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A Novel Optical Burst Switched Core Node with Wavelength Converters and Deflection Routing

Ahmed S. Samra, Ahmed M. Abo-Taleb

Department of Electronics & Communication, Faculty of Engineering, Mansoura University, Mansoura, Egypt

Email: [email protected]; [email protected]

Waleed M. Gaballah

Department of Computer Engineering, Al-Baha Private Collage of Science, Al-Baha, Saudi Arabia

Email: [email protected] hotmail.com

Abstract— The main commonly problem that arises in Optical Burst Switching (OBS) networks is a burst contention. Wavelength conversion and deflection routing are the most important switch fabric strategies to resolve this contention. In this paper, we study a mathematical model for a new proposal optical burst switching core node architecture. A performance measurement has been investigated by analytic the burst loss probability using steady-state occupancy probabilities and Poisson traffic model arrivals. Performance analysis results are presented at different values of the mean burst arrival rates with a core node design parameters such as wavelength conversion capability and deflection routing.

Index Terms— Optical Burst Switching (OBS), wavelength conversion capability, burst loss probability, deflection routing

I.  Introduction

Optical burst switching (OBS) networks are designed to achieve an intermediate solution between Optical Circuit Switching (OCS) and Optical Packet Switching (OPS) networks [1,2]. The OBS network transmits bursts between optical switching nodes that are interconnected via fiber links. Each fiber link supports multiple wavelength channels that assigned independently using Wavelength Division Multiplexing (WDM) [3,4]. Each burst has two parts: Control Burst (CB) and Data Burst (DB). The basic principle is to transmit the CB ahead of the DB by an offset time in order to configure the switches along the burst’s route [5]. Optical switching nodes in an OBS network can either be edge nodes or core nodes [6].  The edge node may be ingress or egress node. The main ingress edge node task is to aggregate the data packets into bursts with an appropriate assembly algorithm [7]. The egress edge node is the destination network node that disassembled bursts into original data packets. While at the core node, the switch is configured to bypass the DB upon its arrival to the destined port processed using appropriate reservation protocol [8]. The core switches consist of an optical cross connect (OXC) and a switch control unit (SCU) [9]. When the SCU receives a CB, it identifies the intended destination and refers the signaling processor to find the intended output port. If the output port is available, when the data burst arrives, the SCU configures the OXC to let the DB pass through. If the port is not available, contention occurs as more than one DB tries to reserve the same wavelength channel on an outgoing link. Then, the OXC is configured to solve that contention depending on the contention resolution policy implemented in the network.

When the contention occurs in the OBS network, one of contending DB is allowed to reserve the wavelength channel. For the other data bursts, one or a combination of contention resolution technique can be applied. The efficient contention resolution strategies are importance in the OBS networks [10], such as wavelength conversion [11], fiber delay lines [12], burst segmentation [13], and deflection routing [14]. The wavelength conversion and deflection routing techniques were shown to be the most effective contention resolution strategies for OBS networks [15-17]. Wavelength conversion is needed to switch the contended burst into other not occupied output wavelength channel at the same output fiber link. The contended burst redirected into another output link of the node using deflection routing. Otherwise, when the output port occupied with other bursts, and there is no any contention resolution mechanism available, then the burst will be blocked.

Various OBS core node architectures are investigated depending on the distribution of contention resolution mechanisms [18].  The aim of this paper is to numerical analyze a new proposal OBS core node architecture with wavelength converters and deflection routing mechanism, presuming the mathematical model in M.H.Morsy et al. [19] to measure the average burst loss probability performance. Unlike the mathematical model in the previous model where the OBS core node performance has been studied with wavelength conversion only using Dedicated Per Input Line (DPIL) switch architecture. In our model architecture that supports Dedicated Per Input/Output Lines wavelength converters and deflected routing switching matrix.

The remainder of this paper is organized as follows. In section 2, we present a detailed description of our proposed model. Including the model architecture, the model assumptions, the state diagram, and the model equations. Section 3 is devoted to representing and discussing results of the derived performance measures for the proposed mathematical model. Finally, we conclude in section 4.

II.  Model Description

A.  The Model Architecture

A variety of optical switch core node architecture is possible depending on the placement and availability of contention resolution mechanisms. For example, wavelength converters may be tunable wavelength converters (TWC) or fixed ones. It can be placed at the input and/or output ports of an optical burst switch. Moreover, each port of the switch may be equipped with its own dedicated converters, or the converters may be shared by all ports [20].

The OBS intermediate node switch architecture is shown in figure 1. The node is equipped with an internally N input/output fiber (IF/OF) lines. For each incoming fiber link, there is an optical multiplexer which separates the incoming optical signal into w wavelength channels and then kept separated until they will be again multiplexed at the output fiber ports. There are r TWCs implemented at each one of the input/output fiber lines, where only r wavelengths from a total w wavelength can be converted to any other free wavelength, r ≤ w, while the remaining  w-r wavelengths are nonconvertible ones. The node is equipped internally with a non-blocking switching matrix with size wN×wN.

             Fig. 1. The OBS core node architecture

In such architecture, there are two stages. In the first stage; after de-multiplexing phase, the burst might be sent to the converters’ pool or not depending on the need of wavelength conversion. If the incoming burst requests a busy wavelength, the burst contends and then it will be converted if available. If the contended burst has not wavelength conversion capability, it will be deflected to some other port in the network. There are N-1 wavelengths in each fiber link are dedicated for deflection routing, were N ≤ w. the switching matrix selects the right wavelength within the interface. In the second stage, the deflected bursts at the output ports will be sent to other converters’ pool or not depending on the need of wavelength conversion.

B.  The Model Assumptions:

Some assumptions are made for the traffic pattern in the switch:

Such model is based on a Continuous-Time Markov Chain (CTMC) [21], assumes Poisson arrivals (rate α bursts/burst time) and exponential service times (average service time 1/µ time unit) which is equal to the average duration of the data burst, or the burst length, and it is constant in our analysis and equal to 50 per burst time.

The output port for the incoming burst is uniformly distributed among all available output fiber ports. Thus, the behavior of a single output port is sufficient to model instead of considering all output ports of the node.

An M/M/w/w queue with limited server accessibility is modeled at the output port. For that queue, there are w servers in the system simulating the available w wavelengths in the node.

The M/M/w/w queue is also characterized by a maximum number of users in the system equal to w where there is no buffering capability in the node which is modeled by a queue length equal to zero.

Our proposal model assumes the availability of 16 wavelengths.

The node conversion capability can be defined as \"γ=\"  \"r\" /\"w\"  .  If =0, this means that the node has no wavelength conversion capability. If =1, the node has full wavelength conversion capability and the w wavelengths are fully accessible. Whereas if 0 <<1, the node has a partial wavelength conversion capability and the incoming burst will be blocked if the required wavelength is busy and nonconvertible.

A deflection routing probability parameter \"p=\"  \"N-1\" /\"w\" , (0≤p≤1) is introduced in our analysis. The bursts which arrive at the node are deflected to all its output ports with the same probability (pk). Therefore, we consider the deflection probability of one of N-1 remaining output ports, p2= …….=pN-1=pN, and ∑_\"k=2\" ^\"N\" ▒〖{\"p\" _\"k\" │\"k≠i\" }\"=p\" 〗 , where N is the number of output ports and p is the total of deflection routing probabilities.

The model does not make any approximation for the distribution of the traffic arrivals.

C. State Diagram:

Figure 2 presents the general state diagram of the OBS network model. The state k where k{0,1,2,……., w} represents the node when it is currently serving k bursts.

This state diagram represents a birth-death process of the Markovian model of M/M/w/w queue with the adjusted birth rate.

In the first stage; the birth rate ηk1 of this chain at state k1 (the transition rate from state k1 to k1+1) is given by:

Birth Rate = arrival rate × [probability that an arrival requests a free wavelength+(probability that an arrival requests a busy wavelength × probability that the requested wavelength is convertible)+( probability that an arrival requests a busy wavelength × probability that the requested wavelength is non-convertible × probability that an arrival deflected)], that is

\"η\" _\"k1\"  \"= \" \"α\" _\"1\"  ([(\"w-\" \"k\" _\"1\" )/\"w\" ]\"+ (\" \"k\" _\"1\"  \".\"  \"α\" _\"1\" /\"w\"  \")+ (\" \"k\" _\"1\"  \".(1-\" \"γ\" _\"1\"  \") .p\" )                          (1)

The death rate at state k1 (transition rate from state k1 to k1-1) is set as k1.µ.

The deflected bursts from the first stage will be rerouted to the second stage with a mean rate α2 given by:

α2 = α1 . (1-BI)                                                                  (2)

where BI is the average burst loss probability for the first stage. The birth rate ηk2 for the second stage will be:

Birth Rate = arrival rate × [probability that an arrival requests a free wavelength+(probability that an arrival requests a busy wavelength × probability that the requested wavelength is convertible)]

\"η\" _\"k2\"  \"= \" \"α\" _\"2\"  ([(\"w-\" \"k\" _\"2\" )/\"w\" ]\"+ (\" \"k\" _\"2\"  \".\"  \"α\" _\"2\" /\"w\"  \")\" )                                                 (3)

D. The Model Equations:

Now, a mathematical analysis is performed to evaluate the model performance measurement; namely, the average burst loss probability Pb. First, we could find the steady-state probabilities k (k= 0,1,2,…w) of the Markov chain explained in the previous part in figure 2, which actually is the steady-state probability that the Markov chain corresponding to Output Fiber (OF) in state k.

The cut equations from the state diagram in fig.2 are as follows:

\"π\" _\"1\"  \"=\"  \"η\" _\"0\" /\"μ\"  \"π\" _\"0\"

\"π\" _\"2\"  \"=\"  \"η\" _\"1\" /\"2μ\"  \"π\" _\"1\"  \"     \" or       \"π\" _\"2\"  \"=\"  \"η\" _\"1\" /\"2μ\"   \"η\" _\"0\" /\"μ\"  \"π\" _\"0\"

\"π\" _\"3\"  \"=\"  \"η\" _\"2\" /\"3μ\"  \"π\" _\"2 \"     or  \"π\" _\"3\"  \"=\"  \"η\" _\"2\" /\"3μ\"   \"η\" _\"1\" /\"2μ\"   \"η\" _\"0\" /\"μ\"  \"π\" _\"0\" ……                                      (4)

Repeating this until reaching an expression for the steady-state probability k  in terms of 0

\"π\" _\"k\"  \"=\" {█(\"η\" _\"0\" /\"μ\"  \".\" \"π\" _\"0\"  \"                  ,k=1\" @(∏_\"i=0\" ^\"k-1\" ▒\"η\" _\"i\"  )/(\"k!\" 〖\"(μ)\" 〗^\"k\"  ) \"π\" _\"0\"  \"               ,k≥2\" )┤                                              (5)

but,\" \" ∑_\"k=0\" ^\"w\" ▒〖\"π\" _\"k\"  \"=1\" 〗 then, \"π\" _\"0\"  \"=\"  \"1\" /(\"1+\"  \"η\" _\"0\" /\"μ\"  \"+\" ∑_\"j=2\" ^\"w\" ▒〖\"1\" /(〖\"(μ)\" 〗^\"j\"  \".j!\" ) \".\" ∏_\"i=1\" ^\"j-1\" ▒\"η\" _\"i\"  〗)                       (6)

substituting from (6) in (5), the steady-state probability k can easily evaluate as next:

\"π\" _\"k\"  \"=\" {█((\"η\" _\"0\" /\"μ\" )/(\"1+\"  \"η\" _\"0\" /\"μ\"  \"+\" ∑_\"j=2\" ^\"w\" ▒〖\"1\" /(〖\"(μ)\" 〗^\"j\"  \".j!\" ) \".\" ∏_\"i=1\" ^\"j-1\" ▒\"η\" _\"i\"  〗) \"                  ,k=1\" @((∏_\"i=0\" ^\"k-1\" ▒\"η\" _\"i\"  )/(\"k!\" 〖\"(μ)\" 〗^\"k\"  ))/(\"1+\"  \"η\" _\"0\" /\"μ\"  \"+\" ∑_\"j=2\" ^\"w\" ▒〖\"1\" /(〖\"(μ)\" 〗^\"j\"  \".j!\" ) \".\" ∏_\"i=1\" ^\"j-1\" ▒\"η\" _\"i\"  〗) \"                ,k≥2\" )┤                           (7)

The average burst loss probability Pb for the first stage BI is the probability that a burst arrival is being blocked or dropped on the average, and can be calculated as follows:

\"B\" _\"I\"  \"=(1-p)[\" \"π\" _\"1\"  \".\"  \"1\" /\"w\"  \".\" (\"1-\" \"γ\" _\"1\"  )\"+\" \"π\" _\"2\"  \".\"  \"2\" /\"w\"  \".\" (\"1-\" \"γ\" _\"1\"  )\"+⋯+\" \"π\" _\"w-1\"  \".\"  \"w-1\" /\"w\"  \".\" (\"1-\" \"γ\" _\"1\"  )\"+\" \"π\" _\"w\"  \"]\"

\"B\" _\"I\"  \"=(1-p)[\" \"π\" _\"w\"  \"+\" ∑_\"i=1\" ^\"w-1\" ▒〖\"π\" _\"i\"  \".\"  \"i\" /\"w\"  \".(1-\" \"γ\" _\"1\"  \")]\" 〗                                         (8)

Deflection routing is not applied (with a probability of 1-p), and the first term indicates the case when an arriving burst finds all w wavelengths channels occupied. On the other hand, the second term considers the case when there are idle channels on the output port but the burst requires conversion and it is dropped due to the lack of a suitable wavelength conversion 1-γ1.

The average burst loss probability for the second stage BII will be:

\"B\" _\"II\"  \"=\" \"π\" _\"w\"  \"+\" ∑_\"i=1\" ^\"w-1\" ▒〖\"π\" _\"i\"  \".\"  \"i\" /\"w\"  \".(1-\" \"γ\" _\"2\"  \")]\" 〗                                                 (9)

Then, the total average burst loss probability for the both stages:

\"P\" _\"b\"  \"=\" \"B\" _\"I\"  \"+\"  (\"α\" _\"2\"  \"×\" \"B\" _\"II\" )/\"α\" _\"1\"   \" \"                                                                    (10)

III. Results and Discussion

In this section, we will illustrate the performance analysis results that present the dependency of the blocking probability of OBS core node on the average arrival rate α, the wavelength conversion capability γ, and the deflection routing capability p in different cases.

Figure 3 describes the variation of the overall blocking probability when increasing the average arrival rate corresponding to the wavelength capability in the two stages of the model and the deflection routing capability.

Obviously the more traffic arrivals the more loss probability. The blocking probability decreases significantly as we use contention resolution mechanisms. While burst traversing the network, in the case of contention of the bursts, some bursts will be either wavelength-converted at the contending node or will be deflected to some other node in the network. The decision for the wavelength conversion of the burst or deflection of the burst will be taken as in the four cases demonstrated as follows:

Case 1, in this case, the arrival burst has no free wavelength and it has not any contention resolution capability (γ1=0, p=0) to avoiding the burst blocking. The blocking probability increases rapidly as increasing the number of burst arrivals.

In case 2, the arrival burst which has no free wavelength can be full wavelength convertible at the first stage (γ1=1). Without deflection routing (p=0) the contended burst can go out with reasonable burst contention probability. The wavelength converters significantly reduce the mean burst blocking probability, particularly at low loads. This case indicates a good consistency with a previous model proposed by Morsy et. al.

In case 3, the arrival burst is blocked and it cannot be convertible, then it is deflected to another link (γ1=0, p=1). The deflected burst not wavelength convertible at the second stage (γ2=0) if there is no free wavelength in the alternate link. Deflection routing marginally outperforms the wavelength conversion as a method to reduce the burst blocking probability compared to the previous case. The blocking probability as the same as the previous case at low loads. However, at high loads, the deflection routing is more effective than wavelength conversion to reduce the burst blocking probability.

Case 4, the arrival burst that is blocked with no wavelength conversion at the first stage (γ1=0) is deflected to another link (p=1). If the deflected burst has no free wavelength in the alternate output link, it will be wavelength convertible (γ2=1). It is clear that the wavelength conversion existence with the deflection routing gives greatest performance gain than other cases overall traffic loads. Therefore, a combination of both contention resolution methods reduces significantly the burst blocking probability especially at low burst arrivals with good results.

IV. Conclusion

Computing the blocking probability of bursts at the core node in an OBS network is illustrated. An analytical model has been created for a proposed new OBS core node architecture to evaluate the switch performance with wavelength conversion and deflection routing as contention resolution mechanisms. Performance analysis results are presented at different values of network average arrival rates at different cases corresponding to the existence of wavelength conversion and deflection routing capabilities. In the first case, the switch has not any contention resolution mechanism, in order to evaluate their individual influence on the switch performance. The result is a high burst loss. In other three cases, the contended bursts will be either wavelength-converted or will be deflected to some other node in the network. From our results, it is clear that using the burst contention resolution mechanism reduces the burst loss probabilities, particularly at low traffic. It can also be observed that using the deflection routing consistently reduces the blocking probability more than using the wavelength converters, especially at high burst arrivals. However, a combination of both methods is required to achieve the greatest performance benefits overall burst arrival rates.

References

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Ahmed Shaban Samra was born in Mansoura, Egypt in 1954. He received the BSc and the MSc Degree in communications engineering from Menoufia University 1977, 1982 respectively, and the PhD degree in optical communications and integrated optics from ENSEG, Grenoble, France in 1988. He is now a professor at the Electronic and Communication dept., Faculty of Engineering, Mansoura University. His research interests are in the field of optical communications and optical measurement techniques.

Ahmed M. Abo-Taleb was received the BSc and the MSc Degree in communications engineering in 1977, 1980 respectively, and the PhD degree in communications from Queen’s University, Kingston, Canada, in 1985. He is now a lecturer at the Electronic and Communication dept., Faculty of Engineering, Mansoura University. His research interests are in the field of computer switching networks and queuing systems.

Waleed Mohamed Gaballah  was born in Mansoura, Egypt in 1977. He received the BSc. in communication and electronics engineering, Msc. in communications engineering from Mansoura University, Egypt, in 1999, 2003 respectively. He is now a lecturer at Al-Baha Private Collage of Science, Saudi Arabia. His research interests are in the field of optical communications, and optical switching networks.

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