An Optimization Model for Routing in Low Earth Orbit Satellite Constellations

Transcription

1 An Optmzaton Model for Routng n Low Earth Orbt Satellte Constellatons A. Ferrera J. Galter P. Mahey Inra Inra Inra Afonso.Ferrera@sopha.nra.fr Jerome.Galter@nra.fr Phlppe.Mahey@sma.fr G. Mateus A. Olvera M. Pchereau UFMG UFMG Inra mateus@dcc.ufmg.br dr@dcc.ufmg.br Marc.Pchereau@nra.fr Abstract In the recent years, a large set of satellte constellatons has been proposed to address communcaton servces wth worldwde coverage and once data s n the sky, a maor ssue conssts of redstrbutng t on Earth n a proper way. Ths work addresses the routng problem n satellte networks. An optmzaton model s presented. In our model, the communcaton flow s not dvded n several routes, the topology s consdered fxed n each state the satellte goes through and the ISL's capactes are predefned. 1. Introducton In the recent years, a large set of satellte constellatons has been proposed to address communcaton servces wth worldwde coverage. Due to the progress n satellte communcaton technologes, t s now feasble to buld a moble communcaton network usng Low-Earth Orbt (LEO) satelltes. LEOs based communcaton systems have multple satelltes orbtng n low orbts. Earth s dvded nto cells wth users n a cell served by one or more satelltes. LEOs are expected to provde wreless moble communcaton servces from any place to any other place on earth and support wreless communcaton from and to areas not covered by cellular or geostatonary phone systems. The term LEO s used to classfy satelltes wth orbtng alttudes between 500 and 2000 km above the Earth s surface. Ths low alttude provdes small end-toend delays and low power requrements for both satelltes and termnals. Therefore, the utlzaton of LEO satelltes has the advantages of dstance and delays reducton n comparson to geostatonary satelltes. Moreover, the satelltes can be connected to terrestral networks va gateways. Some systems, lke Globalstar, make use of bent-ppes satelltes, whch smply redrect any receved sgnal to a terrestral gateway. Other systems, lke Teledesc, have ntegrated a routng system n the ar usng nter-satellte lnks (ISL s), makng the sky network potentally able of end-to-end routng. The ISL s allow the routng of a connecton through the satellte network wthout requrng any terrestral resources Motvaton Once the data s n the sky, a maor ssue conssts of redstrbutng t on Earth n a proper way. The man problem of these satellte networks s that the satelltes as well as ther orbts are not fxed compared to the Earth. The topology of the network changes perodcally. No lnk can be used permanently, snce the satelltes are movng at a sgnfcant speed. The usual speed for a satellte n low earth s around km/h, a speed that exceeds any concevable terrestral movement. Therefore, t s necessary to dynamcally establsh lnks between satelltes as the set of vsble satellte changes. Satellte Network When ths topologcal change takes place, the source or the destnaton termnals on the ground may not stay n the coverage regon of the ntal source or destnaton satelltes throughout the communcaton. Thus, the ntal source and destnaton satelltes may need to transfer the ground source and destnaton termnals to other satelltes whose coverage regons contan the source and destnaton

2 termnals. Ths event s called handover and they occur frequently n LEO systems. Besdes routng and mantenance of ongong connectons, some other ssues must be taken nto account such as overall network performance and qualty of servce. Ths work addresses the routng problem. The approach consdered for solvng ths ssue conssts of tryng to solve the routng problem at gven ponts n tme and usng re-routng algorthms the rest of the tme. The remanng of ths paper s organzed as follows. In Secton 2, there s a bref revew of related work. In Secton 3, the optmzaton model s presented. In Secton 4, the algorthms and data necessary for the experments are descrbed. Fnally, the results are dscussed. 2. Related Work In [3], the satellte network s modeled as a fnte state automaton (FSA). In each state, the LEO satellte network has a fxed topology. The authors solve a combned topologcal desgn and routng problem for each confguraton correspondng to a state n the FSA. The topologcal desgn (or lnk assgnment) problem deals wth the selecton of ISL s whle the routng problem handles the traffc dstrbuton over the selected lnks to maxmze the number of carred calls. A two-step heurstc algorthm that frst solves the topologcal desgn problem and then fnds the optmal routng solves ths NP-complete mxed nteger optmzaton problem. The algorthm s terated usng smulated annealng untl the near-optmal soluton s found. The lnk assgnment and the routng table that are pre-calculated off-lne for each state are loaded nto the satelltes and a new set of these tables are retreved at each state transton. There are some dfferences between the approach used n [3] and our approach. The frst aspect concerns the traffc dstrbuton. In [3], the optmal routng method presented s based on methods developed for the packet swtched data networks. As far as we are aware, the communcaton n satellte constellaton must follow the same path. The second aspect concerns the fact that, n each state, the network topology changes. The satelltes do not have the same lnks or the same neghbors. 3. Our Approach Our model s also based on the dea that consders the network topology as a set of fxed topologes. The dea conssts of calculatng, for each tme nterval, the optmal routng and also usng reroutng algorthms for the next optmzaton. Ths calculaton could not least more than 10 mnutes. Our man goal s to be able to provde routng paths for moble telecommuncaton. It s not possble to dvde the communcaton flow among several routes. The communcaton must take place usng the same route. The network topology s consdered fxed n each state snce the cost to change the antenna orentaton n order to establsh a new connecton wth another satellte s not rrelevant. It s also mportant to say that the ISL s capactes are also predefned Formulaton The optmzaton problem s formulated as a lnear problem wth nteger varables. There s only one type of varables n the model: the decson varables x. They ndcate through whch paths wll the traffc flow. x 1, thedemand usesthe ISL = 0, otherwse The obectve functon and the constrants are: Mn s.t. P ( ) H D P ( ) x x = 1, D x D P ( ) u U Notaton: d C (1) u ( 2 ) u (3) D: set of demand ponts U : set of ISLs for the path d : cost of demand C u : maxmum capacty of s ISL u P(): set of possble paths for the demand H : number of ISLs for the path and demand The obectve s to mnmze the network overall delay as stated n (1). The equaton (2) means that the demand must follow ust one path. The equaton (3) s the lnk capacty constrant and specfes that, for each lnk, the total lnk traffc should not exceed the lnk capacty.

3 3.2. Constellaton Model In ths work, the nterconnecton network model used s descrbed as follows. The orbts are represented as columns. So, for 12 satelltes n 3 orbts, the frst orbt conssts of the satelltes 0, 1, 2 and 3, as shown n fgure- 1. The second orbt conssts of the satelltes 4, 5, 6 and 7. And the last orbt conssts of the satelltes 8, 9, 10 and 11. The satelltes are connected wth the four neghbors (left, rght, above and below). The last satellte of each column s connected wth the frst one on that column. And also the last satellte of each row s connected wth the frst one on that row Paths Calculaton A tool, whch makes reference n the doman of lnear programmng, CPLEX[4], s used to solve the model descrbed n Secton 3.1. To solve ths problem, t s necessary to provde the possble paths to CPLEX. Hence, we descrbe here how the paths were generated. Ths lmt s too large and ncreases quckly beyond N. So, f we try to calculate all possble paths t wll cost a lot of memory. So the strategy s to calculate the best paths. The dea s to defne, for each demand assocated wth a par (,, one area whch contans the satelltes and. The paths could not get out of ths predefned area. Ths restrcts the possble paths to be near the satelltes. Hence, for each orgn-destnaton par (,, the paths wll be calculated wthn a rectangular area wth heght and wdth two unts larger than the rectangular area defned by and. 4. Implementaton CPLEX solves the problem descrbed n 3.1 usng the Branch and Bound technque. But, our model s consdered smple, snce f one varable x 0 0 s fxed n 1, then all the others varables x 0 wll be fxed n 0. The more mportant pont s the generaton of the best s paths. It was also very mportant to generate one example based on real data to test the performance of the model. It was necessary to buld a model of the world s traffc demand. Fgure 2 - Example of 2 Paths n the Constellaton Fgure 1 - Constellaton Model In a constellaton wth N satelltes, the paths could not contan cycles,.e., there are at most N 1 arcs on the path. Snce each satellte has 4 neghbors, there are ntally 4 possbltes. Then, for each node vsted, t has 3 other possbltes. So the lmt on the maxmum path s: $ "% N 3 "& L = 4*3*3*3*3* 2* Load Model It was used n the experments a model of traffc detaled as follows. Pars of users were selected at random, makng the load of the traffc dependent of the dstance between the users.

4 Table 1 World s Traffc Demand The selecton of users was based on the dstrbuton provded by [2]. In ths model, the plansphere s dvded nto 288 cells, wth 24 bands along the longtudes and 12 along the lattudes. The ntensty levels from 0 to 8 n ths model correspond to traffc expectatons for 2005 of 0, 1.6, 6.4, 16, 32, 95, 191, 239 and 318 mllons of addressable mnutes/year respectvely. The world s traffc demand s shown n table 1. Once a par (, of user locatons s selected, assocated wth potental requrements denstes w and w, the traffc requrement T between the two users s gven by: α ) β ( w w T (, = d(, Once a par (, of user locatons s selected, assocated wth potental requrements denstes w and w, the traffc requrement T between the two users s gven by: α ) β ( w w T (, = d(, where α and β are two parameters set by the user, the functon d gves the dstance between and. The values assumed for α and β are 0.6 and 0.5 respectvely. Ths formula assumes that the traffc between (, s the same as the traffc (,). Ths work does not assume that the traffc s symmetrc so the formula was modfed: α β w ) α + β ( w T (, = d(, 4.2. Load Calculaton It was used a program to generate the traffc matrx of our example. The traffc load was calculated based on the followng steps: gven the world s traffc demand, table 1, t was checked for each zone the nearest satellte of the center of the zone the total traffc demand was determned for each satellte, summng up all traffc demand w the dstance between the satelltes and, based on lattude and longtude, was calculated. The constellaton model descrbed n Secton 3.2 was used to test the model Test Fles The generaton program creates the demand fle (table 2) and a matrx (table 3), whch descrbes whch satellte, s responsble for each world regon. The demand fle has the followng tems: the source satellte, the destnaton satellte and the assocated traffc Table 2 - Demand Fle

5 Results The CPLEX was used to solve the model, whch s a lnear problem wth nteger varables(0/1). The executon tme was the metrc used to analyze the results. The equpments used on the experments are descrbed below: Manufacture r System Model Man Memory Number of CPUs Equpment 1 (E1) Sun Mcrosystems Ultra 5/10 Table 3 Satellte Assocated to Each Regon Equpment 2 (E2) Sun Mcrosystems Ultra Enterprse 188 MB 980 MB 1 (269 MHz) 4 (400 MHz) Table 4 Equpments used on the experments Frstly, the model was tested usng a small nput fle. Then other nput fles were used to measure the nfluence of the number of demands and lnks capacty on CPLEX executon tme. Some results are presented on the table 5. CPLEX needs lots of memory to solve the model usng the Branch and Bond technque. It was notced that for more than 80 demands the equpment E1 was not able to solve the problem. It does not have suffcent memory and t was necessary to use the equpment E2. The results show that the CPU tme s hardly affected by the ISLs capacty. Wth 90 demands, the E2 CPU executon tme was ncreased 2.1 tmes when the ISL capacty changed from 140 to 130. The communcaton paths changed and had a tendency to grow as shown by the obectve functon that vared from 168 to 171. CPLEX wll run faster when the ISLs capactes are bgger, showng that the ISLs are far from beng saturated. The CPU tme also ncreases wth the number of demands, when the ISL capacty s fxed. In the results, the column congeston s often maxmal, snce our model uses bnary varables and CPLEX gves prorty to the most mportant, bgger demands frst. Therefore, t can be notced the effect of saturaton on the frst used arcs. Lowerng the ISL capactes, force CPLEX to choose other paths and the consequence s that the congeston decreases whle the executon tme ncreases. The obectve functon s the sum of all lnks used n each communcaton and t s strctly ncreasng. The result s better when the obectve functon does not vary much when there s an ncrease on the number of demands or when there s a lowerng of ISLs capactes. 6. Concluson Nowadays, constellatons of satelltes are a realty. Hence, t s necessary to create models to descrbe and measure the qualty of the communcatons that are takng place. We presented a model that can address some of these ssues. It s necessary to mprove the procedure to generate the paths and also study CPLEX features that can mprove the CPU executon tme, but the model can be used as an opton of calculatng routng paths n the constellaton network. 7. References [1] H. S. Chang, B. W.. Km, C. G. Lee, Y. Cho, S. L. Mn, H. S. Yang and C. S. Km. Topologcal Desgn and Routng for LEO Satellte Networks, Techncal Report Department of Computer Engneerng, Seoul Natonal Unversty, June, [2] H. S. Chang, B. W.. Km, C. G. Lee, S. L. Mn, Y. Cho, H. S. Yang, D. N. Km and C. S. Km. Performance Comparson of Optmal Routng and

6 Dynamc Routng n Low-Earth Orbt Satellte Networks. In Proceedng of VTC 96, [3] H. S. Chang, B. W.. Km, C. G. Lee, S. L. Mn, Y. Cho, H. S. Yang, D. N. Km and C. S. Km. FSA- Based Lnk-Assgnment and Routng n Low-Earth Orbt Satellte Networks. IEEE Transactons on Vehcular Technology, [4] CPLEX CPLEX Optmzaton Inc. Verson 6.5 Reference Manual. [5] J. Galter. A Proposal to study satellte constellaton routng va classcal lnear programmng methods. [6] J. Galter. Geographcal reservaton for guaranteed handover and routng n low earth orbt constellatons. In 1 º Workshop de Comuncação sem Fo. Julho, Equpment ISL Nr of Demands Calculated Paths Congeston CPU Obectve Functon Capacty tme E % 3 mn E % 9 mn E % 3 mn E % 7 mn E % 3 mn E % 4 mn E % 4 mn E % 4 mn Table 5 Results