Radio Resource Caledarig i Cloud-based Radio Access Networks Jocelye Elias, Fabio Martigo, Mira Morcos, Li Che, Tijai Chahed Abstract Badwidth caledarig refers to the possibility of shiftig some bulk data trasfers, typically of large size with less striget real-time costrait, to the momets whe the etwork is less cogested. I this paper, we exploit calederig i radio resource allocatio i Cloud-based Radio Access Networks (C-RANs), where caledarig aturally fits the cetralized C-RAN architecture. We formulate the optimal caledarig problem usig Iteger Liear Programmig (ILP), takig ito accout specific costraits of users coectios ad the C-RAN operator. Give the complexity of the optimizatio problem, we devise effective heuristics producig close-tooptimum solutios i polyomial time. Extesive simulatios, coducted i represetative etwork scearios, demostrate the effectiveess of our proposed approach i improvig the performace of C-RAN schedulig. Keywords: Caledarig, C-RAN, Iteger Liear Programmig, Heuristics. I. INTRODUCTION A emergig tred i Radio Access Network (RAN) architectures is towards Cloud-based RAN (C-RAN), wherei Base Bad Uits (BBUs) are separated from Remote Radio Heads (RRHs) i the base statios ad pooled together i a cetralized fashio [1]. Cetralizatio allows for highly flexible resource allocatio ad sigificat reductio of operatio ad capital costs for mobile operators. Badwidth caledarig (termed as caledarig for brevity throughout the paper) refers to the possibility of shiftig some bulk data trasfers, typically of large size with less striget real-time costraits, to be scheduled o future occasios, whe the etwork is less cogested [2], [3]. Oe such example is a update for a popular applicatio which could be pushed towards user devices at ight. It exploits the kowledge, or estimatio, of future arrivals to pack curret ad future demads i a optimal way i the etwork. Our goal is to apply the cocept of caledarig i the C-RAN cotext for several key reasos: (1) exploit at the maximum the C-RAN architecture that allows the operator to hadle geographically-distat mobile users simultaeously by caledarig their traffic i a smart ad efficiet way, (2) help the C-RAN operator to further reduce latecy ad icrease the istataeous available capacity, guarateeig to J. Elias is with LIPADE Laboratory, Paris Descartes Uiversity, Frace, (email: jocelye.elias@parisdescartes.fr). F. Martigo is with Uiversity of Bergamo, Italy, ad Istitut Uiversitaire de Frace (IUF), (email: fabio.martigo@uibg.it). M. Morcos is with Telecom SudParis ad Laboratoire de Recherche e Iformatique (LRI), (email: mira.morcos@telecomsudparis.eu). L. Che is with the Laboratoire de Recherche e Iformatique (LRI), Uiversité Paris-Sud, Paris, Frace, (email: li.che@lri.fr). T. Chahed is with Telecom SudParis, (email: tijai.chahed@telecom-sudparis). mobile users very small delays ad high badwidth, ad (3) provide the operator with much more flexibility i maagig radio resources with respect to a solutio without caledarig techiques. To the best of our kowledge, our work is the first to apply the caledarig problem i the cotext of C-RAN, which, as a cetrally cotrolled etity, is a atural cadidate for applyig such a techique. Despite the potetial performace ad operatio beefits, applyig badwidth calederig i the C-RAN brigs o-trivial techical challeges. First, i the cotext of RANs, idividual users are typically heterogeeous, e.g., i terms of the quatity of resources required, the service deadlie that eeds to be met, ad the service priority ofte characterized by the valuatio of the resource from the users perspective. Secodly, the optimizatio problem that higes behid the badwidth calederig process is by ature combiatorial, rederig the quest to fid the exact optimum expesive or eve impractical. It is thus crucial to develop efficiet heuristic algorithms that ca strike a balace betwee system efficiecy ad implemetatio complexity. We cosider, i this paper, two categories of user flows: shiftable ad o-shiftable, ad we model the whole rage betwee these two extreme users prefereces i terms of the experieced delay before beig served. To this aim, we first propose a Iteger Liear Program (ILP) which performs the optimal caledarig of users coectios while maximizig the social welfare, i.e., the sum utilities of all the users i the system. Our model is flexible ad takes ito accout differet features of C-RAN systems, icludig the possibility to perform admissio cotrol of coectios o a give timespa. We further propose heuristic approaches, based o greedy algorithms, which provide good solutios, close to the optimum, ad exhibit very low computig time. We perform a thorough simulatio campaig to test our models ad algorithms i several case studies, varyig several key system parameters. Numerical results demostrate the effectiveess of our proposed approach ad models to improve the performace of C-RAN systems. This paper is orgaized as follows. Sectio II discusses related works. Sectio III presets the system model ad the assumptios we made i our work. Sectio IV describes the optimal caledarig model as well as two efficiet algorithms to compute sub-optimal yet good solutios for the resource caledarig problem. Sectio V illustrates umerical results. Fially, Sectio VI cocludes the paper ad briefly discusses the future research issues we deem most promisig.
II. RELATED WORKS Caledarig gaied mometum i trasferrig large, iterdataceter traffic through Wide-Area Networks (WAN) which costitute expesive ad busiess-critical resources [4], [5]. It has bee made possible thaks to Software-Defied Networkig (SDN), which allows for logically cetralized cotrol of resources [6]. Naboo [7], for istace, is a badwidth-odemad ad caledarig SDN applicatio proposed by Cisco which allows customers to dyamically request ad provisio badwidth requiremets, ad which helps i tur to decrease OPEX by schedulig large trasfers at times whe the etwork is less loaded. The work i [8] itroduces the cocept of service egieered path, i the cotext of programmable etworks. Badwidth caledarig is used to schedule a reserved sessio for the users through SDN-orieted API OpeFlow, otably for scheduled dataceter backups. Badwidth caledarig appeared also i the cotext of socalled trasport SDN [9], a extesio of SDN to the trasport layer, which would allow the ed-to-ed ifrastructure, icludig dataceters ad the WAN coectig them, to be maaged by a sigle SDN iterface. Packet Desig is a tool that has bee itroduced i [1], assurig resource maagemet ad orchestratio i SDN-based etworks. The work i [11] reports o Nokia Network Service Delivery Platform (NSP), a SDN-based etwork implemetig caledarig ad o-demad services. It is show that NSP ca achieve eight to ie times more reveue tha a etwork ot implemetig such service. The authors i [12] propose a caledarig mechaism based o the use of deadlies for iterdataceter WAN traffic which eeds to be completed withi a certai service time, while esurig high utilizatio of the etwork. III. SYSTEM MODEL We cosider a cetralized C-RAN operator, servig a set of users, which ca be of two types: o-shiftable ad shiftable (although we will capture i our model all tolerated time shifts betwee these two extremes). The former require to be served upo their arrival, the latter issue a coectio request that ca be served sometime i the future. A coectio request k is characterized by a 3-tuple: (1) the time at which the coectio arrives, deoted by t k, (2) the amout of resources demaded by the coectio, R k, ad (3) the coectio s duratio, m k. Moreover, u k expresses the utility (or satisfactio) of the correspodig user if her coectio request k starts to be served at time slot, with t k. Specifically, u k is a o-icreasig fuctio with respect to, ad expresses the satisfactio of user k as follows: if user k is of shiftable type, her utility u k will be maximum at her arrival time = t k, will decrease with ad be equal to zero at max, where max t k is the maximum time shift that user k ca tolerate. O the other had, if user k is of o-shiftable type, u k will be o-ull (ad maximum) oly at = t k ad zero elsewhere (i.e., for > t k ), sice o-shiftable coectios do ot tolerate ay time shift. As a cosequece, if eough resources are available at time t k, the coectio 1 coectio 2 coectio 3 < t 1 =,m 1 = 7, R 1 = 2 > < t 2 =,m 2 = 5, R 2 = 2 > < t 3 =,m 3 = 8, R 3 = 4 > coectio 4 < t 4 = 2,m 4 = 6, R 4 = 1 > u 1 Figure 1: Example sceario illustratig the utility fuctio of 3 shiftable coectios (1, 2 ad 4) ad 1 o-shiftable oe (coectio 3), as a fuctio of the time-shift experieced by the coectio. user will be immediately served ad her experieced utility will be maximal. If, however, resources are ot eough to accommodate immediately the request, ad the user is of oshiftable type, she will ot be admitted ito the system ad her utility will be equal to zero. Fially, if the user is of shiftable type, her service ca be delayed without exceedig some tolerated rage max. A example sceario is illustrated i figure 1, where coectios 1, 2 ad 4 are shiftable for 3, 2 ad 6 time slots, respectively, with costat utility fuctios whereas coectio 3 is o-shiftable. We deote by R c = {1,..., K} the set of coectios, R b = {1,..., N} the set of resource blocks ad R t = {1,..., M} the set of time slots. Table I summarizes the parameters ad decisio variables itroduced i our model ad heuristics. Due to the C-RAN limited capacity i terms of resource blocks, ot all requests ca be served at their arrival or at the start time they request. I this case, the C-RAN operator ca either delay the shiftable flows for a certai time period so that their service is completed withi a certai time widow, deoted by W, or else reject them. We assume that a accepted flow caot be dropped or iterrupted if it starts to be served. We also assume that the amout of requested resource blocks is costat over the service duratio. u 2 u 3 u 4 1 2 1 2 1 2 IV. CALENDARING IN C-RAN: ILP MODEL AND A. ILP model HEURISTICS We formulate hereafter the optimal caledarig problem usig a Iteger Liear Programmig (ILP) approach. The aim of the C-RAN operator is to allocate resources maximizig the social welfare, expressed as the sum of users utilities, while respectig capacity costraits. Decisio variables are: x k, which is equal to 1 if user k is scheduled to start i time slot ad otherwise, ad r k,j,
Parameter Defiitio K Total umber of coectio requests N Total umber of available resource blocks at each time slot M Total umber of available time slots t k Time slot i which the coectio (or user) k arrives R k Number of resource blocks requested by coectio k alog all the duratio of the coectio m k Duratio of coectio k (expressed i umber of time slots) u k Utility fuctio of coectio k startig to be served at time slot Variable Defiitio x k Biary decisio variable that deotes the time slot i which the coectio starts (is scheduled). This variable is equal to 1 exactly i oe ad oly oe slot, ad elsewhere r k,j Biary decisio variable that tells if the j-th resource block is allocated to user k at time slot. This variable is equal to 1 if true, ad otherwise Table I: Parameters ad variables defiitio which is equal to 1 if the j-th resource block is allocated to user k at time slot, ad otherwise. Maximize u k x k (1) k R c, R t: t k M m k +1 s.t. x k 1, k R c (2) k R c: t k τ R t:τ mi{,m k } j R b =t k 1, R t, j R b (3) x k [ τ+1] = R k ( j R b τ R t:τ mi{,m k }, R t, k R c x k [ τ+1] ), (4) R t : t k, k R c (5) k R c,j R b N, R t. (6) (1) represets the social welfare, which is to be maximized by the C-RAN operator. Costrait (2) esures that a give coectio is scheduled to start at most oce. Note that this costrait permits to implemet admissio cotrol, sice the C-RAN operator is allowed to refuse coectios (which caot be accommodated due to limited capacity ad/or tight schedulig requiremets). If, o the other had, we wat to force the model to perform caledarig o all the coectios give i iput, it suffices to replace the iequality i such costrait by a strict equality. I this latter case, however, it may happe that give etwork istaces are ufeasible. Costrait (3) esures that a give resource block j, at a give time slot, is allocated to exactly oe user, at most. Costraits (4) ad (5) guaratee that a coectio k is served by allocatig to it R k resource blocks durig m k cosecutive time slots. Fially, costrait (6) esures that the capacity at each time slot (expressed by N), is ot exceeded. B. Heuristic Approaches Sice i medium-to-large etwork istaces the ILP model ca take a log computatio time to obtai the optimal solutio, ad this ca be very critical especially for oshiftable coectios, we propose hereafter two greedy approaches that the C-RAN operator ca implemet to optimize the caledarig decisio variables x k ad r k,j. The first approach takes ito cosideratio the umber of resource blocks required by the coectio request as well as the service duratio i terms of time slots. The secod oe, which we cosider as a baselie compariso, does ot rely o such iformatio, which, sometimes, may ot be promptly available at the time the coectio is offered to the etwork. We will refer to them, respectively, as Resource-Aware ad Resource-oblivious approaches. 1) Resource-aware Approach (): This approach cosists of repeatig the followig procedure for every time slot {1,.., M}: At a give time slot ad for all coectio requests k R c that have ot bee served before such time slot, ad that verify the followig coditios: (1) t k, (2) M m k +1 ad (3) u k, the C-RAN operator sorts them based o the followig weight: U k = uk u k +1 R k m k The ratioale is that priority is give to coectios which cotribute the most to icrease the overall utility (umerator), while more demadig coectios (either i terms of demaded resources R k or duratio m k ) are pealized. Secod, after sortig the list of coectios i decreasig order, based o U, k the C-RAN operator will accept coectio requests i order (accordig to the sorted list), oly if the amout of their demads i terms of required resource blocks (R k ) is less tha the available amout of resource blocks. For each accepted request, the correspodig x k is set to 1; resources blocks are assiged to the coectio such that j R b r k,j = R k, ad its demad, R k, is deduced from residual available capacity. Fially, we exclude from the list of remaiig coectios the oes whose demads caot aymore be served i the remaiig, available time widow, i.e., those with m k > M. Algorithm 1 shows the implemetatio for. C k takes the value 1 if user k is beig served ad otherwise. Y is the umber of resource blocks available at time slot. 2) Resource-oblivious Approach (): The resourceoblivious approach is similar to the previous oe; the same procedure is executed at each time slot, but the C-RAN operator cosiders oly the utility variatio i the coectio admissio process. Therefore, oly step 1 of the algorithm detailed i the previous sectio is modified, usig the followig weight: U k = u k u k +1
Algorithm 1 Resource-aware Approach () algorithm Iput K, N, M, u k, tk, m k, R k. 2: Output x k, r k,j R t, k R c Iit Y = N R t ; C k = k R c 4: For = 1 to M For k = 1 to K; 6: if C k 1 & t k & M m k + 1 & u k U k = uk uk +1 R k m k 8: ed ed 1: [B,I]= sort(l), i decreasig order, L = { U}, k B is the sorted list ad I is the list of correspodig coectio idexes. for j = 1 : size(l) 12: k = I(j) if R k N 14: x k 1& C k 1 for l = : m k 1 16: for i = 1 : R k r k,y +l i+1 +l = 1 18: ed Y +l = Y +l R k : ed ed 22: ed ed If we refer agai to the illustrative example of figure 1, with four coectios (3 shiftable ad 1 o-shiftable), figure 2 illustrates two possible caledarig solutios that fit withi our service widow cosistig of M = 12 time slots ad N = 4 resource blocks. I the left-had solutio, the shiftable coectios 1 ad 2 are served immediately, while the shiftable coectio 4 is delayed of 3 time slots; o-shiftable coectio 2 caot be served withi the total timespa, ad is thus rejected (ot admitted i the etwork). This solutio maximizes the social welfare ad is reached by the ILP model as well as. provides aother solutio, show i the right-had side of the figure, i which oly coectio 3 is scheduled. This is because does ot take ito cosideratio the coectio duratio or the umber of resource blocks required by each coectio, ad so it does ot guaratee social welfare maximizatio. V. PERFORMANCE EVALUATION We ow evaluate umerically the caledarig mechaism ad compare the three approaches we proposed i this paper: ILP, ad. We implemeted our proposed optimizatio model i OPL, ad solved it usig the CPLEX commercial solver o a server equipped with a Itel CPU at 2.6GHz ad 64 GByte of RAM. All umerical results are obtaied by averagig 5 radom extractios. N 4 3 2 1 = 1 M N Figure 2: Example illustratig two possible caledarig solutios, for coectios 1, 2, 3 ad 4, that fit withi the service widow cosistig of M = 12 time slots ad N = 4 resource blocks. A. Network settigs We cosider that the C-RAN operator aims at caledarig K coectio requests i a time widow cosistig of M time slots. A percetage s of these coectios are shiftable: we suppose that o-shiftable flows have a utility u k that is equal to 1 if they are scheduled immediately, i.e., at = t k, ad to just after a delay of 1 or more time slots. For shiftable coectios, we cosider two cases: (1) u k equal to 1 for all delays less tha or equal to M m k ad (2) u k decreasig expoetially from 1 at = t k to at = M m k +1. Note, however, that our model ad heuristics are geeral, ad ca be applied to etwork scearios with ay o-icreasig form for the utility fuctio. Table II summarizes the parameter settigs for these two case studies. We specifically measure the objective fuctio (social welfare) ad the percetage of rejected coectios, by varyig the percetage of shiftable coectios (case studies 1a ad 2a ad correspodig Figures 4 ad 7, respectively), the umber of coectios (case studies 1b ad 2b ad correspodig Figures 5 ad 8, respectively), ad fially the umber of resource blocks available at each time slot (case studies 1c ad 2c ad correspodig Figures 6 ad 9, respectively), as detailed i Table II. B. Results ad discussio We observe, i case study 1, where utility fuctios of shiftable coectios are costat, that the performace of the greedy solutio is remarkably similar to the ILP-based oe, i terms of both the objective fuctio (social welfare) ad rejectio rate. I fact, the social welfare is 9% less tha the optimum, i the worst case, ad less tha 6% o average. However, the performace of ca i some cases deviate from the optimal solutio, especially whe plottig is doe versus the umber of coectios (case study 1(b)). Both the ILP ad approaches outperform i terms of social welfare. Ideed, does ot take ito cosideratio the demads i terms of resource blocks (R k ) as well as the duratio, which explais this gap. performs, however, well i case study 1(c) for large umber of resource blocks: whe resources are abudat, the performace gap betwee the proposed model ad heuristics reduces. Similar results are obtaied with case study 2, where utility fuctios of shiftable coectios are expoetially decreas- 4 3 2 1 M
Case study 1 Case study 2 Utility fuctio of shiftable coectio k startig to Costat ad equal to 1 [t k, M Expoetially decreasig from 1 at = be served at time slot m k + 1] t k to at = M mk + 1 Parameter (a) (b) (c) Geeral parameters Number of time slots M = 1 M = 1 M = 1 Number of RB available i a time slot N = N = N [, 1] requests K = 5 K [, 1] K = 5 Percetage of shiftable coectios s [, 1] 5% 5% Per coectio request parameters Arrivig time t k geerated from u.d [, 5] u.d [1, 5] u.d [1, 5] Number of RB requested R k geerated from u.d [1, 5] u.d [1, 5] u.d [1, 5] Coectio duratio m k geerated from u.d [1, 5] u.d [1, 5] u.d [1, 5] Table II: Settigs ad parameters ig. I fact the social welfare geerated by is 1% less tha the oe obtaied by the optimal solutio, i the worst case, ad 7.5% less i average. Fially, we compare the computatioal efficiecy of the 3 proposed models ad heuristics. Figure 3 shows the average computig time (expressed i secods) eeded to obtai the ILP optimal solutio ad to ru the two heuristics ad. We observe that ad achieve a average time savig of about 99.8%, which is ideed remarkable, especially whe the umber of coectios is large. VI. CONCLUSION We cosidered i this paper the problem of caledarig users coectios i C-RAN systems, a atural cotext i which badwidth caledarig ca be applied owig to its cetralized architecture. We cosidered two types of users: shiftable ad oshiftable, ad formulated the optimal caledarig problem usig a ILP approach, implemetig the possibility to perform access cotrol as well. We further proposed two heuristics, which we showed to perform close to the optimum i several etwork scearios, with a polyomial computig time. Ideed, our umerical results demostrate a improvemet i the performace, otably i terms of the overall utility perceived by the users, which icreases up to 3% with respect to the baselie approach. Future research directios iclude the extesio of our work to olie algorithms, i order to perform admissio ad schedulig decisios o-the-fly, based o past observatios of the system. REFERENCES [1] M. Peg, Y. Li, Z. Zhao, ad C. Wag, System architecture ad key techologies for 5G heterogeeous cloud radio access etworks, IEEE etwork, vol. 29, o. 2, pp. 6 14, 15. [2] S. Kadula, I. Meache, R. Schwartz, ad S. R. Babbula, Caledarig for wide area etworks, i ACM SIGCOMM Computer Commuicatio Review, vol. 44, o. 4, May 14, pp. 515 526. [3] M. Dufour, S. Paris, J. Leguay, ad M. Draief, Olie Badwidth Caledarig: O-the-Fly Admissio, Schedulig, ad Path Computatio, i IEEE Iteratioal Coferece o Commuicatios ICC 17, Paris, Frace, May 17, pp. 1 6. [4] C.-Y. Hog, S. Kadula, R. Mahaja, M. Zhag, V. Gill, M. Naduri, ad R. Wattehofer, Achievig high utilizatio with software-drive WAN, i ACM SIGCOMM Computer Commuicatio Review, vol. 43, o. 4, 13, pp. 15 26. [5] S. Jai, A. Kumar, S. Madal, J. Og, L. Poutievski, A. Sigh, S. Vekata, J. Waderer, J. Zhou, ad M. Zhu, B4: Experiece with a globally-deployed software defied WAN, ACM SIGCOMM Computer Commuicatio Review, vol. 43, o. 4, pp. 3 14, 13. [6] L. Gkatzikis, S. Paris, I. Steiakogiaakis, ad S. Chouvardas, Badwidth Caledarig: Dyamic Services Schedulig over Software Defied Networks, i IEEE Iteratioal Coferece o Commuicatios ICC 16, Kuala Lumpur, Malaysia. [7] Badwidth o demad ad caledarig applicatio aboo v1, Cisco, Tech. Rep., 17. [8] The developer ad the etwork: Improvig user experiece by programmig the etwork, David Ward, Juiper Networks, Ic, Tech. Rep., 11. [9] Trasport SDN takes shape, The Dataceter Joural, Tech. Rep., March, 14. [1] SDN: Maagemet ad orchestratio cosideratios, Packet Desig, Tech. Rep., 14. [11] A uified approach to the automatio, cotrol ad assurace of IP/optical etworks, Nokia Network Services Platform, Tech. Rep., 17. [12] H. Zhag, K. Che, W. Bai, D. Ha, C. Tia, H. Wag, H. Gua, ad M. Zhag, Guarateeig Deadlies for Iter-Data Ceter Trasfers, IEEE/ACM Trasactios o Networkig (TON), vol. 25, o. 1, pp. 579 595, 17. Computig time (sec) Figure 3: Computig time
35 28 3 25 15 Percetage of shiftable coectios; K=5 7 6 5 3 Percetage of shiftable coectios; K=5 Figure 4: Case study 1(a) - Costat utility fuctio for shiftable coectios 24 16 Number of shiftable coectios; K=5 6 Number of shiftable coectios; K=5 Figure 7: Case study 2(a) - Expoetially decreasig utility fuctio for shiftable coectios 5 3 1 8 6 Figure 5: Case study 1(b) - Costat utility fuctio for shiftable coectios 35 25 15 5 8 6 Figure 8: Case study 2(b) - Expoetially decreasig utility fuctio for shiftable coectios 5 3 1 8 6 5 3 1 6 Figure 6: Case study 1(c) - Costat utility fuctio for shiftable coectios Figure 9: Case study 2(c) - Expoetially decreasig utility fuctio for shiftable coectios