Solution of a certain class of network flow problems with cascaded demand aggregation and capacity allocation

Transcription

1 Unersty of Wollongong Research Onlne Faculty of Informatcs - Papers (Arche) Faculty of Engneerng and Informaton Scences 2006 Soluton of a certan class of network flow problems wth cascaded demand aggregaton and capacty allocaton Farzad Safae Unersty of Wollongong, farzad@uoweduau I Oueys Unersty of elbourne Publcaton Detals Ths s an electronc erson of an artcle orgnally publshed as: Safae, F & Oueys, I, Soluton of a certan class of network flow problems wth cascaded demand aggregaton and capacty allocaton, Optmzaton ethods and Software, 2006, 2(4), The journal Optmzaton ethods and Software can be found here through Taylor & Francs journals Research Onlne s the open access nsttutonal repostory for the Unersty of Wollongong For further nformaton contact the UOW Lbrary: research-pubs@uoweduau

2 Soluton of a certan class of network flow problems wth cascaded demand aggregaton and capacty allocaton Abstract Ths artcle deelops analytcal models for a class of networkng problems that ncludes two cascaded stages of demand aggregaton and capacty allocaton The solutons to these problems are requred n real tme as the demand fluctuates rapdly The capacty allocaton problem makes a large-scale nteger programmng problem too complex for practcal applcatons Usng the Lagrangan relaxaton technque and a sutably deeloped heurstc for multpler adjustment, the computatonal complexty s reduced to such a degree that a real-tme mplementaton of the algorthm s feasble Ths artcle also deelops effcent heurstcs to aggregate demand The proposed algorthm produces a near-optmal soluton n pseudo-polynomal tme Keywords Optmzaton, athematcal programmng, Lagrangan relaxaton technque, Telecommuncatons Dscplnes Physcal Scences and athematcs Publcaton Detals Ths s an electronc erson of an artcle orgnally publshed as: Safae, F & Oueys, I, Soluton of a certan class of network flow problems wth cascaded demand aggregaton and capacty allocaton, Optmzaton ethods and Software, 2006, 2(4), The journal Optmzaton ethods and Software can be found here through Taylor & Francs journals Ths journal artcle s aalable at Research Onlne:

3 Soluton of a certan class of etwork Flow Problems wth cascaded demand aggregaton and capacty allocaton FARZAD SAFAEI * AD IRADJ OUVEYSI ** * Unersty of Wollongong, Australa, farzad@uoweduau ** The Unersty of elbourne, Australa, radjoueys@yahoocouk Abstract Ths paper deelops analytcal models for a class of networkng problems that nclude two cascaded stages of demand aggregaton and capacty allocaton The solutons to these problems are requred n real-tme as the demand fluctuates rapdly The capacty allocaton problem leads to a large-scale nteger programmng problem too complex for practcal applcatons Usng the Lagrangan relaxaton technque and a sutably deeloped heurstc for multpler adjustment, the computatonal complexty s reduced to such a degree that a real-tme mplementaton of the algorthm s feasble The paper also deelops effcent heurstcs to aggregate demand The proposed algorthm produces a near optmal soluton n pseudo-polynomal tme Keywords: Optmzaton; athematcal Programmng; Lagrangan Relaxaton Technque; Telecommuncatons Introducton Optmzaton of a class of network flow problems has become ncreasngly mportant n certan ndustral applcatons These problems nole two cascaded (but nterrelated) stages of demand aggregaton and capacty optmzaton Typcally, the demand s hghly dynamc, that s, t fluctuates sgnfcantly wth tme Consequently, the optmzaton s requred to be performed on short tme scales, often n real-tme In addton, the demand aggregaton stages are spatally dstrbuted Ths geographcal separaton would necesstate dstrbuton, and to a certan degree ndependence, of decson makng processes for the oerall system optmzaton Fgure shows a representaton of ths class of problems In ths Fgure, there s a supply node on the rght hand sde that s the source of some goods for consumpton of snk nodes on the left hand sde The snk nodes are grouped n seeral geographcal locatons At a gen short tme nteral there s a certan leel of demand from eery snk node for the goods suppled ote that we requre the demand from a partcular snk node to ether be satsfed n full or completely rejected In other words, we cannot accept partal fulflment of demand Eery snk node can access the supply source from a set of demand concentrators (labelled Access Concentrator nodes n the Fgure) In a gen locaton, eery snk node s connected to eery Access Concentrator node, but to aod clutterng, we hae only shown a subset of these lnks There s no capacty lmt on these lnks The supply node, howeer, has a capacty lmt on the amount of goods that t can shp to the Access Concentrator nodes Ths lmt s denoted by k where s an nteger and k s a fxed alue that we call channel capacty The supply node has potental lnks to all the Access Concentrator nodes Howeer, at ** Iradj Oueys s an honorary research fellow wth the Department of Electrcal and Electronc Engneerng of the Unersty of elbourne

4 each nstant of tme at most of these lnks wll be allocated capacty of k There s also a lmt of how many channels can be allocated to a gen locaton In a typcal stuaton, the demand from seeral snk nodes n a gen locaton s aggregated nto a sngle Access Concentrator node so that the total demand s less than k The supply node wll then allocate a channel of capacty k to ths Access Concentrator node and use ths to satsfy the demand For example, Fgure shows that n locaton, three snk nodes are connected to the frst Access Concentrator node and a channel has been allocated to ths node from the supply for ths purpose The problem of nterest to us, therefore, can be summarsed as follows: Gen a network of supply node and snk nodes as descrbed before, we ntent to maxmse the amount of demand satsfed by ths network at each tme nteral by aggregatng a subset of demands from multple snk nodes nto Access Concentrator nodes and then allocatng channel capacty to these There s a cost assocated wth re-allocaton of channel capacty from one lnk to another Channel capacty can only be allocated n whole and partal fulflment of demand for a partcular snk node s not allowed Demand (snk) nodes, 2,,,, Access Concentrator nodes, 2,, j,, Locaton Allocated Channel, Capacty k Total number of allocated channels = Locaton Supply d Demand from snk node n locaton Locaton Q Unassgned Channel, Capacty 0 Fgure : The structure of the network flow problem

5 Example applcaton The aboe problem s frequently encountered n plannng and operaton of telecommuncaton networks to supply broadband Internet access to resdental customers In ths case, an Access Concentrator s stuated n cnty of a group of customers, say a gen street Ths dece s usually called a multplexer n telecommuncaton jargon Seeral of these Access Concentrators n a gen geographcal regon are then connected to the frst pont of entry to the Internet whch s typcally a router nstalled n the Internet Serce Proders premses Ths router performs the role of the supply node n our model and wll deler the nformaton requested by the customers to them The router, howeer, has lmted capacty and t would be ery expense to connect t to all nodes statcally The typcal nterconnecton, therefore, s based on an optcal fbre rng network where a number of channels of gen capacty can be assgned to the Access Concentrators based on demand These channels are mplemented usng dfferent optcal waelengths on the optcal fbre rng Gen that more than 50% of a telecommuncatons carrer s total nestment s n the access network [], the cost sangs of the aboe optmzaton could be substantal 2 The am of ths paper Ths paper deelops mathematcal models and algorthms for optmal supply of demand for the aboe problem There are two phases of channel capacty allocaton and demand concentraton The supply node must dynamcally allocate channel capacty to Access Concentrator nodes as the demand from these fluctuates n tme The Access Concentraton phase requres algorthms to pack as much demand as possble onto the aalable number of allocated channels In practce, these two stages are geographcally dstrbuted and t would not be useful to model the problem as a sngle monolthc problem Instead, one needs to deelop optmzaton algorthms for both phases n such a way that they can operate more or less ndependently on short tme nterals 2 Problem Formulaton Access Concentrator Fgure 2 depcts the Access Concentrator model as used n ths paper There are nputs to the concentrator ndexed by,2,, Each nput has a demand requrement of d It s assumed that these alues are sensble That s, d k, where k s the channel capacty descrbed before It s also assumed that d alues are ntegers (whch can be enforced by selectng a sutable demand unt)

6 d Input e Output c d e j c j d c Fgure 2: Access Concentrator odel For conceptual smplcty, the number of output ports s also equal to The output ports are ndexed by j,2,, The man task of the concentrator s to aggregate as many nputs onto the output ports wthout exceedng the channel capacty k aturally, some of the outputs may be assgned wth no demand These outputs are presented to the supply node for allocaton of channels whch attempts to maxmse the total supply Although not essental, t would be easer to understand the nteracton between the two optmzaton enttes f the concentrator output s ordered To ths end, the weghtng factor c j can be properly assgned to enforce the desred orderng For example, by settng cj j, one can force the Access Concentrator optmzaton routne to prode an ordered set of outputs from maxmum to mnmum Another possblty s to set the alues of c j accordng to the followng: for j,2,, m c j () F otherwse Where F s a large number Ths forces the concentrator to aggregate as much as possble onto the frst m output ports (Commonly, there s a lmt for maxmum number of channels whch can be assgned to a gen locaton due to hardware constrants Ths maxmum alue s denoted here by m) Therefore, the Integer Lnear Programmng model for the Access concentrator can be formulated as follows: n z j e d c Subject to: e, 2,, (2) j j P ed k j2,,, (3) 0, j e, (4)

7 In ths formulaton, e s the decson arable representng the nput-output connecton matrx for the concentrator The constrant set (2) ensures that each nput s connected to precsely one output port and the constrant set (3) enforces the channel capacty lmt 2 Soluton strategy The Integer Lnear Programmng P problem belongs to the class of P-Complete problems It s smlar to the star-star concentrator locaton problem wth the dfference that any termnal here may hae a dfferent demand d Dfferent heurstcs hae been deeloped to sole ths type of problems, among whch 'ADD' and 'DROP' algorthms are often used n the lterature [2] Howeer, n ADD and DROP algorthms a sequence of optmal assgnment problems are soled and hence these approaches quckly become mpractcal as the problem sze grows 22 Greedy Algorthm Here, a Greedy Algorthm for solng P s proded Ths algorthm attempts to sole the problem terately In each step the remanng output port wth the least weghtng alue c j wll be maxmally flled usng the remanng nput demands Denotng the set of remanng nput and output ports by S and Q respectely, and the output port ndex wth mnmum weghtng alue n Q by l, at each teraton of the algorthm the followng ILP sub-problem wll be soled ax z = e l d P2 S Subject to: ed k (5) S e l l, S 0 (6) Problem P2 may be recognzed as a specal case of a 0- knapsack problem (cost and constrant ectors concde) Formally, the proposed Greedy Algorthm can be outlned as follows 22 an Algorthm Step : Gen the number of ports, nput demands d k for 2,,,, where k Z s the output port capacty, ntalze S {, 2,, } and Q {, 2,, } as the set of all unassgned nput and output ports respectely Step 2: Consder an output port l: cl cj j Q Sole the sub-problem P2 accordng to procedure outlned below Let the soluton be Sl S Step 3: Update Q Q\{} l and S S \ S l Step 4: If Q or S stop Otherwse go to Step Procedure for solng P2 The P2 sub-problem can be soled by the dynamc programmng algorthm descrbed n [5], whch s capable of reachng the optmal soluton n pseudo-polynomal tme Wthout loss of generalty, assume that d d d The aboe-mentoned algorthm behaes as follows 2

8 For t, defne {, 2,,} t, and 2,,, t zt ( p) ax el d : el d p, el {0} for p 0,,, k t t The recurson s ntalzed wth d f d p z ( p) 0 otherwse As shown n [5], for t 23,,, and p 0,,, k zt ( p) f d t p zt ( p) axz t ( p), d t z t ( p d t ) f d t p Upon termnaton z ( k) z In the case of multple solutons to P2 (e, more than one possblty for formng S l ), based on Lemma below f these sets are dsjont, a random selecton wll suffce In the case that these sets are not dsjont, the soluton set wth mnmum cardnalty wll be selected It wll be shown n the next sub-secton that ths s more lkely to lead to the optmal soluton as t prodes further opportunty of multplexng n the subsequent teratons 23 Effecteness of Greedy Algorthm The complexty of Greedy Algorthm can be estmated as follows As ndcated n [5], the dynamc programmng algorthm wll sole P2 n O( K) operatons for each teraton of man algorthm As there are 2 teratons, the total complexty s O( K) In general, the output of the Greedy Algorthm as defned n the preous sub-secton may not be optmal As an example, consder the case of Fgure 3 where an Access Concentrator wth 6 and k 20 s depcted Input Demand ux Output (a) Input Demand (b) ux Output 9 9 Fgure 3: on optmal nature of the Greedy Algorthm

9 The alues of c j hae been selected accordng to Equaton wth m 2, that s j,2 c j (7) F otherwse Where F s a large number Ths forces the concentrator to aggregate as much as possble onto the frst two output ports A comparson between Fgure 3-(a) and Fgure 3-(b) wll reeal that the Greedy Algorthm dd not pck the optmal soluton n Fgure 3-(a) (the output alues for j 2 are not shown as these are of no concern) It s nstructe to note that n the example of Fgure 3, there s more than one soluton to the P2 problem when appled to the output node (e, there s more than one way to obtan the alue of 9 from the nput demands) The followng lemma, together wth the aboe obseratons, wll be useful n desgnng an approprate heurstc to deal wth ths case (ths heurstc was explaned n the preous sub-secton) For smplcty, the lemma s proed for m 2 Extenson to general case s also possble Lemma : Let S j denote the set of nputs assgned to output j by the concentrator That s, S j : e Let c j be defned as n Equaton 7 and j denote the output of P2 n the j th teraton of the man algorthm Also assume that there are Sj, j 2, wth soluton alues j, j 2, such that Then the clam s that f S S, the Greedy Algorthm wll result n an optmal soluton Proof: Assume to the contrary that S S, but the output of Greedy Algorthm s not optmal, that s, 2 2 ow, snce, t follows that 2 2 Howeer, S S \ S and S2 S \ S whch mply that 2 (due to optmalty of P2 ) Ths, n turn, mples that, whch s a contradcton and the proof s complete 2 3 Problem Formulaton Supply ode Channel Allocaton The supply node channel allocaton algorthm wll examne the offered demand on regular tme nterals At each tme nteral, some exstng channels are allowed to contnue and some new channels are optmally rearranged Ths assgnment procedure s performed based on the output of the followng mathematcal model for each tme nteral Q : umber of locatons : Index for the locaton number, 2,,, Q : umber of nputs n any locaton : Index for node nputs, 2,,, : Total number of channels aalable to the supply node j : Index for channel numbers, j 2,,, d : Demand at nput number locaton at the gen tme nteral d s assumed to be less than or equal to the channel capacty e f nput n locaton s connected to channel j at the current tme nteral, and s equal to zero otherwse c : Cost of establshng a connecton between channel j and locaton j w j 0, : Connecton status of channel j to locaton before the current tme nteral (an nput to the optmzaton based on the status of the system, not a decson arable) n : axmum number of channels for locaton

10 r j : The reenue from carryng a unt demand on channel j from locaton : The connecton cost of channel j to locaton defned as h j 0 f w j h j c f w j 0 Ths ndcates that the cost of connectng a channel to a gen locaton depends on the preous state of the system before the current tme nteral (no cost arses f the channel was already connected to the specfed locaton) A dummy node s consdered and the followng defned r : Lost reenue from rejecton of a unt demand from locaton e, : Status of rejecton of demand on locaton The ntended problem can then be modelled as the followng nteger lnear programmng problem: Subject to: n Z(P) = Q d e, r Q j h j e Q j d e r j (P3) e,, j Q,2,, ;,2, Q e, j,2,, (8) (9) j e n, (0) 0,, j e, () Constrant set (8) ndcates that a gen nput of locaton can ether be connected to at most one output channel or to the dummy node (demand rejecton) Constrant set (9) ensures that channel j s connected to only one nput and fnally constrant set (0) guarantees that not more than n channels are assgned to locaton 3 Lagrangan relaxaton The nteger lnear programmng (ILP) problem (P3) has Q bnary arables and the total number of constrants s also n the order of Q (A typcal problem wll hae ts n the order of 6000) General relaxaton algorthms, such as Fractonal Cuttng Plane or Branch and Bound algorthms may be used to sole ILP problems [5] Howeer for our bnary ILP problem, consderng the number of bnary arables, these methods would appear to be mpractcal A closer examnaton of the structure of (P3) shows that remong constrant set (0) wll yeld a Lnear n-sum Assgnment problem Therefore, to sole problem (P3), the constrant set (0) s relaxed usng the Lagrangan relaxaton technque [5] and ncorporated nto the objecte functon as a penalty Let,,2,, Q, be the set of non-negate Lagrangan multplers correspondng to the constrants n (0) Then the relaxaton of problem (P3), denoted here by LR ( ), wll be as follows:

11 n Z LR ( ) Q = j e c n LR( ) Subject to: j e,2,, ;,2,,, Q (2) Where: Q e j,2,,, 0,, j (3) e, (4) h j d c d r for j,2,, r j for j It s possble to conert ths problem nto an assgnment problem proded the cost of rejectng a demand can T be consdered suffcently hgh The transformaton of Lagrangan relaxaton problem, denoted by LR ( ), can then be wrtten as Q Q T n Z LR ( ) )= f e LR T ll ( (5) ll ) l l Subject to: Where: Q l Q l e, l,2, Q (6) l l, e, l,2, Q (7) l l, 0, l, l,2, Q e l l, f ll (8) c f l j for l f l for l,2,, Q (9)

12 Q 2 : ode { : j + c Q - 2 : ode { : c Q c 2 ode Q{ : : c Q (a) (b) Fgure 4: (a) Structure of the Lagrangan relaxaton problem (b) Transformaton of the Lagrangan relaxaton problem to an assgnment problem Here, s a ery large number n comparson to the alues of c Fgure 4 prodes a pctoral representaton of transformng the Lagrangan relaxaton problem nto an assgnment problem as descrbed aboe In ths Q Q Fgure, represents a matrx n R wth all the entres equal to The procedure used to sole the assgnment problem s based on transformaton of the assgnment problem to a n-cost Flow problem [3] Ths n turn can be soled, through the well known algorthm by Ford and Fulkerson [4], whch performs shortest path computatons on the network The complexty of the oerall 4 algorthm s n the order of 3 ultpler adjustment and termnaton A proper heurstc procedure for updatng Lagrangan multplers can help to reduce the computatonal tme Let us defne g as the sub-gradent for the relaxed constrants ealuated at the current soluton by g j e n The followng rules can be used to change multpler alues: If g 0, the multpler wll be reduced If g 0, the multpler wll not be changed If g 0, the multpler wll be ncreased Based on experence t was found that ncremental changes n of the order of 0% at each step would prode good conergence Stoppng crteron s based on the complementary slackness condton, that s, g 0 (2) In our mplementaton, the algorthm was termnated when the absolute alue of ths product was less than a predefned small poste number and g 0 ( s non-negate for all ) ote that g 0 represents an nfeasble soluton rrespecte of the sze of g and, therefore, cannot be an acceptable condton for (20)

13 termnaton Another crteron for termnaton was that the total number of teratons be less than a prescrbed upper alue (500 n ths case), although, practcally, ths condton was neer encountered n our smulatons The procedure for multpler adjustment s presented below: 32 Procedure for multpler adjustment: Step : Gen (ncremental factor for adjustment) and S (set of locaton ndexes for whch the complementary slackness or feasblty condtons are not satsfed), ealuate g, S from Equaton (20) Step 2: If g 0 then decrease by percent That s, If g 0 then update accordng to the followng: f 0 n c f 0, j The algorthm for solng the orgnal problem s presented below: Step : Gen (small poste number), and U (upper bound on the number of teratons), set I 0, 0, S Step 2: Ealuate c from Equaton (5); set 00 ax c Step 3: Ealuate, j, T f from Equaton (9) and sole the assgnment problem LR ( ) Update I I Step 4: If I U (maxmum number of teratons), go to step 7 Step 5: If g and g 0 (the complementary slackness condton s almost satsfed, hence, the current soluton s near optmal), go to step 7 Step 6: Set S : g or g 0, update accordng to procedure (a) aboe Go to step 2 Step 7: Stop 4 umercal Results Ths algorthm was used to sole a seres of about 6000 randomly generated problems (wth 6000 ) The aerage runnng tme for each problem was found to be less than one CPU second The problems were selected to exemplfy possble growth scenaros n terms of the market uptake of broadband Internet serces The am was to demonstrate the mpact of usng aboe optmzaton methods on the ablty of the Internet Serce Proder to cope wth growth n both customer base and demand generated by exstng customers To obtan the requred capacty to be deployed by the telecommuncaton carrer, we hae deeloped a network plannng tool that s comprsed of three basc modules: () demand generaton module, () optmzaton module, and () network dmensonng module Each of these s now brefly explaned The demand generaton module was deeloped n an Excel spreadsheet The am was to be able to prode the network traffc requrements of customers accordng to a arety of dfferent growth scenaros In each scenaro, the market penetraton of broadband Internet serces (that s, percentage of households subscrbed to the serce) s modelled oer an eght-year perod based on the characterstcs of the scenaro In addton, the usage pattern of each subscrber (number of hours per week usng the serce, the amount of capacty requred durng the acte perods dependng on the type of serces used) s also modelled oer the same perod Consequently, growth n demand n each scenaro s attrbuted to both ncreased usage of Internet by exstng subscrbers, and also by the take up of these by new customers as the prealence and cost adantages of these serces change the nature of work, entertanment and lfestyle We hae deeloped a range of scenaros from optmstc to pessmstc and tested the algorthm based on these The capacty cures n Fgure 5 are obtaned based on a moderately optmstc scenaro

14 The optmzaton module was wrtten n C and ncorporated the algorthms descrbed n ths paper for both the Access Concentrator and the Optcal Rng The demand alues produced by the demand generaton module form the nput to ths module The Access Concentrator wll attempt to aggregate as much of ths demand as possble onto ts output channels (assumed to be of fxed capacty) The optcal rng optmzer wll attempt to carry as many of these channels as possble on the aalable capacty of the rng Rng Sze n multples of capacty unt o Concentraton Access Concentrator only 5 Access Concentrator Plus rng channel allocaton Years Fgure 5: The requred rng capacty n response to a typcal growth scenaro The network dmensonng module was deeloped n an Excel spreadsheet and ts am s to fnd the most sutable and cost effecte network capacty to carry the optmsed demand produced by the preous module ote that the rng capacty s lmted to dscrete alues as the underlyng optcal technology can only support certan multples of optcal waelengths on each fbre Also, when growng a rng to hgher capacty, there are two optons aalable The frst opton s to ncrease the capacty of the whole rng to the next leel (for example upgradng a rng that can carry 6 channels at 25 Gga bts per second (Gbps) each to one that can carry 64) The second opton s to stack another rng on top of the exstng rng f optcal fbre s aalable wthn the cable sheet The dmensonng module, therefore, wll fnd the most cost effecte opton to prode suffcent capacty for the requred number of channels As the demand grows, more capacty wll be requred and f needed the rng has to be upgraded or stacked wth another rng That s why the capacty upgrades n Fgure 5 are n steps Fgure 5 shows an example result where the capacty requrement s compared for three possble stuatons: - o Concentraton where nether concentraton algorthm s employed; 2- Access Concentrator only where the channel capacty on the rng s statc; and 3- Access Concentrator plus rng channel allocaton where both leels of optmzatons are operatng As edent n the Fgure, by ntroducng the two leels of traffc concentraton, the requred capacty s sgnfcantly reduced n comparson wth a brute force capacty assgnment to customers 5 Conclusons The category of network flow problems dentfed n ths paper has many ndustral applcatons, especally n telecommuncatons ndustry where the cost sangs of optmal archtecture could be ery substantal In ths paper, analytcal models and effcent algorthms for the aggregaton of demand usng an Access Concentrator hae been deeloped The paper also presents an analytcal model for allocaton of channel capacty to Access Concentrator The deeloped algorthms prode near optmal solutons n pseudo-polynomal tme

15 These algorthms could be useful for real-tme operaton and management of certan types of telecommuncaton networks, n partcular, for connecton of resdental customers to Internet 6 References [] Balakrshnan, A, et al, "A decomposton algorthm for local access telecommuncatons network expanson plannng", Operatons Research, Vol 43 o, January-February 995 [2] Tang, D T, et al, "Optmzaton of Teleprocessng etworks wth Concentrators and ultconnected Termnals", IEEE Transactons on Computers, Vol C-27, o 7, July 978 [3] Carpento, G, et al, "Algorthms and Codes for the Assgnment Problem", Annals of Operatons Research 3(988) [4] Ford Jr, LR and Fulkerson, DR, "Flows n etworks", Prnceton Unersty Press, Prnceton 962 [5] emhauser, GL, and Wolsey, LA, "Integer and Combnatoral Optmzaton", Wley, 988 [6] Oueys, I, "A Lagrangan Relaxaton Technque for ult-connected Termnals and Concentrator Locaton Problem", Proceedngs of Australan Telecommuncaton etworks and Applcatons Conference, 5-7 December 994 Bographes Farzad Safae graduated from the Unersty of Western Australa wth the degree of Bachelor of Engneerng and obtaned hs PhD n Telecommuncatons Engneerng from onash Unersty, elbourne, Australa He has more than 5 years of experence n conductng and managng adanced research n the feld of data communcatons and networks Currently, he s the Professor of Telecommuncatons Engneerng and Drector of Centre for Emergng etworks and Applcatons at the Unersty of Wollongong He s also the Program anager of the Cooperate Research Centre for Smart Internet Technology Before jonng the Unersty of Wollongong, he was the anager of Internetworkng Archtecture and Serces Secton n Telstra Research Laboratores (TRL) Hs prmary research nterest s to desgn large-scale telecommuncaton networks that can adapt autonomously to dynamc characterstcs of applcatons, cost, customer demand, or any other crtcal nfluence from outsde Iradj Oueys receed the BSc degree n engneerng from ddle East Techncal Unersty, Ankara, Turkey, n 987, the Sc degree n operatons research from Blkent Unersty, Ankara, n 990, and the PhD degree on telecommuncaton network desgn from the Unersty of elbourne, elbourne, Australa, n 996 Dr Oueys has been workng n the telecommuncaton ndustry for the last 2 years He s also an honorary fellow of the Electrcal and Electronc Engneerng Department, the Unersty of elbourne Hs areas of nterest are network relablty and surablty, optmal locaton theory, polyhedral theory, combnatoral optmzaton, PLS traffc engneerng, PO access

16 networks, optmzaton and traffc management, dynamc alternate routng, and cost modelng n telecommuncaton networks