A Comparison of Optical Time Slotted NetworksArush Gadkar

Department of Electrical and Computer EngineeringThe George Washington University, Washington DC- 20052

Email: arush@gwu.edu

Abstract—To harness the enormous bandwidth potential ofa fiber, Time Division Multiplexing over wavelength channelshas been proposed. In one type of time slotted optical networkcalled as Time Wavelength Switched Network (TWSN), the TimeWavelength-Space Routers (TWSRs) are configured to switchtime slots within a time frame. Another kind of time slottednetwork is the Time Domain Wavelength Interleaved Network(TWIN), which eliminates time switching within the networkby using passive Wavelength Selective Switches(WSSs) in thecore and an intelligent edge utilizing a fast tunable laser toemulate fast switching. In this paper, we provide an integerlinear program to solve the scheduling problem for a static trafficmatrix (of connections) for the TWIN network, and also presenta heuristic algorithm. We then compare the performances of thetwo networks under dynamic traffic and investigate the benefitsof having a fast reconfigurable switch as opposed to WSSs.

I. INTRODUCTION

Time Division Multiplexing of wavelength channels is an at-tractive solution to improve wavelength utilization. One such,connection-oriented optical network is the Time WavelengthSwitched Network (TWSN) [1], where time on every channelis slotted in a TDM fashion and a collection of time slotsconstitutes a frame which repeats in time. A connection isassigned a subset of time slots within the frame and the Time-Wavelength-Space Routers are configured to switch time-wavelength slots. Another type of time-slotted optical networkis the Time-Domain-Wavelength Interleaved Network (TWIN)[3], which eliminates the need for dynamically reconfiguringthe switches by using non-reconfigurable wavelength selectiveswitches (WSS). In TWIN, every node is equipped with atunable laser and a fixed receiver. Nodes intending to senddata to a particular node must tune their lasers to the uniquewavelength assigned to the destination node. Therefore inTWIN, no wavelength assignment is required. The WSS atevery node is pre-provisioned to route a particular input signalon a given wavelength to a particular output port.In [3], a slotted network architecture was considered where

a fixed size slot could accommodate a single burst. The aimof their work was to accommodate a given bursty traffic inas few slots as possible. The authors presented a heuristicalgorithm and compared its performance to a network withzero propagation delays. In this paper we consider a timeslotted TWIN architecture to operate as a connection orientednetwork. Our goal is to compare the performances of theTWSN and the TWIN network under dynamic traffic. Anothercontribution of this paper is to optimally solve the schedulingproblem for the TWIN network for a given static traffic matrix

(of connections) while taking into account link propagationdelays. We present an Integer Linear Program (ILP) to solvethe scheduling problem and also develop a heuristic algorithm.In the case of the TWIN, we use the shortest path algorithm

to pre-provision the WSSs and the the First Available Slot(FAS) strategy to assign slots. In the TWSN, the TWSRsare capable of reconfiguring on a time slot basis. Hence inthis case we need to solve both, the time slot assignment aswell as the wavelength assignment problem. For assigning awavelength to a connection request, we use the Least LoadedWavelength (LLW) [2] and use the FAS strategy for time-slot assignment. There are several papers in the literaturethat deal with time-slotted network architectures. Howevera comparison of this nature has not been performed before.Comparing these network architectures would render usefulinsight to the advantages one gains by using a reconfigurableswitch (TWSR) as opposed to a WSS.The remainder of the paper is organized as follows: In

Section II we present the ILP formulation and the heuristicalgorithm to solve the static traffic scheduling problem for theTWIN network. In Section III we explain the simulation envi-ronment and present the results of our performance evaluation.We conclude the paper in Section IV.

II. OPTIMAL SCHEDULING IN A TWIN NETWORK

The scheduling problem in a TWIN network can be formallystated as follows: given the number of nodes in the network(N ), the number of time slots in a frame (M ) and the numberof transmitters per node (T ), we aim to find a valid schedulesuch that the probability of a connection being blocked (i.e,connection cannot be scheduled) is minimized. In what fol-lows, we present an ILP and a heuristic algorithm to solve thescheduling problem.

A. Integer Linear Program (ILP) Formulation

We consider a demand matrix C of size N × N , whereC(i, j) represents the number of connections to be sent fromnode i to node j. S(i, j, k) is a binary variable equal to 1if node i transmits a connection to node j in time slot k.R(i, j, k) is a binary variable equal to 1 if node j receives aconnection from node i in time slot k. The constraints can bestated as follows:Transmitter constraint: Since each node is equipped with

T transmitters, constraint (1) ensures that no node transmits

more than T connections at any given time slot.N−1∑

j=0

S(i, j, k) ≤ T ∀ i = 0, . . .N−1; k = 0, . . .M−1. (1)

Receiver constraint: In a TWIN network each node isassigned a single receiver of fixed wavelength. The constraintin (2) ensures that no node receives more than a singleconnection in any time slot.

N−1∑

i=0

R(i, j, k) ≤ 1 ∀ j = 0, . . .N−1; k = 0, . . .M−1. (2)

Demand constraint: For every source-destination pair (i, j),we do not want to schedule more connections than the demandfrom node i to node j, i.e., C(i, j). This is achieved by theuse of the following constraint.

M−1∑

k=0

S(i, j, k) ≤ C(i, j) ∀ i, j = 0, 1, . . .N − 1. (3)

Delay constraint: Due to the effect of propagation delay,a connection transmitted by node i in time slot k, will bereceived by node j in time slot k ′. The time slot k′ can becalculated as follows: k′ = (k + dij) mod M . (dij is the totalpropagation delay in slots from node i to node j).

R(i, j, k′) ≤ S(i, j, k)∀ i, j = 0, . . .N − 1; k = 0, . . .M − 1(4)

Since we are interested in minimizing the blocking proba-bility of a connection (defined as the fraction of connectionsthat cannot be scheduled), we achieve it by scheduling as manyconnections as possible from the given demand matrix. Thisis achieved by the following objective function:

maxM−1∑

k=0

N−1∑

i=0

N−1∑

j=0

R(i, j, k). (5)

B. Heuristic AlgorithmThe heuristic algorithm is based on the maximum flow

algorithm implemented on certain constructed graphs. Wemake use of the property of destination trees1 [3] to find a validschedule and consider the slot assignments for the connectionsby considering a sequential order of the destination nodes. Wetake care of transmitter and receiver conflicts (Eqs. (1),(2)) byassigning unique vales to the links in the constructed graph. InFig. 1, for the purpose of simplicity we consider an N -nodeTWIN network with M = 4 time slots per frame. We haverepresented the formulation when the algorithm is schedulingconnections intended for node 1. The links in Stage 1 areassigned a capacity equal to the demand from a node to thedestination node (node 1). The links in Stage 2 are assigneda capacity of M (number of time slots in a frame), whichprohibits us from scheduling more than M connections fromany node. To account for a maximum of T transmissions per

1To avoid a conflict on any link in the network, it is sufficient to ensurethat there are no arrival conflicts at the destination.

time slot (labeled as Ti, i = 1, 2 . . .M ) we assign a capacityof T to the links in Stage 3. The links in Stage 4 represent thetotal delay on links from nodes (i = 2 . . .N ) to the destinationnode 1. In the figure, we have represented these links withdelay values of d21 = 1 and dN1 = 3 time slots respectively.The delay links are assigned a capacity of 1 to ensure thata particular node can transmit only a single connection on agiven wavelength at any given time slot. Finally the links inStage 5 are assigned a capacity of 1, thus making sure thatthe destination node can receive at most 1 connection at anygiven output slot (labeledOj , j = 1, 2 . . .M ). It is easy for thereader to verify that a maximum flow from a dummy sourcenode (S) to the destination node (D) will provide a feasibleschedule. Note that the heuristic algorithm has N iterationsand it is critical to update the the link capacities before everyiteration to avoid over usage of any link.

S D

�

Node 1 Transmitter

Node 2 Transmitter

Node N Transmitter

Node 1 Receiver

Node 2 Receiver

Node N Receiver

M

M

M

T

T

1

1

O1

O2

O3

O4

T

T

T

T

T

T

T

O1

O2

O3

O4

O1

O2

O3

O4

�

T1

T2

T3

T4

T1

T2

T3

T4

T1

T2

T3

T4

T1

T2

T3

T4

T1

T2

T3

T4

T1

T2

T3

T4

T1

T2

T3

T4

O1

O2

O3

O4

T1

T2

T3

T4

T1

T2

T3

T4

T1

T2

T3

T4

�

�

T

T

T

1

1

1

1

STAGE 1 STAGE 2 STAGE 3 STAGE 4 STAGE 5

Fig. 1. Graph formulation for heuristic algorithm.

III. SIMULATION RESULTS

We use the NSFNet topology with N = 14 nodes andL = 21 bidirectional links. The nodal distances used arethe actual geographical distances with the propagation delayon the links equal to 5μs/Km. We consider a time frameof M = 64 slots with a duration of 125μs. The TWINnetwork assigns a single fixed wavelength receiver to eachnode (R = 1). Hence the number of wavelengths in the TWIN(W ) is equal to N . For a fair comparison we consider a TWSNnetwork with W = N wavelengths. For scheduling a statictraffic matrix of connections for the TWIN, we consider a totalofM×W connections (i.e., a normalized load ΓL = 1) and forthe dynamic traffic we considered connections arriving to thenetwork according to a Poisson process with an arrival rate ofAr and a holding time (exponentially distributed) with a meanof 1/μ.The source and destination nodes for each connectionfollowed a uniform distribution. Each connection request isassumed to have a demand of a single time slot.The trafficload offered to the network can be expressed as γ = Ar/μErlang (i.e., normalized load per wavelength-slot of ΓN =γ/(M×W )). The performance metric considered in this paperis the blocking probability of a connection.In Fig. 2 we show the results of the ILP and the heuristic

algorithm (scheduling static traffic in TWIN) obtained for T= 1 and 2 respectively. It can be observed that the heuristic

algorithm performs quite well as compared to the ILP. InFig. 3 we show the performance evaluation of the TWIN andTWSN networks for dynamic traffic with R = 1, T = 1,and W = 14. We note that the two networks have the sameblocking performance. TWIN blocks a connection if it doesnot find an available slot in a frame on the destination nodesassigned wavelength. In TWSN, we do have the flexibilityof transmitting the connection on any wavelength. In thiscase a connection is dropped if there is no free slot on thechosen wavelength. For R = 1, if TWSN is able to schedulea connection (receiver free on a particular slot), the TWINwill also be able, to schedule a connection on that slot on thedestination nodes assigned wavelength. We also show in Fig.3 the performance evaluation of the TWIN network for highervalues of T . It is observed that for T = 2, the performance isconsiderably better (almost an order of magnitude) than thatfor T = 1 for lower loads. However for T = 3 it is onlyslightly better than that for T = 2. These results indicate thatthe performance of the TWIN model is dominated by the factthat it assign a single receiver to every node.

0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 110−5

10−4

10−3

10−2

10−1

100

Normalized load (ΓL)

Blo

ckin

g pr

obab

ility

ILP (T = 1)Heuristic (T = 1)ILP (T = 2)Heuristic (T = 2)

Fig. 2. ILP and heuristic solutions for static traffic scheduling in TWIN.

6 7 8 9 10 11 12 13 14 1510−5

10−4

10−3

10−2

10−1

100

Normalized load per wavelength slot (ΓN)

Blo

ckin

g pr

obab

ility

TWIN ( T = 1 )TWSN ( T = 1) TWIN ( T = 2 ) TWIN ( T = 3 )

Fig. 3. Performance evaluation of TWIN and TWSN under dynamic traffic:R = 1, W = 14.

In Fig. 4 we compare the performance of the TWSN for areduced number of wavelengths. It is observed that W = 8gives almost the same performance as W = 14, implying thatby using reconfigurable switches (TWSN) we obtain the sameperformance as the one obtained by using WSSs (TWIN), withfar fewer wavelengths (almost a 50% reduction in the numberof wavelengths used). In Fig. 5 we compare the performanceof the TWSN for T = 2, R = 2 to that of T = 2 andR = 1 (same as that of TWIN in Fig. 3). It is observed thatby increasing the number of receivers to 2 in the TWSN, we

achieve blocking in the range of 10−4 to 10−5 for more thantwice the normalized load per wavelength-slot.

6 7 8 9 10 11 12 13 14 1510−4

10−3

10−2

10−1

100

Normalized load per wavelength slot (ΓN)

Blo

ckin

g pr

obab

ility

W = 14W = 8W = 7W = 6

Fig. 4. Performance evaluation of TWSN for dynamic traffic: T = 1, R = 1.

13 14 15 16 17 18 19 20 2110−5

10−4

10−3

10−2

10−1

100

Normalized load per wavelength slot (ΓN)

Blo

ckin

g pr

obab

ility

(W = 14 )(W = 8 )(W = 6 )

Fig. 5. Performance evaluation of TWSN for dynamic traffic: T = 2, R = 2.

IV. CONCLUSIONSIn this paper we presented an ILP to solve the scheduling

problem for a given static traffic matrix for the TWIN archi-tecture. We also presented a heuristic algorithm and showedthat it achieves good results. We compared the performance ofthe TWIN to that of the TWSN. Our results have demonstratedthe trade off in switching and number of wavelengths betweenhaving a non-reconfigurable core (TWIN) and an reconfig-urable core (TWSN). We propose to extend the work in thefollowing ways: Formulate a network whereW < N , by usingmulticasting or multihopping strategies. In [1] we presented anoptimal algorithm to solve the connection scheduling problemfor a single TWSR. An extension of the algorithm to a TWSNwill provide yet another means of comparing the two networkarchitectures.

ACKNOWLEDGMENTThis work was supported in part by the National Science

Foundation grant CNS-0434956.

REFERENCES[1] A. Gadkar and S. Subramaniam, “FDL Design in Time-Wavelength

Switched Optical Networks,” in Proc. ICC, May 2008.[2] B. Wen, and K. M. Sivalingam, “Routing,wavelength and time slot

assignment in time divison multiplexed wavelength-routed optical WDMnetworks,” INFOCOM., vol. 3, pp. 1442-1450, 2002.

[3] K. Ross, N. Bambos, K. Kumaran, I. Sainee and I. Widjaja, “Schedulingbursts in time-domain wavelength interleaved networks ,” IEEE. J. Select.Areas Commun., vol.21, no. 9, pp. 1441-1451, Nov 2003.