ICTON 2006 169 We.A3.3

1-4244-0236-0/06/$20.00 ©2006 IEEE

Optimum Numbers of Tunable Wavelength Converters and Internal Wavelengths in the Optical Packet Switch

with Shared FDL Buffer Huhnkuk Lim, Ki-Sung Yu, Changhwan Oh*, Chang-Soo Park**

Supercomputing Center, Korea Institute of Science and Technology Information (KISTI), Deajeon, Korea *Dept. of Computer Engineering, Seoul Cyber University (SCU), Seoul, Korea

**Dept. of I&C, Gwangju Institute of Science and Technology (GIST), Gwangju, Korea Tel: +82-42-869-0628, Fax: +82-42-869-0509, e-mail:hklim@kisti.re.kr

ABSTACT In an effort to reduce switch cost, we, for the first time, present the optimum numbers of tunable wavelength converters (TWCs) and internal wavelengths required for contention resolution of asynchronous and variable length packets, in the optical packet switch (OPS) with the shared fiber delay line (FDL) buffer. To optimize TWCs and internal wavelengths related to an OPS design cost, we proposed a scheduling algorithm for the limited TWCs and internal wavelengths. For three TWC alternatives (not shared, partially shared, and fully shared cases), the optimum numbers of TWCs and internal wavelengths to guarantee minimum packet loss are evaluated to prevent resource waste. Under a given load, TWCs and internal wavelengths could be significantly reduced, guaranteeing the same packet loss as the performance of an OPS with full TWCs and internal wavelengths. Keywords: tunable wavelength converters (TWCs), internal wavelengths, contention resolution, optical packet

switch (OPS), fiber delay line (FDL) buffer.

1. INTRODUCTION

Most of the studies on the optical packet switching have mainly been done with fixed length packets in synchronous networks. Recently, a few research works dealing with asynchronous variable length packets were reported to support internet traffic more flexibly [1, 2, 3]. However, they stayed in the suggestion of new types of scheduling algorithms and buffer structures to efficiently resolve contention of incoming packets and to reduce packet loss. In resolving contention of incoming packets to the OPS, more number of wavelength converters and available wavelengths have a benefit to decrease packet loss further under the fixed optical buffer size. Instead, system cost is increased by more number of converters and their wide conversion range.

An OPS architecture with the fixed wavelength converters (FWCs) could be considered as described in [4, 5], where FWCs could be partially or fully shared to reduce the number of FWCs. However, this could be an obstacle to fully utilize WDM technique inside the FDL buffer. Therefore, tunable wavelength converters (TWCs) are generally used for converting the wavelengths of incoming packets to specific wavelengths available in the optical buffer (i.e., optical fiber delay line (FDL) buffer) [3, 6]. In this case, the available wavelength number (L) is decided by the conversion range of TWC. The already reported works assumed that the switch resources such as TWCs and internal wavelengths are fully supported, so they only focused on finding an outgoing channel available in the destination output fiber for an incoming packet [1, 2, 3]. However, in large capacity OPS with a large number of inputs/outputs or channels per input/output, the number of TWCs and the conversion range (i.e., available wavelength channels in each FDL) become important issue because they are related to system cost. Therefore, the efforts to optimize the number and range are needed together with the reduction of packet loss.

In this paper, the optimum numbers of TWCs and internal wavelengths, guaranteeing a minimum packet loss, are investigated and evaluated for three TWC alternatives, which are not shared, partially shared, and fully shared TWC structures, with a new scheduling algorithm for the limited TWCs and internal wavelengths in OPS.

2. OPTICAL PACKET SWITCH WITH SHARED FDL BUFFER

The OPS with the shared FDL buffer consists of four major functional blocks (the input part, the FDL buffer, the output part, and the switch control unit), as shown in Fig. 1. The input part, the FDL buffer and the output part are connected by space switches.

TWCs with a conversion range of Lλλλ ,.....,, 21 in input part are employed to provide L internal wavelengths for incoming packets, which enable incoming packets to exploit one of L WDM channels in the FDL buffer. Three TWC structures in input part are possible, which is not shared, partially shared, and fully shared cases as shown in Fig. 2. TWCs can be partially shared (Fig. 2b) or fully shared (Fig. 2c), to reduce

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TWCs by the help of statistical multiplexing effect. When a channel to accommodate an arrival packet using a fiber delay line is found in the destination output fiber, nN TWCs (n TWCs per input) can be considered, to perfectly neglect the packet loss due to the lack of TWCs. To prevent resource waste connected with system cost, however, the optimized number of TWCs should be evaluated for each TWC alternative, especially for an OPS with relatively a number of N and n.

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Figure 1. Optical packet switch with the shared FDL buffer.

The shared FDL buffer has a set of FDLs (1, 2,.., i,.., B-1, B) where thi FDL represents the fiber delay line having the length iD corresponding to i times of delay line length D of the FDL buffer, 1 ≤ i ≤ B. By default, it is assumed there is an FDL with zero delay time denoted by 0D . Also, nN internal wavelengths can be considered, to perfectly neglect the packet loss due to the lack of WDM channels in the shared FDL buffer. However, the number of WDM channels possible in a fiber is limited to several tens of channels (assuming 100 GHz channel spacing). Therefore, the number of internal wavelengths should be optimized to a value under the number of WDM channels possible in a fiber, especially for an OPS with a number of inputs/outputs N and channels n per inputs/outputs.

Fixed wavelength converters (FWCs) in the output part perform wavelength conversion to a scheduled channel in an output fiber for each buffered packet. n FWCs per an output fiber should be considered. The switch control unit (SCU) controls each switching element for switch reconfiguration after packet scheduling. Routing function for each scheduled packet is performed through the management of switching elements by SCU.

Figure 2. Three possible TWC structures.

3. PROPOSED SCHEDULING ALGORITHM FOR THE LIMITED TWCS AND INTERNAL WAVELENGTHS

First, let t be the packet arrival time to the switch. By using a function Channel_Search (k), an outgoing channel

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(a) Not shared (b) Partially shared (c) Fully shared)(0 pNMq −≤≤np ≤≤0( , , ) 0=qnp ≤<0 ( , , )0=p Mq ≤<0nNM ≤ nNM ≤ nNM ≤( , , )

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ICTON 2006 171 We.A3.3

q having the smallest gap between the delayed time iDtk += and the end of last packet is found. All possible delay times provided by the FDL buffer (from 1D to BD ) is considered when searching for an available outgoing channel q. Therefore, the LAUC (latest available unscheduled channel) algorithm [6] was used for searching for an outgoing channel q with the proposed scheduling algorithm for the limited resources. If an available outgoing channel q is found at the delayed time iDtk += , it is checked whether a channel in the selected thi FDL is available. If a channel in the selected thi FDL is available, it is checked whether a TWC is available for converting the wavelength of the arrival packet, otherwise the arrival packet is lost. If a TWC is available, then the wavelength queue information of the selected outgoing channel q is updated by a function Update_Information (q), otherwise the arrival packet is lost. Finally, when an outgoing channel q is not found using all possible delay times of the FDL buffer, the arrival packet is lost.

An example of channel selection using the LAUC algorithm is described in Fig. 3. There is no an available channel to accommodate the packet at the packet arrival time tk = and the delayed time 1Dtk += . The gaps for each channel at the delayed time 2Dtk += are 12 tDt −+ , 22 tDt −+ and 32 tDt −+ , respectively ( 22 tDt −+ < 12 tDt −+ < 32 tDt −+ ). Therefore the channel 2λ having the smallest gap at the delayed time

2Dtk += is selected. However, it can be finally determined as an outgoing channel, when there is an available channel in the nd2 FDL and an available TWC.

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Figure 3. Example of channel selection using the

LAUC algorithm (The wavelength queue information for t h e d e s t i n a t i o n o u t p u t fiber of an arrival

packet is described; channel 2λ is selected).

Figure 4. Packet loss probability as a function of delay line length D (Not shared TWC structure(p=16)

was considered; N = 16, n = 16, B = 10, α = 1.2, ρ = 0.8).

4. NUMERICAL RESULTS

The OPS allowing three TWC structures in Fig. 1 was considered for simulation. The traffic model is self similar aggregate traffic with ON/OFF periods, where the ON and OFF periods represent packet bursts of packets and inter-arrival times, respectively. Each burst of packets corresponding to the ON period is treated as a single entity, and is uniformly distributed to the destination output fibers [1][3]. The length T of each period is modeled according to the Pareto heavy-tail distribution and are represented as ⎣ ⎦α/1/ UlengthTon = and

⎣ ⎦α/1' /UlengthToff = respectively, where U is a uniform random variable on ( ]1,0 and ⎣ ⎦ indicates the floor function [1]. The Hurst H and α parameters are related as H=(3-α )/2, where H has a value on [0.5, 1] for self similar traffic. The length was determined as 400 bytes to represent the minimum duration of ON periods (i.e., the minimum burst length) [1, 3].

First, the optimum delay line length of the FDL buffer was determined. By applying the proposed scheduling algorithm to the OPS with the shared FDL buffer (B = 10), the packet loss probability as a function of delay line length (D) was simulated for each different internal wavelengths (L), when the buffer depth (B), the α parameter and a load ( ρ ) was 10, 1.2 and 0.8, respectively. As shown in Fig. 4, the optimum delay line length to guarantee the minimum packet loss increased with an increase in the number of internal wavelengths (L). For 32, 64 and 128 internal wavelengths, the optimum delay line lengths were 400, 500, and 700 bytes, respectively. The optimum delay line length was not related to the structures of TWC and the number of TWCs.

Figure 5 shows packet loss probability as a function of p (the number of converters that is not shared per input fiber) or q (the number of converters that is shared for all input fibers) for each TWC structure. For not shared case (Fig. 5a), packet loss probability was almost saturated at p = 13 regardless of the number of internal wavelengths (L). This result represents that 13 TWCs per input (p = 13) was enough resource to guarantee minimum packet loss when the number of inputs/outputs (N), the number of channels per input/output (n), buffer depth (B) of the FDL buffer, α parameter and load ( ρ ) are 16, 16, 10, 1.2 and 0.8, respectively. For partially shared case (Fig. 5b), only 9 TWCs that is shared for all inputs (q = 9) could contribute to guarantee minimum packet loss, when the number of TWCs that is not shared per input is 10 (p = 10). For fully shared case (Fig. 5c),

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only 110 TWCs that is shared for all inputs (q = 110) was enough resource to guarantee minimum packet loss. Therefore, the total numbers of converters (M) to guarantee minimum packet loss were M= 1316⋅ =208 for not shared case, M = 1016 ⋅ +9 = 169 for partially shared case and M = 110 for fully shared case, respectively.

Figure 5. Packet loss probability as a function of p or q for each TWC structure (N = 16, n = 16, B = 10, α = 1.2, ρ = 0.8), (a) Not shared, (b) Partially shared (p = 10), (c) Fully shared.

Figure 6 shows packet loss probability as a function of the number of internal wavelengths (L) for each TWC structure. For each TWC structure with the number of TWCs optimized from Fig. 6, packet loss probability was simulated with an increase in the number of internal wavelengths L (each optimum delay line length matched to each internal wavelengths (L) was used for simulation). For all TWC structures, only 48 internal wavelengths (48 WDM channels) in the FDL buffer could contribute to accommodate arrival packets and to guarantee minimum packet loss.

5. CONCLUSIONS

The optimized TWCs and internal wavelengths were presented for three TWC structures in an OPS, with the proposed scheduling algorithm for the limited TWCs and internal wavelengths. Among three TWC structures, 110 TWCs in the fully shared case and 48 internal wavelengths could be the optimized resources to guarantee minimum packet loss without resource waste, when the number of inputs/outputs (N), the numbers of channels per input/output (n), buffer depth (B) of the FDL buffer, α parameter and load ( ρ ) were 16, 16, 10, 1.2 and 0.8, respectively.

Figure 6. Packet loss probability as a function of L for each TWC structure (N = 16, n = 16, B = 10, α = 1.2, ρ = 0.8).

REFERENCES

[1] L. Tančevski, S. Yegnanarayanan, G. Castanon, L. Tamil, F. Masetti and T. McDermott, “Optical Routing of Asynchronous, Variable Length Packets,” IEEE J. Select. Areas Commun., vol. 18, no. 10, pp. 2084-2093, Oct. 2000.

[2] L. Tančevski, L. Tamil and F. Callegati, “Nondegenerate Buffers: An Approach for Building Large Optical Memories,” IEEE Photon. Technol. Lett., vol. 11, no. 8, pp. 1072-1074, Aug. 1999.

[3] H. Lim and C.-S. Park, “Performance Evaluation of the Optical Packet Switch with Hybrid Buffer Structure for the Contention Resolution of Asynchronous Variable Length Packets,” IEICE Trans. Commun., vol. E87-B, no. 5, pp. 1421-1426, May 2004.

[4] F. Callegati, G. Corazza, and C. Raffaelli, “Design of a WDM optical packet switch for IP traffic,” in Proc. IEEE GLOBECOM. 2000, vol. 2, pp. 1283-1287, Dec. 2000.

[5] F. Callegati, G. Corazza, C. Raffaelli, “Exploitation of DWDM for Optical Packet Switching with Quality of Service Guarantees,” IEEE J. Select. Areas Commun., vol. 20, Issue 1, pp. 190-201, Jan. 2002.

[6] Y. Xiong, M. Vandenhoute and Hakki C. Cankaya, “Control Architecture in Optical Burst-switched WDM Networks,” IEEE J. Select. Areas Commun., vol. 18, no. 10, pp. 1838-1851, Oct. 2000.

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Number of internal wavelengths L (Optimum delay line length)

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