4 0 0 0 0 5 35 35 35 35 6 3 3 3 3 7 0 0 0 0 8 0 0 0 0 9 35 35 35 35 10 14 14 14 14 Case : Gven a physcal layer network topology of degree 4 wth 30 nodes and 60 lnks, we set the departure rate μ as 80 unts. (a) Lght external traffc demands: For a 30 nodes network, there are 30 9 dstnct source-destnaton node pars. Therefore 870 external traffc demands are generated randomly from 0 to 9 unts correspondng to the 870 dfferent source-destnaton node pars. Smulatons are done over 10 dfferent topologes wth proposed four dfferent routng algorthms to route the traffc. In all dfferent scenaros, the total blocked traffc s 0. The average delay s shown n Table 3. (b) Heavy external traffc demands: 870 external traffc demands are generated randomly from 0 to 10 unts correspondng to the 870 dfferent source-destnaton node pars. Smulatons are done over the 10 dfferent topologes wth proposed four dfferent routng algorthms to route the traffc. The average delay s shown n Table 4.1. The total blocked traffc n dfferent scenaros s shown n Table 4.. The proposed three new routng algorthms are compared aganst the LCP algorthm, whch s based on routng that mathematcally mnmzes the end-to-end delay. The LCP algorthm routes as much as possble traffc through the least cost path untl the mum lnk utlzaton 0.8 s reached. Because of ths reason, LCP does not, under heavy traffc load, dstrbute traffc evenly over all avalable paths. 78
Internatonal Journal of Hybrd Informaton Technology Vol., No., Aprl, 009 Table 3. Average delay (ms) 1 16.0 16.0 16.07 16.07 3.91 5.13 4.53 4.59 3 0.01 0.84 0.98 0.99 4.78 4.46 3.94 4.35 5 0.46 1.37 1.44 1.49 6 3.51 6.66 4.81 5.85 7.48 4.11 3.71 3.99 8 19.0 19.40 19.6 19.63 9.1 4.0 3.0 3.35 10 18.3 18.9 18.58 18.84 Table 4.1. Average delay (ms) 1 17.35 17.61 17.37 17.37 4.40 5.67 4.1 4.1 3.86 4.10 4.08 4.31 4 6.88 9.9 8.37 8.99 5 3.44 5.05 4.86 5.1 6 7.04 33.40 9.56 31.15 7 5.48 6.87 7.50 7.0 8 1.44.17.19.3 9 5.88 8.08 7.06 7.65 10 0.19 1.04 0.58 1.0 Table 4.. Total blocked traffc (unts) 1 0 0 0 0 154 154 154 154 3 0 0 0 0 4 0 0 0 0 5 0 0 0 0 6 0 0 0 0 7 44 83 14 49 8 0 0 0 0 9 0 0 0 0 10 0 0 0 0 Snce the proposed MHLB algorthm does dstrbute the traffc more evenly by settng at frst a lnk utlzaton lmt of 0.6, and then ncreasng t up to 0.8 f necessary, MHLB s expected to result n better performance than LCP n most cases. Note also that whle LCP determnes the route after a computatonally ntensve process, MHLB doesn't requre the 79
Internatonal Journal of Hybrd Informaton Technology Vol., No., Aprl, 009 computaton of lnk cost pror to determnng the route. It smply routes the traffc based on the hop count of the path, subject to, the lmts on lnk utlzaton. Further, for the LCP algorthm, the lnk cost depends on the traffc, and the traffc n turn depends on the routes chosen. Because of the exstence of ths feedback condton, nstabltes may result [13]. The other three routng algorthms, ncludng the MHLB, are not subject to such nstablty. Smulaton results show that for small szed FSO networks, under lght traffc demands, performance of the three proposed algorthms are smlar to each other; under heavy traffc load, the proposed MHLB routng algorthm results n mnmum average delay. For large szed FSO networks, smulaton results show that, under lght traffc demands, MHLB results n mnmum average delay n most cases; under heavy traffc load, t results n mnmum average delay and least blocked traffc n most cases. Compared wth LCP, MHLB performs better for small szed FSO networks. For large szed FSO networks, even though LCP results n less average delay than MHLB, MHLB s expected to outperform LCP wth the ncrease of the nodal degree because of ts traffc load balancng feature. 8. Conclusons Ths paper has proposed and analyzed three routng algorthms for degree-constraned FSO mesh networks of dfferent szes under varyng traffc demands. In each case, the cost s characterzed by average delay. The mum lnk utlzaton s set as 0.8. Traffc that exceeds ths constrant s regarded as blocked traffc. Smulaton results show that for small szed FSO networks, under lght traffc demands, the performance of the three proposed algorthms are smlar to each other; under heavy traffc load, the proposed MHLB routng algorthm outperforms the others n most cases. For large szed FSO networks, smulaton results show that MHLB performs best n most case. References [1] Zpng Hu, Pramode Verma, and James Sluss, Jr., "Improved Relablty of Free-space Optcal Mesh Networks Through Topology Desgn," Journal of Optcal Networkng Vol.7(5), pp.436-448 (008). [] A. R. Mohd Sharff and M. E. Woodward, "A Delay Constraned Mnmum Hop Dstrbuted Routng Algorthm usng Adaptve Path Predcton," Journal of Networks Vol.(No.3), pp.46-57 (007). [3] R. Bhandar, "Optmal dverse routng n Telecommuncaton Fber Networks," presented at the Proc. of the 13th IEEE INFOCOM conference on networkng for global communcatons, Toronto, 1994. [4] R. Guern and A. Orda, "Computng shortest paths for any number of hops," IEEE/ACM Trans. on Networkng Vol.10, pp.613-60 (00). [5] G. Cheng and N. Ansar, "Fndng All Hops Shortest Paths," IEEE Communcaton Letters Vol.8(No.), pp.1-14 (004). [6] S. Bak, A. M. K. Cheng, J. A. Cobb, and E. L. Less, "Load-balanced Routng and Schedulng for Real- Tme Traffc n Packet-Swtch Networks," presented at the 5th Annual IEEE Internatonal Conference on Local Computer Networks, 000. [7] M. Curado and E. Montero, "A Survey of QoS Routng Algorthms," presented at the Proc. of the Internatonal conference on Informaton Technology, 004. [8] U. V. Fang Lu, and Stuart Mlner, "Bootstrappng free-space optcal networks," IEEE Journal on Selected Areas n Communcatons Vol. 4(No.1), pp.13- (006). [9] A. Kashyap, K. Lee, M. Kalantar, S. Khuller, and M. Shayman, "Integrated Topology Control and Routng n Wreless Optcal Mesh Networks," Computer Netwroks Vol.51(15), pp.1-13 (007). [10] K. Lee and K. Km, "Dynamc Topology Control and Routng n Wreless Ad Hoc Networks," IEICE Trans. on INF. & SYST. Vol.E89-D(No.5), pp.167-1675 (006). 80
Internatonal Journal of Hybrd Informaton Technology Vol., No., Aprl, 009 [11] A. Desa and S. Mlner, "Autonomous reconfguraton n free-space optcal sensor networks," IEEE Journal of Selected Areas n Communcatons VOL. 3(NO. 8), pp. 1556-1563 (005). [1] L. Klenrock, Queueng Systems.Volume II. Computer Applcatons (Wley, New York, 1976). [13] W. Stallngs, Hgh-Speed Networks and Internet: Performance and Qualty of Servce, nd Edton ed. pp.415 (Prentce Hall, New Jersy, 00). 81