CENTRALIZED BUFFERING AND LOOKAHEAD WAVELENGTH CONVERSION IN MULTISTAGE INTERCONNECTION NETWORKS

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1 CENTRALIZED BUFFERING AND LOOKAHEAD WAVELENGTH CONVERSION IN MULTISTAGE INTERCONNECTION NETWORKS Mohammed Amer Arafah, Nasir Hussain, Victor O. K. Li, Department of Computer Engineering, College of Computer and Information Sciences, P.O.Box 8, King Saud University, Riyadh, KSA Department of Electrical and Electronic Engineering The University of Hong Kong Pokfulam Road, Hong Kong ABSTRACT In this paper, methods to alleviate the problem of internal blocking in interconnection networks based on WDM are studied. In an ordinary 8x8 Omega network, only % of all permutations are permissible in one pass, and it gets worse with larger switches. However, using WDM technology, the performance of these networks can be improved. In this paper, several architectures based on Omega network using the WDM technology are considered and in turn algorithms to resolve the problem of internal blocking in a centralized fashion are introduced. Performance of the Omega network is analyzed by simulation. It is shown that by using a few buffers and lookahead wavelength converters a considerable amount of improvement in the system performance is achieved. Keywords: Omega Networks, Multistage Interconnection Networks, Internal Blocking, Buffering, Wavelength Conversion, Wavelength Division Multiplexing. I. INTRODUCTION Recently, significant developments have been made in photonic switching based on Wavelength Division Multiplexing (WDM). Therefore, researchers have used this technology to implement switches such as the Crossbar or Multistage Interconnection Networks (MIN) and to upgrade the performance of the available systems that use these networks. An N N crossbar switch is a single-stage, strictly non-blocking network with N input ports and N output ports. It can realize N! permutations (any one-to-one mapping between the set of inputs and the set of outputs). Therefore, it does not suffer from internal blocking. However, the hardware complexity of an N N crossbar is O(N ) since it consists of N cross-points. Therefore, it is expensive and only appropriate for small switches, say, with N. The other class of interconnection networks is the Multistage Interconnection Networks (MINs) which consist of a few stages of a number of smaller switch elements. MINs with only a few stages suffer the problem of internal blocking. However, it is cheaper and faster. For example, by using switch elements, only log N stages are required to achieve full access capability in an N N switch. Using, switch elements, data might go through some unwanted changes when the two input channels try to access the output channel simultaneously. To resolve this problem, it is suggested to use two queues, one at each output port []. However, using the same switch based on WDM, two or more packets may share the output channel provided they use different wavelengths. For this reason and other advantages [] [], WDM is used in our network. Therefore, a switch with additional configurations is introduced, namely the upper and lower mergers, and the upper and lower splitters. The internal blocking is redefined as two or more packets with the same wavelength trying to access a channel simultaneously. This problem can be eliminated by increasing the number of switch elements [], the number of stages [], or the size of the switch element []. However, all these techniques increase the cost and delay of such networks. Therefore, in this paper, utilizing the same few switch elements while maintaining full accessibility is attempted. To alleviate the problem of internal blocking in MINs based on WDM, buffers [] or wavelength converters [] are used. The advantage of wavelength conversion over buffering is the ability to utilize the available channel bandwidth and to send a packet to its destination without waiting for the next switching cycle. Buffering and wavelength conversion techniques have been studied in detail in all-optical networks based on circuit switching and crossbar switches [8] [9]. Several algorithms are introduced defining the behavior of the central controller which acts as an interface in front of the MIN to resolve any internal blocking. Once the central controller resolves the internal blocking by buffering, wavelength conversion, or dropping of the packets, it directs the packets through the network without any collision. Section II briefly describes our target multistage interconnection network, namely, the Omega network based on WDM. Section III presents an algorithm which also incorporates the concept of wavelength conversion. Section IV presents the concept of lookahead wavelength conversion. The performance of these algorithms is evaluated by simulation in section V. The final section concludes the paper. II. ARCHITECTURE OF OMEGA NETWORKS BAD ON WDM Based on the previously discussed characteristics of MINs, an N N Omega network, first developed by Laurie (9) [], is best suited for WDM implementation. It consists of log N identical stages, and each stage consists of a perfect shuffle connection followed by N/ of switch elements as illustrated in Fig..

2 I I I I I I I I Fig. An 8 8 Omega network Since this network is based on WDM, and each input link can carry at most ω packets, each with a different wavelength from the set of available wavelengths, Λ= (λ, λ,..., λ w-, λ w ), one may merge both inputs of a switch element and forward them to either the upper or lower output link when the sets of wavelengths on both input links are disjoint. Therefore, two configurations are to be considered, namely, upper merger and lower merger as illustrated in Fig. c. Note that these two configurations would have been considered as internal blocking in an ordinary Omega networks. Moreover, two additional configurations are required, namely, the upper splitter and lower splitter as illustrated in Fig. d to satisfy the requirements of one-to-one mapping. (a) O O O O O O O O W : s n-...s s s d n- W : s n-...s n s n- d n-... W i : s n-i- s n-i-... s s d n- d n-...d n-i... W n- : s d n- d n-...d d A window W i, illustrated in Fig., has N rows, each with log N bits. If W i is a permutation, i.e., no two rows in W i are equal, then, it is guaranteed that there is no internal blocking in any switch element in stage i; otherwise, there is at least one switch element in stage i with both of its inputs competing on the same output link, which causes internal blocking in the ordinary Omega network. Since WDM is used, the switch element can be configured to either upper merger or lower merger. However, if the sets of wavelengths on both inputs of that switch element are disjoint, then there will be no internal blocking; otherwise, there will be internal blocking, and it can be resolved by either packet buffering or wavelength conversion. I I I I I I I I O O O O O O O O Straight (b) Exchange s s s s s s s s d s d s s d d d d s d d d Upper Merger Upper Splitter (c) (d) Lower Merger Lower Splitter Fig. Configuration of a switch element The set of permutations realizable by an Omega network is characterized by having n- windows, where n=log N, and each of them is a permutation. To understand this concept, concatenate the binary representation of all sources, s n- s n-...s s, and the binary representation of the corresponding destinations, d n- d n-...d d. This generates a table with N rows and n columns, and which can be represented by (d n- d n-...d d s n- s n-...s s ). Now, n- windows can be defined as, Fig. No internal blocking if W and W are permutations The main drawback of this architecture is that there is only one path between any source and any destination. Therefore, failure of any path causes a loss of full access capability. To increase the reliability of Omega networks, redundancy is added [] [][]. III. 8X8 OMEGA NETWORKS WITH WAVELENGTH CONVERSION W In this section, Wavelength Converters are included in the central controller of the Omega network as illustrated in Fig.. The purpose of a wavelength converter is to convert the wavelength λ i of a packet to another wavelength λ j, with λ i not equal to λ j. Therefore, if there is internal blocking, and wavelengths of packets that cause the internal blocking are converted, then the number of packets to be buffered by the central controller can be reduced, and the performance of the W

3 network will improve. Note that a packet can have at most one wavelength conversion and this happens inside the central controller. The number of packets which can have their wavelengths converted is limited by the number of available converters. Packets which will cause internal collision and cannot be wavelength converted are buffered. If no more buffers are available, packets are dropped. I I I I I I I I Central Controller With Buffers and Wavelength Converters Fig. Architecture of a collision free Omega network Fig. illustrates an example of resolution of internal blocking in Omega network by wavelength conversion. Assuming that the arriving set of packets to the input port (I ) uses wavelengths {λ, λ }, and the arriving packet to the input port (I ) uses wavelength {λ, λ }, and both are sent simultaneously to the same output port, then there will be internal blocking by the packets that use wavelengths λ. However, if the wavelengths λ of one of the packets is converted to λ 8, then there will be no internal blocking at that switching element, and its output port can forward the set of packets with wavelengths {λ, λ, λ, λ 8 } to the next stage. I ={λ, λ, λ } I ={λ, λ } I ={λ, λ, λ 8 } I ={λ, λ } I ={λ } I ={λ, λ } I ={λ } I ={λ, λ } λ is converted to λ 8 No wavelength conversions since wavelength sets of input ports and are disjoint Packet using wavelength λ of input port is converted to wavelength λ 8 O O O O O O O O Fig. Resolution of internal blocking in Omega network by wavelength conversion No Internal Blocking {λ, λ, λ, λ } {λ, λ, λ, λ 8 } O ={λ } O ={λ, λ, λ } O ={λ, λ } O ={λ } O ={λ, λ 8 } O ={λ, λ } O ={λ, λ, λ 8 } O ={λ, λ } s s s d d d To design the algorithm, a one-to-one mapping of the set of sources and the corresponding destinations is considered to be switched by an Omega network. By concatenating the binary representation of the sources, s n- s n-...s s, and the binary representation of the corresponding destinations, d n- d n-...d d, n- windows are generated such as: W i = (s n-i- s n-i-...s s d n- d n-...d n-i ) for i=,,...,n- Algorithm Notations: B is the number of buffers in the central controller. W is the number of wavelength converters in the central controller. Λ is the set of all possible wavelengths. S is the number of elements in a set S. I u is the set of wavelengths arriving to the upper input port of a switch element. I l is the set of wavelengths arriving to the lower input port of a switch element. SW is the shared wavelengths between I u and I l. It can be represented as: SW = I u I l NU is the set of wavelengths that are not used by either input port of a switch. It can be represented formally as: NU = Λ ( I u I l ) O k is the set of wavelengths that utilizes output port k without any internal blocking. Wavelength Conversion Algorithm: Step : Let i=. Step : Choose the corresponding W i. Step : Set switch elements at stage i. If W i is a permutation, go to step. Step : For every two rows in W i which are equal to a value, say, k, perform the following on switch number k/ at stage i: If (SW = φ), then, - Set X= I l - O k = I u X Otherwise, - Compute NU - If SW <= NU, then, - Convert all wavelengths of the lower input link that are included in SW. This conversion is limited by the number of available converters (W). The resulting set of converted wavelengths is denoted by X - O k = I u (I l SW) X Otherwise, - Convert only NU wavelengths of the lower input links that are included in SW. This conversion is also limited by the number of converters (W). The resulting set of converted wavelengths is denoted by X - Buffer the packets of the lower input link that are included in SW and not converted. If no buffers are available (B=), discard the packets - O k = I u (I l SW) X

4 Step : Tag the unused outputs of Stage i, and compute the new sets of inputs for the stage i+. Step : Let i=i+. If i < n=log N, then go to step. Step. Set the switches of stage n, and stop. Given a permutation, a central controller initially can detect any internal blocking, and then it converts, if possible, some of the wavelengths, and buffers other wavelengths if required. This can all be done by the controller before the network performs the given permutation. Therefore, the network is collision-free. IV. LOOKAHEAD WAVELENGTH CONVERSION In this section, a Omega network with arbitrary connections is considered; i.e., the one-to-one mapping constraint has been relaxed. Therefore, the architecture of this network will be similar to Fig. except it is and the switch element has the general configuration shown in Fig. a. Considering the following problem, if a packet with wavelength λ i is converted to λ j to avoid collision at the first merger, and there is a packet with the same wavelength λ j at the other input of the following merger, then this causes unnecessary internal blocking due to the poor choice of the first wavelength conversion as illustrated in Fig.. Therefore, an algorithm to avoid these unnecessary wavelength conversions is to be developed. λ is converted to λ λ is converted to λ I ={λ{λ } } I I I I ={λ } I I I I 8 ={λ } I 9 I I I I I I {λ, λ } Fig. Example shows unnecessary wavelength conversion To reduce the complexity of this algorithm, the following approach is used to resolve internal blocking. Since an Omega network is well defined, it is easy to figure out the sources of all packets of any path from a source to a destination. In addition, all switch elements with lower or upper merger configuration are also known. Therefore, the central controller of this network can compute all wavelengths to be converted or buffered before forwarding these packets through the network. The Lookahead Wavelength Conversion Algorithm: O ={λ } O ={λ } O ={λ } O O O O O O 8 O 9 O O O O O O By inspecting the destinations of the packets at the head of the N input links, the controller can calculate the N paths through the network. Phase : Creating the list of sources that utilize a link. For (j=; j<n; j++) /* n is number of stages */ For (i=; i<n; i++) /* N is the number of input channels */ Compute the sources that use the output channel of (i,j). /* (i,j) is a switch element indexed by i and j */ END FOR i. END FOR j. Phase : Creating the conflict lists for every source. For (i=; i<n; i++) For (j=; j<n; j++) Compute the output channel of (i,j). If ((i,j) is MERGE) Add the sources that share the output channel to the conflict list of source i (excluding the source i itself and any redundant source). END FOR j. END FOR i. Phase : Resolving the internal blocking by wavelength Conversion and buffering. For (i=; i<n; i++) For (j=; j<k; j++) /* k is the maximum number of wavelengths per channel */ IF (Conflict List is not empty) IF (Other source has the same wavelength j) Add this wavelength j to the Collision List of source i. IF (all sources including source i not using wavelength j) Add this wavelength j to the Free List of source i. END FOR j. /* Wavelength Conversion */ Convert as many wavelengths in the Collision List to the wavelengths available in the Free List. This conversion is of course limited by the number of converters (LWC>). /* LWC is the number of lookahead wavelength converters in the central controller */ Buffer the rest of the packets (wavelengths not converted) in the Collision List. If no buffers are available (B=), discard the packets. END FOR i. The computational complexities of these phases are Nlog N, Nlog N, and Nk, respectively. Therefore, the central controller can perform the computations and identify the necessary wavelength conversion and buffering in real time. V. PERFORMANCE RESULTS This section presents the performance of a Omega network with arbitrary connections. Three configurations are considered: First, a network with limited number of buffers. Secondly, a network with limited number of lookahead wavelength conversions and finally, a network with limited

5 number of lookahead wavelength conversions in addition to limited buffering. The performances of these configurations have been analyzed by simulation. the curves increase linearly, then start to saturate due to the increase in the number of packets. The Simulator consists of two programs. The first one randomly creates, arbitrary connections and set of inputs. Each input channel has at most random packets with different wavelengths. The first program will be executed times for different arrival rates. The second program simulates the behavior of that network. Also, it reads the data generated by the first program and generates the performance parameters such as packet dropping probability and buffering probability. Fig. 8 Buffering probability versus arrival rate (limited buffers and no wavelength conversion) Fig. Dropping probability versus arrival rate (limited buffers and no wavelength conversion) Considering a network with a limited number of buffers, Fig. illustrates the packet dropping probability versus arrival rate. As expected, the packet dropping probability decreases with increasing number of buffers. Fig. 8 illustrates the probability of buffering versus arrival rate. We define the probability of buffering as: when a random packet arrives to this network, the probability that this packet will be stored in a buffer and will be forwarded in Omega network in the next switching cycle. Initially, probability of buffering for different number of buffers increases linearly with the network load because the load of the network is satisfied with the available buffers. However, at some point these curves start to saturate and then go down. The reason is that the number of packets in the network becomes very large with respect to the available buffers and some of them are dropped. Also, Fig. 8 shows that the point of saturation moves to the right with the increase of buffers. Using the concept of lookahead wavelength conversion, a considerable improvement can be achieved. Fig. 9 illustrates packet dropping probability versus arrival rate. It shows that a network with a few wavelength converters can improve considerably the network performance. Fig. illustrates packet wavelength conversion probability versus arrival rate. Initially, Fig. 9 Dropping probability versus arrival rate (lookahead wavelength conversion and no buffering) Fig. Packet wavelength conversion probability versus arrival rate (lookahead wavelength conversion and no buffering)

6 CONCLUSION Several architectures and algorithms have been introduced to alleviate the problem of internal blocking in WDM-based Omega networks. The first architecture is a collision-free Omega network based on buffering, the second one uses wavelength converters, in addition to buffering, and the last one considers lookahead wavelength conversion which eliminates unnecessary wavelength conversions. Also, the last algorithm is more appropriate for larger networks where arbitrary connections may be desired. It is shown that a few buffers and lookahead wavelength converters will considerably improve the system performance. Fig. Dropping probability versus arrival rate (lookahead wavelength conversion and buffering) A network can achieve the most improvement when both lookahead wavelength conversion and buffering are used. Fig. illustrates packet dropping probability versus arrival rate. As expected, the simulator shows the dropping probability will decrease when either the number of converters or the number of buffers is increased. Finally, Fig. shows a comparison among different configurations. It shows that the performance is worst when using random wavelength conversion. This is due to the increase of unnecessary wavelength conversion. The network can improve by adding buffers. Also, the performance will be improved further by using lookahead wavelength conversion. Finally, best performance is achieved by using both buffering and lookahead wavelength conversion. Fig. Dropping probability versus arrival rate (comparison among different configurations) ACKNOWLEDGEMENT The author wishes to thank the Research Centre in the College of Computer and Information Sciences and the College of Computer and Information Science, King Saud University for funding of this work. REFERENCES []. David K. Hunter et al., " Buffered Switch Fabrics for Traffic Routing, Merging, and Shaping in Photonic Cell Networks", IEEE Journal of Lightwave Technology, Vol., No., January 99. []. Charles A. Brackett "Is there an Emerging Consensus on WDM Networking", IEEE Journal of Lightwave Technology, Vol., No., January 99. []. Paul E. Green, Jr., "Optical Networking Update", IEEE Selected Areas in Communications, Vol., No., June 99. []. G. Hugh Song, "Asymmetric Dilation of Multiwavelength Cross- Connect Switches for Low-Crosstalk WDM Optical Networks", IEEE Journal of Lightwave Technology, Vol., No., March 99. []. Chiung-Shien et al., "Extended Baseline Architecture for Nonblocking Photonic Switching", IEEE Journal of Lightwave Technology, Vol., No., May 99. []. Antony S. Acampora and Mark J. Karol, "An Overview of Lightwave Packet Networks", IEEE Network, pp. 9-, JanuaA Wideband All-Optical WDM Network," IEEE Selected Areas in Communications, Vol., No., Junuary 989. []. Richard A. Barry and Pierre A. Humblet. "Models of Blocking Probability in All-Optical Networks with and without Wavelength Changers", IEEE Selected Areas in Communications, Vol., No., June 99. [8]. K.C. Lee and V.O.K. Li, "A Wavelength-Convertible Optical Network", IEEE/OSA Journal of Lightwave Technology, vol., No., May 99, pp [9]. K.C. Lee and V.O.K. Li, "A Wavelength Rerouting Algorithm Wide-Area All-Optical Networks'', IEEE/OSA Journal of Lightwave Technology, April 99. []. Duncan H. Lawrie, "Access Alignment of Data in an Array Processor", IEEE Trans. Comput., vol. C-, No., Dec. 9. []. George Adams, III, and Howard J. Siegel, "The Extra Stage Cube: A Fault-Tolerant Interconnection for Supersystems", IEEE Trans. Comput., vol. C-, No., May 98. []. Krishnan Padmanabhan and Duncan H. Lawrie, "A class of Redundant Path Multistage Interconnection Networks", IEEE Trans. Comput., vol. C-, No., Dec. 98. []. Anujan Varma and C. S. Raghavendra, "Reliability Analysis of Redundant-Path Interconnection Networks", IEEE Trans. on Reliability, vol. 8, No., April 989.

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