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Blocking Behavior Analysis of OpticalSwitching Networks

TANVIR KAUR

Department of Computer Science and Engineering,

Thapar University,Patiala, Punjab, India

RINKLE RANI AGGARWAL

Department of Computer Science and Engineering,

Thapar University, Patiala, Punjab, India

Abstract:

One of the issues in optical networks is the problem of blocking which should be considered in order tofully exploit the benefits of the high speed optical networks [Pan,et.al.(1999)]. The strictly non-blockingconditions for the optical networks usually cause a lot of hardware cost so a new class of networks cameinto being called the rearreangeable networks [Yeh and Feng,(1992)] in which there was no need of anyextra planes and a conflict free path can be established by rearrangement of the existing connections. Thispaper is a survey paper, which provides an overview of the strictly non blocking conditions for thenetworks and explain in detail various routing options available for rearrangeable networks.

Keywords: Blocking, Strictly non-blocking networks(SNB), Rearrangeable networks.

Introduction

Optical switching networks not only have the potential to steer network traffic at the speed of hundreds of

terabits per second or higher, but they also can be more cost-effective than their electronic counterparts, even forapplications requiring lower throughput. Therefore owing to the exponential growth in the bandwidth demandfrom large number of users in multimedia applications and scientific computing, the optical networks havegained considerable importance. Large scale optical switching networks are built by grouping numerous SEs inmultiple stages along with the optical links which are arranged in a specified interconnection topology betweenadjacent stages. The basic SEs and the interconnecting optical links form a switching network such that theoptical flows arriving at inputs can be switched appropriately to outputs as requested.

The main focus of this paper is to address the problem of blocking that occurs in the optical switching networkswhen the simultaneous connections of more than one terminal results in a conflict thereby hampering thenetwork performance. Combining the horizontal expansion and vertical stacking [Y u,et.al.(2006)] of opticalbanyan networks is a general scheme for constructing banyan-based optical switching networks. The resultinghorizontally expanded and vertically stacked optical banyan (HVOB) networks usually take either a highhardware cost or a large network depth to guarantee the non blocking property. Moreover the high degree of

connection capability in case of SNB is at a very high hardware cost whereas the RNB networks[Yu,et.al.(2006)] are usually constructed with a lower hardware cost and can establish a conflict free path for theconnection from any idle input to any idle output if the rearrangement of the existing connections is allowed.

The rest of the paper is organized as follows: In section 2, the problem of blocking is discussed in case of opticalnetworks. Then in section 3, the strictly non-blocking conditions for the optical networks have been presented.The rearrangeably non-blocking conditions for the networks and the corresponding routing algorithms havebeen presented in section 4 and the conclusions have been discussed in section 5.

Tanvir Kaur et al. / International Journal of Engineering Science and Technology (IJEST)

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Blocking in optical networks

A request is a pair of input and output requesting a connection; once routed, a request turns into a connection,which is a path link-disjoint to all other connections but sometimes the simultaneous connection of more thanone terminal result in a confliction in the use of network communication links, which is referred to as blocking.So, the challenge here is to remove this problem of blocking and thus make a non-blocking network. Nonblocking interconnection networks can be classified into following three levels.

Strictly non blocking (SNB) - A network is SNB [Rajgopal,(2005)] if the permutation can be realized by edge-disjoint paths without rearranging active connections, any idle path can be used for each new connectionrequest. In other words, any permutation can be dynamically realized.

Wide-sense non blocking (WSNB) - A network is WSNB [Rajgopal,(2005)] if the permutation can be realizedby edge-disjoint paths without rearranging active connections subject to the condition that a selected path isused for each new connection request. In other words, any permutation can be dynamically realized with thehelp of a wise algorithm.

Rearrangeably non blocking (RNB) or rearrangeable- A network is said to be RNB [Rajgopal,(2005)] if anypermutation can be realized by edge-disjoint paths when the entire permutation is known. In other words, anypermutation can be statically realized. The word rearrangeable refers to that if the connection requests in apermutation arrive dynamically, the permutation can be realized with possible rearranging active connections.

Banyan Type Networks

Banyan type networks have recently gained considerable attention because they are the class of self-routingnetworks which means that any connection can be established only by the address of its source and thedestination regardless of the other connections which means that no complicated control mechanism is neededfor establishing a connection. A network belonging to this class satisfies the following properties:

It has N=2n inputs, N=2n outputs, n-stages, and N/2 SEs in each stage.

There is a unique path between each input and each output.

Let u and v be two SEs in stage I, and let Sj(u) and Sj(v) be two sets of SEs to which u and v can reach in stage j,0

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Fig1: A combination of horizontal expansion and vertical stacking of banyan networks. [Yu,et.al.(2006)]

Strictly Non-blocking Conditions for MIN

3.1 Banyan networks

(1) A replicated Banyan of size NN with SE bb with K planes is strict-sense nonblocking.[Zadedyurin,et.al.(2008)] if and only if:

K nc+1, where

nc=2(bn-1/2-1), n-odd.

nc=bn-2/2(b+1) -2, n-even.

The number of replicated planes needed for the Banyan in order to achieve the non blocking property has beenanalyzed using this formula.

(2) Another necessary and sufficient condition [Busi and Pattavina,(1998)] that make a N x Nnetwork made byvertical replication of horizontally-expanded banyan networks each with n +mstages (0 m n - 1) a strictly

non-blocking network is given. It is specified by the number Kof networks vertically stacked that is:

K 2(n-m)/2+m-1, when (n+m) is even.

K 2(n-m+1)/2+m-1, when (n+m) is odd.

3.2 Shuffle exchange networks

(1) The maximum number of paths that can be blocked in the internal shells of a Shuffle Exchangenetwork [Busi and Pattavina,(1998)] with s stages is found to be equal to that of recursive banyan networkswith n +m =s stages and thus given by:

Nb= 2(s/2) 2(s-n+1), when s is even

Nb= 2(s+1)/2 2(s-n+1) , when s is odd

Where Nb=no of blocked paths.

When s= n+1 stages:

An Nx N network made by vertical replication of K Shuffle Exchange networks with s =n+1 stages is strictlynon blocking if and only if:

K 2(n-1)/2, when n is odd

K 2n/2, when n is even.


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When s = n+2 stages:

Nb= 2(n+2)/2 8, when n is even

Nb= 2(n+3)/2 8, when n is odd

When s =n+3 stages:

Nb= 2(n+3)/2 16, when n is even

Nb= 2(n+4)/2 16, when n is odd

Routing in Rearrangeably Non-blocking Networks

The Benes networks is one of the choices for optical networks because of its simple topology and easyscalability with low degree. An NN Benes network is a well-known rearrangeable multistage interconnectionnetwork (MIN), with (2n-1) stages (n=log2 N), that can connect its N inputs to its N outputs in all possible waysthus enabling non-blocking communication between any pair of idle terminals through reassigning the exitinglinks. An NNBenes network, which is also called B(k), can be constructed by adding one stage including N / 2( N =2k) switching elements at the left and the right of two copies of B(k-1) respectively. Baseline-baseline,omega-omega-1, baseline-omega-1, banyan-1-banyan [Yeh and Feng,(1992)] are some examples of the class of

rearrangeable network which are topolologically equivalent to Benes network. An example of the Benesnetwork is given in the figure.

Fig. 2: 88 Benes Network [Zhang and Gu,(2002)]

Routing algorithms aim to seek a path that packets travel between any pair of source and destination nodes.Several routing algorithms have been developed for Benes network [Nassimi and Sahni,(1982)] [Zhang andGu,(2002)] [Rajgopal,(2005)] [Yoon,(1987)] [Kim and Maeng,(1997)].

4.1 Partially adaptive routing algorithm [Zhang and Gu(2002)]

The algorithm enables 2k1 different paths for packets traveling the Benes network between a particular pair ofsource and destination nodes. Packets can select any one of these paths routed to the final destination accordingour routing algorithm. This approach reduces the possibility of congestion effectively. The partially adaptiverouting algorithm is described as follows:

The partially adaptive routing algorithm for NNBenes network:

Index Terms:

Current node: the current node is given by : C(position, stage)

Destination node: the destination node is represented by : D(position, 0)

N =2k.


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p (1pk ) is an integer.

Steps:

If the local node address( y>=1&&

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Fig. 3: (a)-(d) Sub-matrices format for a 1616 Benes Network [Chakrabarty,et.al.(2009)]

4.3 Dynamic Path Selection algorithm [Chakrabarty et.al.(2009)] :

A. Phase 1

Input: Input Permutation P0:(N1).

Output: Set the switching element at stage 0 and (2logN 2).

Step 1: Start with the first switching element, SE[k, 0], 0 k (N/2) 1, set the switching element to STATE[k,0] =0. Set the STATE of the output switching element SE(P(i)), 0 i (N 1), to 0 or 1 depending on therequested output. For the request, if Subnetwork =0 and requested Port =0, set STATE[r, (2logN 2)] =0, 0

r (N/2) 1 else set to 1.

Step 2: Check if any port remains at SE(P(i)), after Step 1. If yes then goto Step 3. Else goto Step 4.

Step 3: Start with the remaining port of SE(P(i)), 0 i (N 1). Check the state of the corresponding switchingelement at stage 0. If STATE[k, 0] =NULL, 0 k (N/2) 1, set the switching element to either 0 or 1depending whether the connection is coming from upper or lower subnetwork and the requested port is even orodd.

Step 4: If any port remains at the input switching element after step 3, then set up paths between that port i andcorresponding output port P(i). Set the state of the output switching element if its state was NULL.

Step 5: Continue Step 2 to Step 4 till all the connections forms a logical connected graph with at maximum N/2complete cycles. This connecting graph will indicate that all the switching elements in stage 0 and stage (2logN 2) are set.

B. Phase 2

Input: Input Permutation P0:(N1).

Output: Set the state of the switching elements from stage 1 to (2logN 3).

Step 1: Start with switching element, SE[0, 1], check the the status variable for SE[0, 1]. If STATE[0, 1] =NULL, set it to 0 or 1 depending on the value of input port. If PORT =0, set to 0, else 1 and go from stage s to(s +1), 1 s (logN 2). If the SE[0, 1] was set before, then use the unused port.


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Step 2: From stage (logN 1), use first (logN 2) MSB bits of the output port for establishing path from (logN 1) to (2logN 3).

Step 3: If there is any blocking, call Phase 3. Else goto Step 4.

Step 4: If any port remains at the switching element last used in step 2 at stage (2logN 3), use that port forreverse routing. Go to stage (logN2) from (2logN3) by following the switching element setting rules used instep 1 and from (logN 2) to stage 1 apply step 2. Else goto stage 1 and start with any available switchingelement with STATE[k, 1] =NULL, 0 k (N/2)1. Phase 2 can set up paths for all input-output request, if noblocking arises inside the switching elements between stage (logN2) and (2logN3). In case of any blocking,call Phase 3 and resolve the conflict by selecting alternative paths for the request and continue its execution tillit reaches the end of all the request.

C. Phase 3

Input: Blocking between stages (logN 2) and (2logN 3).

Output: Alternative blocking free paths.

Step 1: For forward routing follow Step2, else follow Step 3

Step 2: Blocking at stage k, (logN1) k (2logN3), go back to switching element SE[i, j] at stage j using

link pattern Lj , 0

i

(N/2)

1 and 1

j

(logN

2) and choose the alternative port of that switchingelement. If alternative port is not free, go back to next step and choose the alternative port of the switchingelement at that stage and continue routing. If no alternative path is available goto. Step4.

Step 3: Blocking at stage k, 1 k logN, go back to switching element SE[i, j] at stage j using link pattern Lj,(logN1) i (2logN3) and logN j (2logN3). and choose the alternative port of that switching element.If alternative port is not free, go back to next step and choose the alternative port of the switching element at thatstage and continue routing. If no alternative path is available goto Step4.

Step 4: In case where it is not possible to find any available path for the request, drop the request and start withany other available request at stage 1.

4.4 Self routing algorithm [Raghavendra and Boppana,(1991)]:

The self- routing algorithm routes a tag as follows:

If the i-th bit is connecting bit for a stage, then the i-th bit of the tag called the routing bit is used for routingthrough that stage, it is routed to the upper(lower) routing line of the switch if the routing bit is 0(1).

When the routing bits of both the tags at a switch are the same then there exists a conflict in setting up theswitch since both them specifies the same output line.


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Fig. 4: Routing a linear permutation [Raghavendra and Boppana,(1991)]

Algorithm:

For the first n-1 stages, the switches are set up such that input line with smaller destination tag value is routedaccording to its routing-bit.

For the next n stages, the switches are set up using the above 2 steps.

In case of any conflict, the algorithm gives priority to the tag having the smallest value.

Conclusion

The problem of blocking needs to be taken care of in order to exploit fully the performance of optical switchingnetworks. The strictly non blocking conditions for the networks turn the networks into non blocking ones butincur a lot of cost so there occurs a need for rearrangeable networks and different types of routing algorithms aredevised for them. Depending on the time complexity of the algorithms, the most appropriate one is chosen.Deterministic algorithms can provide (rearrangeably) nonblocking performance for unicast switch, but arecomputationally complex. Faster algorithms select paths at random i.e. they are partially adaptive but achieve

poor blocking performance than the deterministic algorithms.

References

[1] Busi, I. ,Pattavina, A.(1998) : Strict-Sense Non-Blocking Conditions for Shuffle Exchange Networks with Vertical Replication,Proceedings IEEE INFOCOM, The Conference on Computer Communications, Vol.1, pp.126-133.

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Conference on Computational Intelligence, Communication Systems and Networks, pp.23-28.[4] Chakrabarty, A., Collier, M. ,Mukhopadhyay, S. (2009) : Matrix-Based Nonblocking Routing Algorithm for Bene Networks,

Computation World: Future Computing, Service Computation, Cognitive, Adaptive, Content, Patterns pp.551-556.[5] Kim, M.K., Maeng, S.R.(1997): On the Correctness of Inside-Out Routing Algorithm, IEEE Transactions on Computers, Vol. 46,

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[8] Lu, E., Zheng, S.Q.(2005) : Parallel routing algorithms for non blocking electronic and photonic switching networks, IEEETransactions on Parallel and Distributed Systems, Vol.16, No.8.

[9] Nassimi, D., Sahni, S. (1981): A Self-Routing Benes Network and Parallel Permutation Algorithms, IEEE transactions on computers,Vol. C-30 No.5, pp.332-340

[10] Nassimi, D., Sahni, S.(1982) : Parallel algorithm to set up the Benes permutation network, IEEE Transactions on Computers,Vol.31,No.2, pp.148-154.

[11] Opferman, D.C., Tsao-Wu, N.T.(1971): On a Class of Rearrangeable Switching Networks, The Bell System Technical J ournal, Vol.50,No.5.

[12] Pan, Y., Qiao, C., Yang, Y.(1999): Optical Multistage Interconnection Networks: New challenges and approaches, IEEECommunications Magazine, Vol.37, No.2, pp. 50-56.

[13] Raghavendra, C.S., Boppana, R.V. (1991): On Self-routing in Benes and Shuffle Exchange Networks, IEEE Transactions onComputers, Vol. 40, No.9, pp. 1056-1064.


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[14] Rajgopal, K. (2005): The KR-Benes Network: A Control optimal Rearrangeable Permutation Network, IEEE Transactions onComputers, Vol. 54, No. 5.

[15]Yu, C., Jiang, X.H., Horiguchi, S., Guo, M.(2006): Overall blocking behavior analysis of General Banyan-based Optical SwitchingNetworks, IEEE Transactions on Parallel and Distributed Systems, Vol.17, No.9, pp.1037-1046.

[16]Yoon, K.(1987): A New Benes Network Control Algorithm, IEEE Transactions on Computers, Vol.C-36(6), pp. 768-772.[17]Yadav, R., Aggarwal, R.R.(2010): Survey and Comparison of Optical Switch Fabrication Techniques and Architectures, Journal of

Computing, Vol.2, Issue 4,ISSN 21519617.[18]Yeh, Y.M., Feng, T. (1992): On a class of Rearrangeable networks, IEEE Transactions on Computing, pp.1361-1379.[19] Zhang, J., Gu, H.(2009): Partially adaptive routing algorithm for Benes network on chip, Proceedings on IEEE, pp. 4244-4520.[20] Zadedyurina, O., Ofek, O., Pattavina, A. (2008): Space and Time Blocking versus Cost in A ll-Optical Banyan Networks, Proceedingsof IEEE, pp.5338-5343


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