A Simple Tool

7/30/2019 A Simple Tool

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82 Bell Labs Technical Journal xJa n ua ryJu ne 2001 Co pyrig h t 2001. Lu ce nt Te ch no lo g ie s In c. All rig h ts re se rve d.

Introduction

Optical components and systems are ready to play

a key role in next-generation backbone an d enterprise

netw orks. Routers w ith optical interfaces, dense w ave-

length division multiplexing (DWDM) systems, and

optical cross connects of unprecedented capacities are

on the verge of large-scale commercial deployment.

This ma ssive buildu p of optical equipmen t calls for

careful plan ning and provisioning of th e basic units of

transmissionthe optical lightpaths.

This paper presents techn iqu es for efficient a nd

reliable design of optical netw orks through fa ilure-

resilient lightpath provisioning. We consider a range of

routing options, their associated tradeoffs for optimiza-

tion of wavelengths, and lightpath protection against

optical fiber and interface failures ranging from decen-

tralized dedicated protection to shared path-based

mesh restora tion. This evalua tion calls for novel net-

w ork design softwa re that n ot only employs the rele-

van t optimization solvers but also has th e flexibility to

solve for a variety of routing and protection mecha-

nisms. The rela tive m erits of distinct core a rchitectures

and provisioning schemes can therefore be measured

for any specific netw ork. Furthermore, new routing

protocols can be quickly evaluated in terms of their

comparative efficiency and restoration properties.

SPIDER is a softw are tool built at Bell Labs to h elp

evaluate the v arious options for design an d provision-

ing of lightpa ths in core optical netw orks. In this

paper, we review both SPIDER and t he problems it

solves in som e deta il.

In th e next section, w e discuss basic optical design

and routing problems from an algorithmic point of

view and describe the routing an d protection/restora-

tion a lgorithms currently incorporated into SPIDER. In

the section follow ing it, w e describe the softw are

arch itecture of SPIDER, including its brow ser-based

user interface, Java*-based visualization, and spread-

sheet input/output capabilities. In a subsequ ent sec-

SPIDER: A Simple and Flexible Tool forDesign and Provisioning of ProtectedLightpaths in Optical NetworksR. Drew Davis, Krishn an Kumaran , Gang Liu , and Iraj Saniee

Opt ical devices are poised to fo rm th e core of th e next generation o f b ackbon e and

ent erprise netw ork s. Opt ical rout ers, dense wavelengt h division mult iplexing

(DWDM ) syst ems, and cross connects of unp recedent ed capacit ies are on t he verge

of large-scale comm ercial dep loyment . This massive bu ildup of opt ical gear necessi-

t ates carefu l plann ing and p rovisionin g of th e basic uni ts of tr ansmissionthe ligh t-

pat hs. This paper p resent s a range of techniq ues fo r eff icient and reliable o pt ical

net w ork d esign, covering decentr alized dedicated pr ot ect ion t o shared pat h-based

mesh resto rati on. These algo rit hm s have been incorpo rat ed in to SPIDER, an ext ensi-

ble sof tw are to ol w ith a brow ser-based user int erface, Java*-based visualizatio n, and

spreadsheet inpu t/ou tp ut capabil it ies. We d escribe SPIDER and repor t on recent core

netw orking appl ications using t his to ol, w hich also i l lustrat e th e key tradeoff s in

opt ical netw ork d esigns involving a variety o f grades of prot ection and t he balance

betw een eff icient u se of w avelength s and resto ration t ime.


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Bell Labs Technical Journal xJanua ryJune 2001 83

The follow ing sections describe three possible net-

w ork architectures applicable to optical netw orks w ith

their associated routing a nd protection m echanisms.

1 + 1 Dedicated Protection

In th is routing scheme, node pairs that have

demand are connected with a sufficient number of

wavelengths on an active path and an identical num-

ber of protection w avelengths on a diversely routed

protection path . Note that all w avelengths betw een

tw o nodes need not follow the same path. The protec-

tion wavelengths are dedicatedfor each node pair for

each w avelength, but th e fibers carrying active or pro-

tection wavelengths for different node pairs may be

shared, as show n in Figure 1. The schem e for recov-

ery from link failure generally entails:

Propagation delay an d recognition of failure by

each affected node pair (~ 10 ms) and

Switching to the dedicated protection w ave-

length(s) (~20 to 40 ms).

Propagation delays ma y be eliminated by duplicate

transmission on the protection paths and selection of

the best signal at each destination node (this is called

1 + 1 protection). Otherwise (that is, when no transmis-

tion, w e give examples of a SPIDER core optical design

for a U.S.-w ide netw ork. We complement th is w ith

the output of various SPIDER runs to measure the

netw ork and cost efficiency of various design schemes

versus their restoration times. In the final section, w e

conclude w ith the implicat ions of these routing

schemes for nea r-real-time and proposed new light-path provisioning protocols such as extended open

shortest path first (E-OSPF) an d optical netw ork nav i-

gato r (ONN).

Bandwidth Efficiency Versus Restoration Time

In th is section, w e describe techn iques for routing

of lightpa ths in core all-optical netw orks in w hich

100% (or any desired degree of) recovery is required

for a singlenetw ork link or node failure. (Doshi et al.1

provide an overview of different restoration schemes

an d proposals for new restoration protocols.) Optima ldesign an d routing for such netw orks, taking the cost

of failure recovery into account, is a difficult compu-

tat iona l problem (see , for exam ple , the w ork of

Rajagopalan et al.2). The effectiveness of a proposed

routing mechanism is judged not only by the result-

ing efficiency in th e use of ava ilable w avelengths but

also by its complexity of provisioning and speed of

restoration in operation al netw orks. Each of our

schemes described below best fits a given grade o f

protection, such as platinum (below 50 ms), gold

(50 to 100 ms), and silver (~ 1 to 10 s) restorat ion,and can be implemented by the majority of emerging

optical n etw orking protocols, such a s multiprotocol

lambda sw itching (MPS).

For prior work on routing and design of networks

using synchronous optical netw ork (SONET) or logical

rings, see Ritchie3 an d Tillerot et a l.;4 for DWDM and

restoration, see Lee and Li;5 for asynchronous transfer

mod e (ATM), see Irascho and Grover;6 and for mesh

netw ork design, restoration optimization, a nd w ave-

length assignment, see Mukherjee et al.,7 Saniee,8 and

Bouillet and Bala.9 Mukherjee et al.7 and Stern and

Bala10 provide general background on optical net-

w orks. Cosares et al.,11 Doshi and Harshavardhana,12

and Doshi, Dravida, and Harshavardhana13 describe

recent w ork on softwa re tools for broadband netw ork

design.

Panel 1. Abbreviations, Acronyms, and Terms

APSautomatic protection switching

CGIcommon gateway interface

CGI.pmCGI Perl module

CPANComp rehe nsive Perl Archive Net w ork

DWDMdense w a veleng th d ivision m ulti-

plexingE-OSPFexten de d o pen shortest p at h f irst

I/Oinp ut /out pu t

IDidentification

LPlinea r prog ram ming

MPlSmultiprotocol lambda switching

NSFNational Science Foundation

OC-192opt ica l carrier dig ita l signa l rat e o f

9.953 Gb /s in a SONETsyste m

ONNoptical netw ork navigat or

OTUopt ica l termina ting unit

OXCopt ical cross conn ect

PCpersonal computer

PerlPractical Extraction Report La ng ua g e

SDHsynchrono us dig ita l hierarchy

SONETsynchro no us op tica l ne tw ork


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84 Bell Labs Technical Journal xJanua ryJune 2001

sion occurs on the back-up path until failure), for each

w avelength, the equ ipment u sed at end nodes per-

forms an operation identical to the automatic protec-

tion sw itching (APS) ava ilable in th e earlier SONET

and synchronous digital hierarchy (SDH) hardw are

technologies (this is called 1 : 1 protection). The speed of

recovery is thu s a few tens of m illiseconds. The solu-tion method ology for both 1 + 1 and 1 : 1 protection

consists of finding a disjoint pair of active and protec-

tion paths for each demand, aggregating these to

obtain the tota l number of wavelengths on each fiber,

and then determining the cost of the overall design.

Phase 1 can be carried out in a t least tw o w ays. For

example, each demand can be routed on its shortest

path (by counting hops or distances, or by using an

adaptive cost metric that keeps track of the fill of a

fiber), and dedicated protection w avelengths can be

routed over the disjoint residual graph. Alternatively,

all node pairs w ith th eir disjoint routes can be routed

simultan eously using a cost-optimization a pproach.

We give a heuristic routing algorithm for th e 1 + 1

or 1 : 1 protection scheme. The key idea of th is algo-

rithm is to define an iterative sha dow cost for each

netw ork resource, then route each deman d along its

least-cost feasible path . The cost m odel is as follow s:

1. Cost ofl-channel. Each l-channel requires a channel

in a fiber. To optim ize fiber usage, t he u se of

l-channels in some existing fibers is encouraged.

This is ach ieved w ith a l-channel cost of the form

,

w here is the ma rginal cost of unit l-channel,

is the length of the link, is the num ber of

l-channels in use on link (i,j), Wis the number

of l-channels that can be carried by a f iber,

is the cost per unit length of fiber, and

depends on whether a wavelength converter

existed. In the case of wavelength continuity

(no converter at any node) , when the wave-

length l is currently not available on link ( i,j),

; otherwise, and tis set em-

pirically. The shape of as a function of is

show n in Figure 2.

2. Cost of port. Each end of a l-channel requires a

port on an optical cross connect (OXC) installed

at the corresponding node. Each OXC may con-

tain a finite number, X, of ports. Similar to the

l-channel cost, port cost can be given in the form

, w h e r e i s

the marginal cost of a port at node i, is the

number of ports in use at node i, Xis the total

num ber of ports in an OXC, is the cost per

OXC, an d tis selected em pirically.

3. Cost of ampl if ier. Assume that an ampli f ier is

needed for each given length, La, o f fiber. The

am plifier cost can be integrated into the l-channel

cost if w e redefine the unit distance cost ascf

pOXC

ui

xixi5pOXC

Xa X2 uimod 1X21ui mod 1X21 12t 1 1b

wijyij

aij1l25 1aij1l25 0

aij1l2pf

wijlij

yij

yij1wij,l25pflijW

a W2 aij1l2wijmod 1W21aij1l2wijmod 1W21 12t 1 1b

6

5

1

3

2

8

7

4

Figu re 1.

Diversely routed p rotect ion (dot ted l ine) w avelength s for

deman ds betw een node pairs 1&2, 2&4, and 3&8 using

act ive (sol id l ine) w avelength s (bot h t ypes can share

f iberfor examp le, on l inks 1-3 and 2-3).


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Bell LabsTechnical Journal x Janua ryJune 2001 85

(Cost o f regenera tor s i s added s imi la r ly inSPIDER.)

4. Cost of transmi tters. Since the number of transmit-

ters needed depends only on the total number of

demands rather than the routing algorithms, we

ignore the cost of transmitters in the routing pro-

cedure. How ever, it w ill be counted in the total

netw ork cost computation.

Using the cost model given abov e, w e can give the

algorithm for dedicated protection as follows:

1. Generate candidate ring l ist. For each demand in the

demand list, generate kshortest cycles (rings)p a ss in g t h r o u g h t h e t w o e n d n o d e s o f t h e

d e m a n d . A m o d i f i e d ve r s io n o f e i t h e r t h e

A*Prune algorithm 14 or th e Suu rballe-Tarjan

algorithm15 can be used to generate such krings.

All the generated rings are listed by their increas-

ing lengths.

2. Li st candidate path pairs for each demand. For each

ring in the ring list, generate tw o path pairs along

the ring if both end nodes of the demand are on

the ring. At most, 2Rsuch path pairs for each

demand can be generated, where Ris the totalnum ber of rings in th e ring list.

3. Compute/update the marginal cost for each candidate

path pair . The m arginal cost of a ca ndida te path

pair pi s the sum o f th e shadow cost s o f a l l

resources required by pand can be defined as

.

4. Order the demand li st. The d ema nd list can be in

random order.

5. Perform one-round routi ng. Do the follow ing steps

for each demand in the demand list:

a. Remove the route assigned to the demand if it

has any, and free all the resources acquired by

the demand.

b. Update the marginal cost for all candidate path

pairs affected by th e removed rou tes.

c. Route the demand along its least-cost path

pair. This includes find ing th e least-cost pa thpair and reserving all necessary resources (such

as w avelengths and ports) along the path pair.

d. Update the marginal cost for all candidate path

pairs affected by the previous step.

6. Fine-tune by loop routi ng. Repeat the procedure of

one-round routing until a converged routing is

reached. A routing is considered to be converged

if the total netw ork cost given by th e current-

round routing is the same as that given by the

previous-round routing.

Shared Protection Using Logical Rings

In this architecture, node pairs are grouped into

logical DWDM rings, each of w hich carries no m ore

than the predefined num ber of w avelengths per fiber

for active as w ell as protection w avelengths. Active

paths are defined for all node pairs on the same logical

C 1p25 a1i,j2P

p

1yij1xi1xj21 costof amplifier /La.cf 5 unitlength cost of fiber

yij(wij, ):

Weight function

t= 2.2

t= 0

pfli j:Cost o f new f iber

pfli j/W:

Cos t o f add ing a

new -channel

0 1 2 3 W (o ne f ib er) 2W Number o f

-channels used

Wi j

Figu re 2.

Funct ion ofl-channel cost yijbased on ut i l i zat ion wijand i terat ion parameter t .


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ring, and protection w avelengths are reserved in the

complementary routes on the ring for each node pair,

as shown in Figure 3. The nu mber of protection

w avelengths for each deman d is thus the same a s the

num ber of active wa velengths used for carrying the

deman ds allocated to each ring. However, non overlap-

ping demands on the same ring can shareprotectionwavelengths. For example, demands between nodes

1-3 and 3-2 can share protection w avelengths on th e

ring 1-3-2-5-6-1. The rings 1-4-7-2-5-6-1 an d 1-3-2-

5-6-1 can share fibers on links 2-5, 5-6, and 6-1.

Although in principle it is possible to share protection

wavelengths acrossrings using OXCs, w e do not use

such sharing due to the complexity of recovery w hen

failures occur.

The schem e for recovery fro m fa ilure is on ly

somewh at m ore complex than dedicated protection,

described above. Similar to dedicated protection, onlythe end n odes of each w avelength affected by the fa il-

ure need to take care of the failure (~ 10 ms). Once a

failure condition is recognized, the sw itch over to pro-

tection w avelength s is made. In ou r logical ring design

solution, each demand is mapped to a single ring.

Therefore, it w ill not be necessary to coordina te mu lti-

ple rings for recovery. The single ring au torecovery

takes ~ 50 ms, allow ing for ~ 40-ms cross-conn ect

remapping in the intermedia te nodes. OXCs are

needed for autorecovery on each logical ring and for

sharing of fibers. Withou t fiber sharing, w avelength-

selective cross connects w ould be adeq ua te. Using the

same shadow cost as in th e previous section, th e rout-

ing algorithm for logical rings is given a s follows:

1. Generate candidate ring l ist. Use the same procedure

as that used for the dedicated protection algo-

rithm given in the 1 + 1 Dedicated Protection

section.

2. Li st candidate paths for each demand. For each ring

in the ring list, generate tw o paths along th e ring

if both end nodes of the demand are on the ring.

At most, 2Rsuch paths for each demand can be

generated, w here Ris the total nu mber of rings in

the ring list.

3. Compute/update the marginal cost for each candidate

path. The m arginal cost of a ca ndidate pa th

retrieved from ring ris defined a s

.

Here, is 1 if is the first path to invoke a

new protection chan nel; otherw ise, it is 0.

4. Order the demand li st. The deman d list is preferred

in the decreasing order of the length of its short-

est rings so tha t the dema nd w hich invokes a

larger ring is routed first.

5. Perform one-round routi ng. Do the follow ing steps

for each demand in the demand list:

a . Let dbe the demand to be routed.

b. If dhas a l ready been ass igned a rou te p,

remove route pand free all the resources

acquired by p. Assume pis originally protected

by the ring protection channel r. Remove rif

there are no oth er w orking chan nels to be pro-

tected by r.

c. Update the marginal cost for a ll candidate

paths affected by the remov ed routes.

d. Route the demand a long its least-cost r ing

path . This includes findin g th e least-cost ring

path and claiming a ll necessary resources along

the ring path.

e. Update the marginal cost for all candidate ring

paths a ffected by the rou ting procedure (step 3).

6. Fine-tune by loop routing. Use the same procedure

as that used for the dedicated protection algo-

prd 1r,p21 d 1r,p2a1i,j2Pr1yij1xi1xj2

C

1r,p25

a1i,j2Ppr1yij1xi

1xj2

pr

6

5

1

3

2

8

7

4

Figu re 3.

Shared-protect ion w avelength s for demands betw een

1&3 and 3&2 o n ring 1-3-2-5-6-1, and shared f ibers on

l inks 2-5, 5-6, and 6-1 fo r th e rings 1-4-7-2-5-6-1 and

1-3-2-5-6-1.


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Bell Labs Technical Journal xJanua ryJune 2001 87

rithm given in the 1 + 1 Dedicated Protection

section.

Both dedicated protection and logical ring protec-

tion algorithms can a lso ha ve va riant versions, such a s

shortest-path routing or wavelength-continuity rout-

ing. The sho rtest-path routing version routes a ll

dema nds along their shortest paths. The w avelength-

continuity case can be handled by selecting the appro-

priate va lue of in the cost mod el.

1 :NProtection on Single Demand

A computationally simple method for the shared-

protection m esh netw ork design can be obtained by

considering shared-protection routing for single point-

to-point demands. We first address only the sharing

among multiple candidate paths between the source

and the destination for the single demand under con-

sideration, as show n in Figure 4.

How ever, these single-dema nd solutions can sub-sequently be combined to account for sharing across

dema nds. The procedure can thus be used in designing

a reliable netw ork from the start ( greenfield sce-

nario), and it provides a fast an d a pproximate solution

to a more comprehensive mesh design to be discussed

in the next subsection. We refer to this algorithm as

the 1 : Nprotection algorithm in our numerical results

later.

Consider the restoration-adapted version of the

standard mu lticommodity flow problem:

(1)

w hich seeks to minimize the tota l w avelength distance

traversed in th e netw ork w hile protecting against sin-

gle link/nod e failures. As explained earlier, w e focus

on a single source-dest ina t ion pair s-t, wh ich i s

assumed multiply connected by Nnode-disjoint candi-

date paths, each path iw ith a given cost ciof carrying

unit flow . The costs may be ordered as c1 c2 .... cN.

For single-path failure reliability, it is easy to see that

that is, the set of candidate paths may be

pruned in this ma nner w ithout loss of optimality. We

seek to route, at minimum cost, a total demand D

betw een san d talong the paths so that service is not

interrupted by single-path failure. This problem h as

the follow ing simple linear programming (LP) formu-

lation directly derived from (1) above:

. (2)

Letting , the above LP formulation

is written a s a classical knapsack problemfor fixed D:

(3)

It can be show n th at (3) has the following simple

solution: Let .

Further, a simple search over D:

produces the globally opt imal xk independent of

w hether or n ot they are restricted to ta ke integer val-

ues. The en d result of this procedure is that the opti-

ma l set of chosen path s for large dema nds w ill satisfy

. This relation ha s the int eresting

interpretation that the optimal solution, independent

of D(for large D), chooses to add new paths to route

the demand only until the incremental additional cost

of unit restoration capacity continues to decrease,

1

K2 1

aK

k51

ck , cK11

D / 1N2 12# D9 # DxK5 D 2 1K2 22D9 .xk 5 D94 k , K ;xk 5 04 k . K ;

K5


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beyond which it load balances among the previously

chosen path s. This implies (except for int egrality o f

flow s) equ al allocation of flow s to the set of chosen

path s. It is also possible to show tha t complete load

b a l a n c in g o ve r a l l p a t h s , t h a t i s , t h e ch o ice

is never more than a factor of 2 in

total cost from the optimal solution. Finally, all of the

above conclusions can be generalized for the cases of

reliability against multiple failures, individual capacity

limits for each path, variable degrees of protection

ranging from full backup of the affected demand to a

smaller percentage, and differing fixed installation

costs for each path.

Motivated by the above-described tractability of

the single-dema nd rou ting problem, w e propose the

follow ing heuristic solution to the more general shared

mesh netw ork design that accounts for sharing across

dema nds. The solution is as follow s:

1. Solve the rout ing problem for each demand

sequentially using a precomputed set of path s.

2. Choose the low est-cost K 1 paths as primary

paths for each deman d.

3. Cumu late the primary f lows on each l ink to

determine its prima ry capacity.

4. To compute to t a l l ink capac i t ies , f a i l one

link/node a t a time an d determine the ma ximum

net flow on surviving links w hen a ffected flow s

are routed on their respective Kth paths.

This algorithm provides a limited form of sha ring

between demands, as well as between routes for a

given d emand , an d produces a suboptimal approxima-

t io n t o t h e f u l l y sh a r e d m e sh n e t w o r k d e sig n .

How ever, it provides a simple solution to the routing

and restoration problem that is easy to compute,

update with new demands, and manage w hen failures

occur. Note that on ly the dema nds affected by a partic-

ular failed link/node need to be rerouted, a nd, fu rther,

the rerouting for the affected set dema nds is alw ay s

the same, thus making fault isolation unnecessary.

When the dem ands a re small and grooming/packing

efficiency is important, it is possible to adapt the

heuristic to pack more efficiently by altering the choiceof prima ry paths w ithout losing the desirable features

of the result.

Optimal Shared-Protection/Mesh Design Using Mixed-Integer Linear Programming

This architecture genera lizes the sha red-protection

ring schem e described above w ithou t explicit parti-

tioning into rings. As before, active and restoration

paths are constructed for all node pairs, but the

restoration capacities, computed as the maximum

number of wavelengths required on each link when a

single failure occurs, are fu lly sha red. This scheme

optimizes the redundant (or spare) capacity require-

ments but has increased restoration complexity com-

pared to the ring method. Figure 5show s a simple

exam ple in w hich protection path 2-3-1-8 for demand

2-8 on path 2-8, protection path 2-3-1-4 for demand

2-4 on path 2-7-4, and the active path 1-3-2 for

deman d 1-2 on path 1-3-2 all can share w avelengths

on edges 2-3 and 3-1.

This schem e requires careful preplannin g for an

efficient implementation. Each failure invokes an opti-

mally recomputed reconfiguration map at each node,

w ith possible w avelength conversion to avoid collision

on the same set of links during path restoration events.

The m aps can be precomputed u sing o ptimization. The

objective is to minimize the total num ber of wa ve-

lengths needed . The resulting ma ps are stored in each

xk 5


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OXC. Pa th restoration is not conditional on isolation o f

fault: by using multiple alternative disjointprotection

paths for each active path, the end nodes initiate the

recovery procedure once the signal loss is registered,

and the disjointness of restoration routes ensures their

ava ilability w hen th e single failure condition disables

the normal route(s). Once the end nodes encounter afailure condition on a path (~ 10 ms), they comm uni-

cate the restoration rou tes of the w avelength s to be

restored to each intermediate OXC on alternative

paths and the maps to be uploaded by each OXC

(40 to 80 ms). These maps change, often only incre-

mentally, w hen new demands are added. In the case

of topology changes, all active and back-up routes may

require updating, but topology changes surely affect

other a rchitectures as w ell. To reuse and extend th e

notation introduced in the previous sections, let

N= set of all netw ork nodesE= set of all network edges

K= set of all node pairs

P= set of all paths for all node pairs

D= set of all node-pair demands

= demand for node pair k

= f low (in units o f l) assigned to path p

= set of all paths for node pair k, assumed to

be (node) edge disjoint

= set of all paths that include edge e

= capac it y ( in number o f w ave leng ths) on

edge e= distance of edge e

= f low (in units o f l) assigned to path pwhen

edge fis in failure mode.

To e n su r e t h a t b id i r e c t io n a l d e m a n d s a r e

rout ed the same w ay, w e restrict to .

Furthermore, to reduce problem dimensionality, w e

include a path in Ponly if its end nodes have demand .

To ensure th at restora tion from failures does not

require fault isolation, w e assume th at path s in each

are disjoint for each commodity k. Therefore, w hen an

end node pair recognize a fault in (one of) their pri-

mary path(s), the node pair initiate restoration over

the remaining path s, w hich, due to their being disjoint

from the failed path, must be operational in cases of

single (link) failures.

To see how the m esh netw ork should be designed

and its demand routed using the above notation, con-

sider the follow ing problem:5

These conditions ensure th at:

1. Demand for each node pair kis met and

2. Link capacities are not exceeded.

Thus, an y allocation of flow to path pthat meets

conditions 1 an d 2 is considered fea sible. To a void

solutions with m eandering pathsthose that either

are unusually long or visit the same node more than

oncethe set of paths Pneeds to be carefully gener-

ated. Examples include paths that do not exceed pre-

specified hop counts or distance limits between their

end nodes. Further, more careful path generationreduces the problem complexity, as w ill be show n in

the follow ing discussion. In general, K-disjoint paths

that meet path qualifications are generated for each

node pair w ith non zero dema nd for a sufficiently

large K. The mesh network routing problemcan be for-

mulated according to a variety of criteria using the

foregoing notation. For example, it may be important

to route as much of the demand as possible on the

shortest possible routes. In this case, the natural crite-

rion w ould be the sum of w avelengths times the dis-

tance each w avelength traverses. Alternatively, it ma y

be desired to spread the load as evenly as possible so

that all the edges in th e netw ork carry m ore or less the

same nu mber of w avelengths. For the latter criterion,

the following formulation results:

P1:(even_load = L)

Constraint set 1 ensures that deman ds (in n umber

of wavelengths) are met for each node pair, and con-

straint set 2 gua ran tees tha t link/DWDM capacities are

132 apPQe

xp # L4ePE

122

apPQexp # Ce4ePE

112 apPPk

xp $ dk4kPK

Subject to :

Minimize L

xp

122 apPQe

xp # Ce , each ePE

112 apPPk

xp $ dk , each kPK

P0: Find xp 4pPP

Pk

i,j1i,j2PK

yfp

le

Ce

Qe

Pk

xp

dk


9/16

90 Bell LabsTechnical Journal x Janua ryJune 2001

not exceeded. Constraint set 3 evens out the load on

the n etw ork. The same routing design problem w ith

the minimum sum of w avelength distances as the

objective function is as follow s:

Constraint set 3 for P2 counts the number of

w avelengths used on each edge w ithin the objective

function. For the m esh netw ork restoration problem,

the same set of objective functions as P1 and P2 apply.

This time, ho w ever, additiona l constraints needed toensure 100% protection against failure are also pro-

vided. Let denote the overflow assignment of w ave-

lengths to path pwhen edge fis in fail condition.

Then, the assignment of normal routes and restora -

t ion rou tes fo r the min imized sum o f w ave-

length*distance objective (as in P2) is given by the

solution of

We refer to this formulation as the restoration

problem. Note that in this formulation, a large number

of reconfigurations may be necessary for each failure

condition, since the overflow variables are only con-

strained to meet demand and not exceed edge capaci-

ties. To en force reconfiguration only for routes affected

by the failure condition, a slightly different set of con-

straints is needed. This formulation is given below :

Note that in formulation P4 of the restoration

problem, w e have a lso allow ed a m ore general recov-ery percenta ge for each node pair kthan recovery of

all paths disrupted by each link failure, = 1 or 100%

recovery, which is what was done in P3. However, this

extension a dds no complexity to the problem a nd sub-

stan tially simplifies the execution of restora tion . The

above formulation can be further enriched to allow for

situations in w hich fau lt localization is difficult or too

time consuming to achieve (this is done in SPIDER).

How ever, these models give a sufficient description to

illustrate the necessary trad eoffs between restoration

efficiency and time, as described in the Examples of

Network Design and Numerical Results section.

Soft w are Architecture f or SPIDER

As we have shown, there are a variety of design,

routing, and protection schemes for optical core net-

w orks. It is likely tha t, in the near future, hybrids or

even new schemes w ill be invented and implemented

by Lucent Technologies and ot her ma nu facturers.

Since SPIDER aims to accurately model current and

future routing schemes, protection schemes, and pro-

tocols, its softw are needs to be highly flexible an d

mo du lar. This calls for separatio n of application ,

input/output (I/O), visualization, an d com putation al

engines. To th is end, the SPIDER application w as built

of five parts:

A text-based (comma-separated value) front

rk

rk

152 apPQe2Qf

yfp 1 apPPk2Qf

xp # le 4e 2fPE

142 apPPk2Qf

yfp 1 apPPk2Qf

xp $ dkrk 4fPE,4kPK

132 le # Ce 4fPE122 a

pPQe

xp # le 4ePE

112 apPPk

xp $ dk 4kPKSubjectto :

Minimize aePE

le*le

P4: 1l*distance2

162 le # Ce4fPE152 a

pPQe2Qf

yfp # le4e 2fPE

142 apPPk2Qf

yfp $ dk4fPE,kPK

132 apPQe

xp # le4ePE

122 apPQe

xp # Ce4ePE

112 apPPk

xp $ dk4kPK

Subjectto :Minimize a

ePE

le*le

P3: 1l*distance2

yfp

xp

yfp

132 le # Ce4ePE122 a

pPQe

xp # le4ePE

112 apPPk

xp $ dk4kPK

Subjectto :Minimize a

eP

E

le*le

P2: 1l*distance2


10/16


end for netw ork and da ta I/O,

A graphical (Java) front end for visualization

an d graph ical I/O,

A comm on gatew ay interfa ce (CG I)-scripted

Web interface in Practical Extraction Report

Language (Perl) for client/server architectu re,

Ba ck-end glue in Perl, and

Ba ck-end a lgorithm processing in C w here

heavy-duty optimization processing is imple-

mented.

Evolution

At first , we solved the a lgorithmic problems

using C, and, in some instances, w e used third-party

softwa re such as MINOS16 and CPLEX.17 Follow ing

test runs and verification of designs, w e init iated

implementation of the Java front end to allow for

graphical entry a nd v isualization of the n etw ork. We

implemented the original front end as a standaloneJa va 1 application. We were less than thrilled with the

challenges of implementing a graphical interface on

the Java 1 base and eventually learned that this front

e n d w a s n o t w e l l m a t ch e d t o t h e n e e d s o f t h e

intended users of the application.

What the users wanted was to be able to collect

their netw ork definitions in spreadsheets using the

Microsoft* Excel application and then feed the spread-

sheet data to SPIDER. We also realized that delivering

the application as something to install on a personal

computer (PC) wou ld leave us with con figuration

ma na gement problems. Our preference w as to keep

the application on a central server and provide access

to it via Web brow sers. We ha ve been reasona bly

pleased w ith the result of that decision bu t ha ve found

there are still challenges due to the variety of Web

brow sers in use. We had read elsew here18 of the dan-

gers of an application getting too close to the propri-

etary formats of Excel. To a void th is problem, w e

opted for a particularly simple format that Microsoft

calls comma-separated value (CSV)or, simply, a flat file

forma t. We believe this forma t w ill likely remain

usable w ithout problems for us as Microsoft potentially

ma kes changes to Excel in future releases.

The n ext problem to solve w as how to interact

w ith the user to tran sfer his/her spreadsheet da ta over

to our application on its central server. Since w e did

not have a lot of prior experience implementing Web-

based applications, and this did not look like it should

be a rare aspect of such applications, w e did not w ant

to reinvent the wheel. We looked for standards and

found RFC1867.19 Without too much more searching,

w e located an inexpensive commercial product tha t

implemented that standard in a Java applet.20 The

vendor, Infomentum, made a free evaluation period

for its softw are ava ilable to us.

Unfortun ately, w e encountered problems during

the evaluation . Source code for the product wa s not

ava ilable to us, so we turned to th e prospective sup-

plier for h elp. They w ere responsive to e-mail but

unable to determine the cause of our difficulties. We

suspect the troubles w ere caused by variat ions in Java

implementation from PC to PC. Even when the same

brow ser is used (for example, Microsoft Internet

Explorer), there are still more versions of tha t brow serand the underlying Java implementation than we

w an t to ha ve to consider. The experience leaves us

questioning the viability of the hoped-for market in

applets,20 at least for the case of applets sold as black

boxes w ithout access to the source code.

Fortunately, we found an open source implemen-

tation of RFC1867 in the CGI Perl module (CGI.pm)21

and enough documentation to be able to figure out

how to make it work.22 The CG I.pm implementation

of RFC1867 did not q uite do everything that w as pro-

vided by the Infom entum product, but it wa s goodenough and seemed much more stable in our testing.

Later, w e decided tha t the application n eeded a visual

display of its results and returned to Java for that dis-

play. This time w e used Sun Microsystems Java 2

plug-in w ithin the brow ser. The libraries for graphical

display generation in J ava 2 w ere much more satisfac-

tory, and we are hoping the users will be able to han-

dle the automatic installation of the plug-in to their

brow sers.

Security

There are obvious concerns associated w ith mak-

ing an application available on the Web. Deploying it

on a Web server inside the Lucent firewa ll wo uld

block access from th e w orld at large but w ould still

make our application accessible to more than 100,000

Lucent a ssociates and potential users. Since w e w ere


11/16


unprepared to vouch for everyone w ith computer

access within Lucent, w e needed a wa y to contain the

application. Our standard Web server in Lucent s

Mathematical Sciences Research Center runs on a

computer that allows a user ID of nobody. That

w ould not d o for all of our applications (such as

CPLEX,17 for exam ple, since its license only allow s it to

run o n a Lucent com puter w ith a specific licensed

na me). Therefore, w e needed a Web server tha t could

have access to the third-party softw are. Our solution

w as to set up a new user ID, SPIDER, and an Apache

Web server on a PC running Linux* in our lab. Since

the Web server is strictly for our application, it can run

w ith the SPIDER user ID. We then needed to m ake

sure that the SPIDER user ID is only able to access

software and data we do not need to protect from the

va st Lucent int erna l user comm un ity. This met our

objective of not having to administer user accounts,but w e recognize that the system is possibly more

open than our users might w ant it to be.

Lessons Learned

The o ld ad age, Plan to throw one away , is

applicable here. In fact, w hen learning a n ew language

w ith the complexity of Java, yo u ma y be w ell advised

to plan to throw more than one aw ay. Time spent

searching for standards and available libraries instead

of reinventing the w heel is time w ell spent. Black-

box third-party softwa re is more challenging to live

w ith th an o pen source libraries. We still have our

fingers crossed about how well Java will work out

for us in the fielda ma ze of tw isty virtual machines,

all different.

The project needs to have con trol of its environ-

men t. The Linux base for our front end w as invalua ble

to us. We w ere able to tw eak the Web server configu-

ration and update the Perl libraries w ith new modules

from th e Comprehen sive Per l Archive Netw ork

(CPAN) as we needed them, without having to push

for time from people outside of our project to make

those updates for us. We w ould like to try this new

library is not a request that typically gets high-priority

attention from overburdened system administrators.

The dow nside is tha t it means our project mu st con-

tinue to pay attention to system administration of

Linux into th e future. Keeping a Linux box up to date

w ith security updates is nontrivial w ork.

In retrospect, w e should have set up more than

one instance of our application. With real users, it is

impractical to make and test changes. A simple first

step w ould be to m odify all hard-coded paths.

Examples of Network Design and NumericalResults

An idealized National Science Foundation (NSF)

backbone n etw ork w as assumed to consist of 10 nodes

an d 17 fiber-optic links, as show n in Figure 6. The

variable link thickness is proportional to the number

of w avelengths/fibers through it, as show n w hen th e

cursor is positioned on the Seattle-Chicago link (red).

The topology an d load da ta for a SPIDER study of this

network are show n in Tables Ian d II. Network visu-

alization in SPIDER is show n in Figure 7.

To illustrate SP IDER, this netw ork w as designedunder five different protection plan alternatives,

ranging from no-protection shortest-path routing

(base) to a complete mesh w ith shared protection.

The results a re presented in Table III. This compa ra-

tive study assumed the follow ing costs and associated

parameters:

80 = number of bidirectional w avelengths per

fiber pair

$100K to $1M = cost of OXCs without any

ports/plug-ins

256 = size of OXC (maximum number ofw av elength-pair terminations)

$5K = cost of optical terminating unit (OTU) used

for signal regeneration and wavelength

conversion

$1.5K = cost of general-purpose 10G fiber pair

per km (including am plifiers)

$100K = cost of a pair of DWDM multiplexers

$50K = cost of regenerators per fiber pair

600 km = regeneration distance

Our experiments assumed the presence of OXCs

at each node, which are almost certainly required for

robustness and flexibility in the core of all-optical net-

w orks. Un der this assumption, mesh-restoration-

based shared-protection architectures seem to be the

most cost effective and efficient. From the standpoint

of recovery time, dedicated protection solutions, for


12/16


the immediate future, have an advantage over alter-na tive designs, w ith th e shared-protection ring-based

designs closely behind. M esh restoration, how ever, is

likely to be the architecture of choice in the future

due to its greater flexibility and faster provisioning.

We also observed that the solutions differ substan-

tially in th eir efficiency of use of the w avelengthresource (l-efficiency), w hich is the total nu mber of

w a ve len g t h s ( o r l*km) used to rou te demands

divided by the total nu mber of w avelengths (or l*km)

needed for both routing and 100% protection against

single failures (row 5 in Table III). Thus, w e observe a

Node Node Distance (km) Sparels Node Node Distance (km) Sparels

Sea t t le Chica g o 1,200 0 Da lla s Ka nsa s 300 0

Sea t t le St ockton 800 0 Da lla s D.C. 800 0

Stockto n Chica g o 1,400 0 Da lla s At la nt a 600 0

Stockto n Cheyenne 600 0 Chica g o Ka nsa s 300 0

Stockto n D.C. 2,000 0 Ka nsa s D.C. 600 0

Stockto n Ria lto 300 0 Chica g o Phila delphia 800 0

Ria lto Da lla s 800 0 Phila d elphia D.C. 150 0

Cheyenne Ka nsa s 400 0 D.C. At la nt a 800 0

Table I. Fiber network topology with distances and spare capacity on each link.

Figu re 6.

An ideal ized NSF backbone net w ork designed f or 5 to 20 OC-192 circui ts betw een al l nod e pairs.


13/16


Seattle Stockton Rialto Cheyenne Chicago Kansas Dallas Philadelphia D.C. Atlanta

Sea t t le 20 20 10 10 10 10 20 20 15

Stockto n 20 10 10 10 10 20 20 15

Ria lto 10 10 10 10 20 20 15

Cheyenne 5 5 5 10 10 10

Chica g o 10 10 20 20 20

Ka nsa s 5 10 10 10

Da lla s 10 20 10

Phila d elphia 20 20

D.C. 20

Atlanta

Table II. Projected node-pair demands in units of OC-192 (demand is assumed symmetric; the lower triangular portion isnot shown).

Figu re 7.

Netw ork visual izat ion in SPIDER show ing how each l ight path (blue) is rout ed tog ether w ith i ts prot ect ion (po ssibly

shared) l ight path (green).

reverse relationship between efficiency an d cost ratio

(row 12 in Table III) on th e one ha nd a nd recovery

speed on the oth er, wh ich leads to natu ral differentia-

tion of lightpath services based on the required grade

of protection.

Conclusions

SPIDER is a softw are tool for netw ork design cost

optimization an d comparative routing as w ell as pro-

tection performance evaluation of opaque and trans-

parent optical core netw orks. It currently includes


14/16


novel and very efficient implementations of path-

based restoration algorithms for w avelength routing

an d protection und er single-physical-layer netw ork

failures. The modularized Ja va-based visualization , thebrow ser-based graphical user interface (GUI), and the

library of routing a nd n etw ork design engines in

C/C+ + provide a flexible platform from w hich to eval-

uate and compare different designs and capacity

expansions as w ell as ma ke inform ed decisions for

specific netw orks. The flexible linkage betw een the

routing/design engines and the visualization modules

ma kes it possible to add n ew routing engines easily as

needed. As an example, w e expect to add the specific

instances of algorithms used in Lucent s centralized

(SoftWave) and decentralized (ONN) routing schemes

to SPIDER in the near future.

The exam ples in th e previous section illustrate the

kinds of tradeoffs that exist for routing and protection

in next-generat ion all-optical netw orks. As the degree

of protection sharing increases from purely 1 + 1 dedi-

cated protection, the netw ork efficiency increases and

the o verall netw ork cost decreases, but intelligent

nea r-real-t ime provisioning of lightpat hs w ill be

needed to ta ke advanta ge of this added efficiency. Theincrease in restoration t ime is moderate a nd w ell

w ithin the accepted thresholds in optical netw orking.

Of course, for any specific lightpath and grade of pro-

tection, th e appropriate protection w ill be utilized.

These a re nea r-real-time issues that link SPIDER to

lightpath provisioning systems, such as SoftWave, w ith

significant implication s for emerging a pplications, such

as bandwidth trading.

The m ost recent ad ditions to SP IDER include

tw o modu les for transparent a nd partially transpar-

ent routing w ith use of w avelength -selective cross

connects and an optimization module for ultralong-

reach transport systems. Preliminary studies show

selective transparency to hold much promise for

post-opaque optical design in future generations of

netw orks.

No protection 1 + 1 protection 1 :N protection Shared- Shared-protection ring protection mesh

Eq u ip me n t/co st Nu mb e r Co st ($) Nu m be r Co st ($) Nu m be r Co st ($) Nu m be r Co st ($) Nu m be r Co st ($)o f unit s o f unit s o f unit s o f unit s o f unit s

Bidirectional ls 1,215 N/A 3,081 N/A 3,117 N/A 2,739 N/A 1,967 N/A

Bidirectional l*km 688K N/A 1,837K N/A 1,799K N/A 1,687K N/A 1,270K N/A

l-efficiency 100% ~40% ~40% ~40% ~60%

Opt ica l cross co nnect s 20 2,000K 34 3,400K 34 3,400K 30 3,000K 25 2,500K

B id ir ect io n a l O TU s 3, 640 18, 200K 7, 372 36, 860K 7, 444 37, 220K 6, 688 33, 440K 5, 144 25, 720K

DWDM MUX pa irs 23 2,300K 43 4,300K 45 4,500K 39 3,900K 27 2,700K

Bidirect ional f iber km 14,200 21,300K 26,450 39,675K 27,400 41,100K 24,450 36,675K 16,700 25,050K

Reg enera to rs 10 500K 19 950K 20 1,000K 18 900K 12 600K

To ta l co st s N/A 44,300K N/A 85,185K N/A 87,220K N/A 77,915K N/A 56,570K

Cost ratio 1 1.9 1.9 1.7 1.2

Opera t iona l co mplexit y None Ea sy Mod era t e Mo dera te Complex

Rea l-t ime provisioning Simple Impra ct ica l Ea sy Ea sy Ea sy

Resto ra tion t ime N/A ~ 10 to 100 ms ~ 50 to 100 ms ~ 50 to 100 ms ~ 50 to 200 ms(including end -to -endpropagation delays)

Table III. Comparison of five distinct designs using SPIDER.

DWDM Dense wa veleng th division mu ltiplexing

MUX Multiplexer

OTU Optical tra nslato r unit


15/16


Acknowledgments

We w ish to tha nk Debasis Mitra of Bell Labs as

w ell as K. G. Ramakrishnan a nd Eric Bou illet, formerly

of Bell Labs, for their substantial contributions to the

SPIDER effort ; Tho ma s Mueller of Lucen ts Optical

Netw orking G roup as w ell as Deirdre Doherty and

Mohcene Mezhoudi of Bell Labs Advan ced Tech-nologies for providing mu ch perspective on netw ork

provider needs; an d Bh arat Doshi of Bell Labs for help-

ful and detailed comments on an earlier draft of this

paper.

*TrademarksJa va is a tradem ark of Sun M icrosystems, Inc.

Linux is a registered trad ema rk of Linus Torva lds.

Microsoft is a registered trademark of MicrosoftCorporation.

References

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2. B. Rajagopalan, D. Pendarakis, D. Saha ,R. S. Ramamoorthy , and K. Bala , IP overOptical Netw orks: Architectu ral Aspects, IEEECommun. Mag., Vol. 38, No. 9, S ept. 2000,pp. 94102.

3. G . R. Rit ch ie, SONETLays the Roa dbed forBroadband Netw orks, Networki ng Management,Vol. 8, No. 3, Mar. 1990, pp. 3035.

4. F. Tillerot, E. Didelet, A. Daviaud, and

G. Claveau , Efficient Netw ork Upgrade Ba sedon a WDM Optical Layer w ith Automa ticProtection Sw itching, Optical Fiber Commun.Conf. (OFC 98) Tech. Digest, San Jose, Calif.,Feb. 2227, 1998, pp. 296297.

5. K.-C. Lee and V. O. K. Li, A Circuit ReroutingAlgorithm for All-Optical Wide-Area Netw orks,Proc. I EEE Conf . on Compu ter Commun .

(INFOCOM 94), Toron to, J une 1994, pp. 954961.6. R. Irascho and W. Grover , Optimal Capacity

Placem ent fo r Pat h Restora tion in STM or ATMMesh-Survivable Netw orks, IEEE/ACM Trans.on Networki ng, Vol. 6, No. 3, June 1998,

pp. 325336.7. B. Mukherjee, S. Ramamurthy, D. Banerjee,an d A. Mukherjee, Some Principles forDesigning a Wide-Area Optical Netw ork, Proc.IEEE Conf. on Computer Commun . (INFOCOM 94),Toron to, J un e 1216, 1994, pp. 110119.

8. I. Sa niee, Optimal Routing Designs in Self-Healing Com mun ications Netw orks, In tl. Trans.

in Operati ons Research, Vol. 3, No. 2, Apr. 1996,pp. 187195.

9. K. Bala, E. Bouillet , and G. Ellinas, Ben efits ofMinimal Wavelength Interchan ge in WDMRings, Optical Fiber Commun. Conf. (OFC 97)Tech. Di gest, D allas, Tex., Feb. 1621, 1997,pp. 120121.

10. T. E. Stern and K. Bala, Mult iwavelength Optical

Networks: A Layered Appr oach, Addison-Wesley,Reading, Mass., 1999.

11. S. Cosares, D. N. Deutsch, I. Saniee, andO. J . Wasem, SONETToolkit: A DecisionSupport System for Designing Robust an d Cost-Effective Fiber-Optic Netw orks, Interfaces,Vol. 25, No. 1, Jan. Feb. 1995, pp. 2040.

12. B. T. Doshi and P. Harshavardhan a, BroadbandNetw ork Infrastructure of the Future: Roles ofNetw ork D esign Tools in Techn ologyDeployment Strategies, IEEE Commun. Mag.,Vol. 36, No. 5, May 1998, pp. 6071.

13. B. T. Doshi, S. Dravida, and P. Harshava rdhana,

Overview of INDT: A New Tool fo r Next-Gen eration Netw ork Design, Proc. IEEE GlobalTelecommun. Conf. (GLOBECOM 95), Vol. 3,Singapore, Nov. 1317, 1995, pp. 19421946.

14. G. Liu and K. G. Ramakrishnan, A*Prun e: AnAlgorithm for Finding KShortest Pat hs Subjectto Mu ltiple Constraints, Proc. IEEE Conf. onComputer Commun. (INFOCOM 01), Anchorage,Alas., Apr. 2226, 2001.

15. J. W. Suurballe an d R. E. Tarjan, A QuickMethod for Finding Shortest Pa irs of DisjointPaths, Networks, Vol. 14, No. 2, Summer 1984,pp. 325336.

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(Man uscri pt approved Apr il 2001)

R. DREW DAVIS, a member of technical staf f i n t he M athe-

mat ics of Netw ork s and System s Research

Departm ent at Bell Labs in M urray Hill,

New Jersey, is w orki ng on sof tw are design

and implementat ion f or telecomm unicat ion

netw orks. He holds a B.S. in in dustrial eng i-

neering and operatio ns research from Cornell University

in Ithaca, New Yo rk, and an M .S. in comput er, inform a-


16/16


t ion, and control engineer ing from the Universi ty of

M ichigan in Ann Arbor .

KRISHNAN KUM ARAN is a mem ber o f t echni cal staf f

in th e Math emat ics of Netw orks and

System s Research Dep art men t at Bell Labs

in M urray Hill , New Jersey. He hol ds a

B.Tech. degr ee in mechani cal eng ineerin gfrom th e Indian Inst i t ute of Techno logy in

M adras and a Ph.D. in physics fro m Rut gers University

in New Brunsw ick, New Jersey. Dr. Kum arans interests

are in mo delin g, analysis, and simu latio n of resour ce

man agemen t and schedulin g issues in commun ication

networks.

GANG LIU was fo rmerly a member of technical staf f in

th e Mat hematics of Net w orks and System s

Research Dep artm ent at Bell Labs in M urray

Hill, New Jersey, w here he w orked o n op ti-

cal netw ork design and plann ing, rout ingalgor i thm s, opt imizat ion techniqu es, and

econo mic mod eling an d strat egy analysis fo r telecom-

mu nication netw orks. He holds a B.S. in m echanical

engin eering f rom Chin a University of Science and

Techno logy in Hefei, an M .S. in op tics from Peking

University in Beijing , and an M .S. in comp ut er science

from Colum bia Universi ty in New York.

IRAJ SANIEE, a techn ical manag er in t he M ath emat ics

of Netw ork s and System s Research Depart -

men t at Bell Labs in M urr ay Hill, New Jersey,

ho lds B.A. and M .A. degrees in math emati cs

and a Ph.D. in o peratio ns research an d con-

trol f rom Cambridge Universi ty in England.

Dr. Saniee s curren t research pr ojects are in app ro xima-

t ion and op t imizat ion t echniques, data netw orking,

algor i thm s for rou t ing and prot ect ion in op t ical net-

w ork s, mult iscaling m odels of d ata netw orks, VoIP

traf f ic and congest ion mod el ing, and netw ork design.

He was th e leader of t he team t hat r eceived INFORM s

Franz Edelm an Runn er-Up Aw ard in 1994. x

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