A Tool for Multi-Hour ATM Network Design considering Mixed Peer-to-Peer and Client-Server based Services

Transcription

1 A Tool for Muli-Hour ATM Nework Design considering Mied Peer-o-Peer and Clien-Server based Services Conac Auhor Name: Luis Cardoso Company / Organizaion: Porugal Telecom Inovação Complee Mailing Address: Rua Eng. José F. Pino Baso, 3810 Aveiro, Porugal Telephone Number: Facsimile Number: Address: luis-o-cardoso@pinovacao.p Co-Auhors: Carlos Lopes; Amaro de Sousa; Rui Valadas Theme: Revoluion in Nework Planning: Tools and Mehods Sub heme: Designing for Varying Performance Levels Absrac This paper presens a nework design ool for ATM neworks, which allows for muli-hour dimensioning of neworks supporing simulaneously peer-o-peer and clien-server based services. The dimensioning procedure assumes aggregaion of Virual Circui Connecions ino fied bandwidh end-o-end Virual Pah Connecions. In peer-o-peer services, connecions are esablished beween all node pairs of he service. In clien-server based services (e.g., video-on-demand, fas Inerne access), connecions are beween service nodes and servers. In his case, he dimensioning procedure allows for he selecion of he bes server for each node. The design model is formulaed as a linear ineger programming problem, which is solved hrough a heurisic based on Lagrangean relaaion wih subgradien opimizaion. This approach allows he compuaion of a heoreical lower bound, which is very useful in assessing he qualiy of he obained soluion. The nework design ool includes a graphical inerface for an easy inroducion and ediion of he nework parameers. Resuls show ha he ool can design large neworks wih reasonable compuaional speed and good accuracy. 9 h In. Telecomm. Nework Sraegy and Planning Symposium (NETWORKS2000), Torono, Canada, Sepember, 2000

2 1 Inroducion ATM neworks need o suppor a variey of services wih differen raffic profiles and Qualiy-of-Service (QoS) requiremens, a boh call and cell level. In ATM, flows of Virual Circui Connecions (VCCs) can be aggregaed in Virual Pah Connecions (VPCs). Using VPCs, i is possible o configure differen logical neworks on op of he physical nework [1]. We assume ha VPCs are end-o-end and are assigned a fied bandwidh. The dimensioning of an ATM nework aims a finding he nework configuraion (he bandwidh and roue of each VPC) ha achieves he lowes cos given he operaional cos of he nework elemens and he call and cell level QoS requiremens [2] [3]. Several feaures can be considered in he process of nework design. For eample, i is common sense ha eising services do no have he same raffic behaviour during ime. In general, business services have higher offered raffic in periods ha are complemenary o residenial services. If he nework has dynamic reconfiguraion capabiliies, i.e., ime is pariioned in periods and he nework configuraion is allowed o change beween periods, a muli-hour design procedure can lead o significan savings in he overall nework cos [4]. Typically, eising services are eiher peer-o-peer or clien-server based. In peer-o-peer services, calls or connecions (depending on wheher he services are swiched or permanen) can be requesed beween any pair of nodes wih aached users. Thus an end-o-end VPC mus be configured for each user node pair. In clien-server services (e.g., video-on-demand, fas Inerne access), a user can reques a call (or a connecion) o one of he server nodes of he service. Thus an end-o-end VPC mus be configured beween each user node and a server node. As far as we know, eising design ools deal only wih peer-o-peer services. This paper presens a sofware ool for he design of ATM neworks, called PTPlan ATM. PTPlan ATM performs muli-hour design and considers mied peer-o-peer and clien server services. Furhermore, in he case of clien-server services he ool allows he selecion of he bes server node for each user, from a se of pre-defined candidae server nodes. In secion 2 we presen he model and problem formulaion used in he design ool. In secion 3 we show he main feaures of he design ool. In secion 4 we discuss a case sudy and presen some conclusions. 2 Model and Problem Formulaion The design procedure can be separaed in he following seps: (i) VPC bandwidh assignmen; (ii) link capaciy calculaion, rouing opimisaion and server selecion (for clien-server services). The las sep can be joinly addressed by he linear ineger programming formulaion presened bellow. Since VPCs are end-o-end, he capaciy assignmen problem can be addressed individually for each VPC by (i) calculaing he number of VCCs ha observe he specified blocking probabiliy and (ii) calculaing he VCC bandwidh ha observes he specified cell level performance parameers. The firs sep can resor o he Erlang B formula, under he usual assumpions of Poisson arrivals and independence beween he arrival process and he service disribuion. The second sep can be solved assuming peak bi rae allocaion or, more aggressively, eploiing poenial saisical mulipleing gains hrough he use of appropriae saisical mulipleing models. Le he nework be represened by an undireced graph (N, A) whose nodes and arcs represen ATM swich locaions and available ransmission faciliies beween swich locaions. Each elemen of A is defined by an undireced arc (i, j), wih i, j N. The se of possible inerface ypes o insall in any arc is denoed by T and α is he bandwidh of inerface ype T. Le 2

3 Y denoe he maimum number of inerfaces of ype T ha can be insalled on (i, j). The operaional and mainenance cos associaed wih he use of one inerface of ype T in he arc (i, j) is denoed by C. Le H be he se of ime periods h. Each VPC k h is defined by he origin node o(k h ), he se of possible desinaion nodes d(k h ) D(k h ), he bandwidh in he direcion from origin o desinaion b(k h ), and he bandwidh in he direcion from desinaion o origin b(k h ). Se D(k h ) is a single desinaion for peer-o-peer services and he se of server nodes for clien-server services. The opimisaion model uses he following se of variables. Ineger variables y ha define he number of inerfaces of ype ha are insalled on arc (i, j) A. Roue binary variables ; when equal o one, defines ha VPC k h passes hrough arc (i, j) A in he direcion from node i o node j. Roue binary variables ; when equal o one, defines ha VPC k h passes hrough arc (i, j) A in he direcion from node j o node i. The following ineger programming model deermines he lowes cos physical nework given by he opimal roues for each VPC and he opimal server locaions: Minimize Subjec o: ( i, j) A T C y (1a), : { =1 =1} is a pah from o(k h ) o d(k h ) D(k h ), k h K h, h H (1b) Kh Kh ( b( ( b( + b( + b( ) ) < T < T α, (i,j) A, h H (1c) y α, (i, j) A, h H (1d) y y < Y, (i, j) A, T (1e) {1,0}; {1,0}; y > 0 and ineger The objecive funcion (1a) represens he oal cos of he nework soluion as a funcion of he number of inerfaces of each ype insalled in each nework arc. Consrain (1b) forces he soluion o choose a pah from origin o desinaion for all VPCs o be suppored by he nework. Consrains (1c) and (1d) impose ha he oal bandwidh insalled in each arc is enough o suppor he bandwidh occupied by he VPCs ha cross he arc defined in (1a) and (1b) in all ime periods. Finally, consrain (1e) imposes ha he number of inerfaces of each ype in each arc is no greaer hen a defined maimum value. This model does no separae he deerminaion of he nework opology from he link capaciy dimensioning. Some eising soluions deermine he nework opology a priori in order o reduce he arc se A and reach a nework dimensioning problem which is smaller and easier o solve. Separaion of he wo problems resuls in a procedure ha, alhough faser, leads o higher cos soluions. The soluion o he opimisaion problem is obained using Lagrangean relaaion wih subgradien opimisaion. Deparing from he original opimisaion problem, a new opimisaion problem is obained by applying Lagrangean relaaion o consrains (1c) and (1d), which we will refer o as he LLBP (Lagrangean Lower Bound Problem). To derive he LLBP, a se of 3

4 Lagrangean mulipliers is inroduced, one for each of he relaed consrains. For any arbirary se of non-negaive Lagrangean mulipliers, he soluion of LLBP is a lower bound of he original problem [5]. To compue differen ses of Lagrangean mulipliers, we use subgradien opimisaion [6]. This echnique is an ieraive process ha, for a given se of Lagrangean mulipliers, calculaes anoher se of mulipliers ha ry o maimize he objecive funcion value of he LLBP. A he end of he procedure, a final soluion and a heoreical lower bound for he original problem can be calculaed. The soluion of he LLBP for he variables is a shores pah calculaion. The sandard procedure uses he Dksra algorihm in each ieraion and, in his case, any VPC roue can become par of he final soluion. Alernaively, he user can specify a priori a se of candidae roues for each VPC and, in his case, he LLBP will selec only from his se of candidae roues. This feaure can be used o rade-off accuracy and eecuion ime, in neworks wih a large number of nodes. The deailed procedure can be found in [7]. 3 The Nework Design Tool In PTPlan ATM, he user inpus he nework opology, he service characerisics, a case sudy definiion and (opionally) i can impose one or more roues. Using hese daa he ool performs nework design and raffic growh analysis. PTPlan ATM runs on a Windows plaform and includes a graphical inerface (Figure 1) where he user can ener and edi he nework opology (nodes and links beween nodes). The user can creae a library of inerfaces ha he nework nodes can selec from. Eamples of inerface ypes are PDH 34 Mb/s and SDH 155 Mb/s. A library of nodes can also be creaed. Each node is defined by he se of inerfaces i can suppor. Afer node definiion, each link is auomaically assigned he se of inerfaces ha are common o is adjacen nodes. In addiion he user can associae a disance and a maimum uilizaion o each link and define he maimum number of inerfaces of each ype ha he link can suppor. Boh swiching and ransmission coss can be assigned o each inerface in each link. Transmission coss can be based on link lengh. The cos of each inerface is calculaed as 2 swiching cos + ransmission cos link lengh. There is also he possibiliy of creaing subnes. In he service characerizaion window (Figure 1.a), services can be seleced as being permanen or swiched, VBR or CBR, and peer-o-peer or clienserver. Permanen services are characerized by cell level QoS requiremens and swiched services by boh call level and cell level QoS requiremens. A his window, he user can also define he blocking probabiliy, he mean call duraion, he source raffic model parameers a) b) Figure 1 Graphical user inerface of PTPlan ATM. 4

5 (peak bi rae, mean burs size and uilizaion), and also he buffer size and cell loss raio required for he calculaion of he effecive bandwidh. There is a choice of effecive bandwidh models. In he case sudy window (Figure 1.b), he user defines he number of ime periods (for muli-hour designs), which nodes have aached users and, in he case of clien-server nodes, which nodes can have servers. The ool auomaically generaes he origin-desinaion pairs, in he case of peer-o-peer services, and he origin nodes in he case of clien-server services. Afer ha he user is asked o define he offered raffic for each origin-desinaion pair. Afer defining all nework parameers, he user may perform uni-hour or muli-hour designs. The resuls are he VPC roues, he number of inerfaces of each ype o insall in each link and he overall nework cos. 4 Case sudy In order o illusrae he capabiliies of he design ool we have defined a nework scenario wih he following characerisics. The nework opology is he one represened in Figure 1, wih 21 nodes and 46 links. There are 3 inerface ypes: PDH 2 Mb/s, PDH 34 Mb/s and SDH 155 Mb/s wih associaed swiching coss 100, 1000 and 3000, respecively, and associaed ransmission coss 1, 10, and 40, respecively. We have considered wo services and wo ime periods. The services are (i) a swiched VBR peer-o-peer service wih peak bi rae 128 Kb/s, mean burs period 10 s, uilisaion 0.2, cell loss raio 0.01, grade of service 0.01, mean call duraion 20 s; (ii) a permanen CBR clien-server service wih a rae of 40 Kb/s in he clienserver direcion and 4000 Kb/s in he server-clien direcion. There are end users for boh services a all he nodes and wo servers for he clien-server service a Poro and Lisboa. The offered raffic was assigned randomly using a uniform disribuion beween 0 and 100 channels for he CBR service and 0 and 100 calls/s for he VBR service. We designed his nework in several cases: shores pah VPC roues (wih disance based link meric), uni-hour and muli-hour design. In addiion, for he clien-server service, we considered wo cases: (i) fied server, where each user is aached o he closes (in number of hops) server, and (ii) seleced server, where he ool is allowed o selec he bes server for each node. The resuls are as follows: Cos (ime) Shores pah Uni-hour Muli-hour Fied Server (2.92 sec.) (18.29 sec.) (33.12 sec.) Seleced Server (2.91 sec.) (18.45 sec.) (33.50 sec.) As epeced gains are obained when adoping a muli-hour approach and a seleced server sraegy: (i) in he seleced server case here is a 9.7% gain beween muli-hour and uni-hour; (ii) seleced server is superior o fied server, 1.7% in muli-hour and 4.2% in uni-hour; (ii) here is a gain of 13.5% beween uni-hour / fied server and muli-hour / seleced server. We noe ha, alhough he resuls can very significanly wih he nework scenario, in general considerable gains are obained by resoring a muli-hour approach and seleced server sraegy. To appreciae he effec of saisical mulipleing we have convered he VBR service ino a CBR service wih he same peak bi rae. In he muli-hour case, he cos increased o In [7] we esed he performance of he dimensioning procedure. The resuls reproduced in Figure 2 show ha, in he uni-hour case, he dimensioning procedure can design small neworks (up o 30 nodes) in less han one minue and medium sized neworks (up o 50 nodes) in less han four minues. In he muli-hour approach used wo differen ime periods, and as such, he required ime is approimaely wo imes larger han he ime required by he uni-hour approach. These resuls were obained using a 200 MHz Penium MMX wih 128 5

6 MB of RAM running MS Windows 98 operaing sysem. Figure 2 also shows he dualiy gap (bes and work case calculaed over 10 runs) which is given by (S-B)/B, where S is he bes soluion and B he heoreical lower bound, for he uni-hour case. The dualiy gap is a measure of he qualiy of he soluion since he opimal soluion is always beween he obained soluion and he heoreical lower bound. Resuls show ha he dualiy gap improves for neworks wih higher number of nodes. This behavior is very imporan since for small neworks, here are sandard linear programming algorihms ha calculae he opimal soluion for he dimensioning problem Time (sec) Uni Hour Muli Hour Dualiy Gap (%) Bes Wors Number of nodes Number of Nodes a) b) Figure 2 Performance of he design procedure in erms of a) speed and b) dualiy gap. 5 References [1] R. Valadas, Dimensioning and Resource Managemen of ATM Neworks, Proc. 7 h IFIP/ICCC Conference on Informaion Neworks and Daa Communicaions - INDC 98, Aveiro, Porugal, June 15-17, 1998, pp [2] T. Bauscher, M. Perske, L. Turczyk, Advanced Broadband Nework Planning wih SICAP-ATM, Proc. 8 h Inernaional Telecommunicaions Nework Planning Symposium Neworks 98, Ialy, 1998, pp [3] K. Ramakrishnan, D. Mira, J. Morrison, VPN DESIGNER: A Tool for Design of Muliservice Virual Privae Neworks, Proc. 8 h Inernaional Telecommunicaions Nework Planning Symposium Neworks 98, Ialy, 1998, pp [4] D. Medhi, Muli-Hour, Muli-Traffic Class Nework Design for Virual Pah-Based Dynamically Reconfigurable Wide-Area ATM Neworks, IEEE/ACM Transacions on Neworking, Vol. 3, No. 6, 1995, pp [5] J. Beasley, Lagrangean Relaaion, Modern Heurisic Techniques for Combinaorial Problem, Ed. by Colin Reeves, Blackwell Scienific publicaions, [6] M. Held, P. Wolfe, H. Crowder, Validaion of subgradien opimisaion, Mahemaical Programming, vol. 6, pp , [7] A. de Sousa, R. Valadas, L. Cardoso, A. Duare, ATM Nework Dimensioning for Mied Symmerical and Asymmerical Services wih Dynamic Reconfiguraion in a Muli-Nework Provider Environmen, Proc. Third IFIP Workshop on Traffic Managemen and Design of ATM Neworks, 1999, pp. 5/1-5/15. 6