Performance evaluation of the OCDM/WDM technique for optical packet switches

The performance of the Optical Code Division Multiplexing/Wavelength Division Multiplexing (WDM/OCDM) technique for Optical Packet Switch is investigated. The impact on the performance of the impairment due to both Multiple Access Interference and Beat noise is studied. The Packet Loss Probability due to output packet contentions is evaluated as a function of the main switch and traffic parameters when Gold coherent optical codes are adopted. The Packet Loss Probability of the OCDM/WDM switch can reach 10−9 when M=16 wavelengths, Gold code of length L=511 and only 24 wavelength converters are used in the switch.


I. INTRODUCTION
T HE switching speed of Internet router directly impacts the performance of the entire network. To improve switching speed and the bandwidth utilization, all-optical routers such as multiprotocol MPλS, Optical Packet Switching (OPS) and so on are proposed [1] to avoid the electricity switching bottleneck. MPλS [2] uses a wavelength as an optical channel in the router, but the capacity granularity MPλS may sometimes be too large to accommodate the traffic between node pairs. In the OPS [3]- [5], the label is attached to the head of a packet and routing of packets is based on label switching. The throughput is restricted because the packets are carried in serial on the same wavelength. Optical Code Division Multiplexing (OCDM) paths were proposed in [6]- [8] where each bit in the packet, including the header is encoded by a specific optical code. The OCDM paths can overlap with each other and that enables the router to process packets in parallel. To achieve satisfactory performance in the OCDM system, coherent timespread optical-Code (OC) generation and recognition based upon Superstructure Fiber Bragg Gratings (SSFBG) using the gold code is employed [9]- [13]. The combination of OC-and wavelength-based routing has been presented in [6] where it is shown that the joint use of WDM/OCDM improves the efficiency of bandwidth utilization and obtains high flexibility in providing stable service owing to its independence of burst duration time and a simple architecture with nonbuffer operation.
In this paper we propose an analytical model, validated by simulation, to dimension the Optical Codes on any wavelength of a WDM/OCDM system so that the Packet Loss Probability due to both Multiple Access Interference (MAI) and beat noise is limited to a given threshold value. Next we evaluate the V. Eramo [14] using Gold Optical Codes dimensioned according to the proposed analytical model. The output packet contentions in the switch are solved in both the code and wavelength domains. The organization of the paper is as follows. In Section II we describe the WDM/OCDM switch in question. The scheduling algorithm according to which the wavelength and code conversions are performed is described in Section III. We discuss the effectiveness of the WDM/OCDM technique in solving output packet contentions in Section IV. Our main conclusions and further research topics are discussed in Section V.
II. WDM/OCDM OPTICAL PACKET SWITCH ARCHITECTURE We consider the WDM/OCDM optical packet switch with N Input/Output fibers (IF/OF) reported in Fig. 1. Each fiber supports M wavelengths denoted λ 1 , · · · , λ M . On each wavelength up to F packets are carried out by using Optical Code Division Multiplexing. Let L be the code length and {OC k , k = 1, . . . , F } the set of Optical Codes (OC) of a wavelength on which the packets can be carried. An input (or output) channel is identified by the triple (i, λ j , OC k ), where i (i = 1, · · · , N) identifies one of the input (or output) fibers, λ j (j = 1, · · · , M) identifies one of the wavelengths on that IF (OF) and OC k (k = 1, · · · , F ) identifies one of the optical codes on that wavelength.
The operation mode of the architecture is synchronous, meaning that all arriving packets have a fixed size and their arrival on each input channel is synchronized on a time-slot basis. The synchronization operation, not shown in Fig. 1, is realized by means of synchronizers located at the ingress of the switch.
The WDM/OCDM optical packet switch illustrated in Fig.  1 performs the following operations: i) the packets are wavelength demultiplexed and code decoded by means of one WDM demultiplexer and M ·F OC decoders for each IF; ii) the unit control, not shown in Fig. 1, processes the packet headers and decides which packets have to be wavelength converted and which Output Wavelength Channels (OWC) and Output Optical Codes (OOC) are assigned to the packets to transmit; iii) the Switching Fabric SF c routes the packets towards either the bank of r Wavelength Converters (WC) or the Output Switching Fabrics SF i (i = 1, · · · , N) according to decisions taken by the control unit; iv) the converted packets are routed towards the SF i (i = 1, · · · , N) where in output the packets are code and wavelength multiplexed by means of M · F OC coders and one WDM multiplexer.
One of the advantages of the proposed OPS is to reduce the number of WCs used because the control algorithm [15]   first tries to solve the contention in code domain by changing the packet code and only if this operation is unsuccessful, the contention is solved in wavelength domain by using one WC of the shared pool. This strategy, preferring the use of passive devices like OC decoders and coders rather than active elements like WCs, allows for the reduction of the switch cost. In CC phase, illustrated in Fig. 2, the packets that can be directed without wavelength conversion are scheduled and the contentions are resolved by changing the code. In WC phase, described in Fig. 3, the packet contentions are resolved in the wavelength domain by using the WCs.
In CC phase, for each wavelength λ j (j = 1, . . . , M), the control unit randomly schedules up to F packets, chosen among the packets arriving on wavelength λ j , to be transmitted without wavelength conversion. The set Λ i,j initially contains all the output channels on wavelength λ j and optical codes OC k (k = 1, . . . , F ) which are used to forward without wavelength conversion up to F packets belonging to I i,j set. The following actions are performed by the control unit for each wavelength λ j : i) one packet a and one output channel (i, λ j , OC k ) are randomly selected from sets I i,j and Λ i,j respectively; ii) the packet is scheduled to be forwarded on output channel (i, λ j , OC k ); iii) the sets I i,j and Λ i,j are updated by removing the elements a and (i, λ j , OC k ) respectively. The CC phase complexity is O(F · M ) because in the worst case at the least one operation for each output channel is performed.
In WC phase the control unit tries to forward with wavelength conversions the remaining packets on output channels not used in CC phase. The packets not scheduled and the free output channels for i − th OF, are stored in I i and Λ i respectively. The following actions are performed by the control unit until either I i or Λ i (or both) are empty and one WC is available: i) one packet a and one output channel (i, λ j , OC k ) are randomly selected from sets I i and Λ i respectively; ii) the packet is scheduled to be forwarded on output channel (i, λ j , OC k ); iii) the sets I i and Λ i are updated by removing the elements a and (i, λ j , OC k ) respectively; iv) the available number r a of WCs is decremented by one.  Before the end of WC phase, the control unit checks if there are packets in I i which are yet to be scheduled and in this case they are discarded. The WC phase complexity is O(min(r, M · F )) because in the worst case at the least one operation is performed for each output channel until WCs are available. Because the operations in CC and WC phases are performed for each OF, the computational complexity of the proposed scheduling algorithm equals O(N · F · M ).

IV. NUMERICAL RESULTS
This section will be devoted to illustrating the main results on the performance of WDM/OCDM switches as a function of the main traffic and switch parameters when the Optical Codes are dimensioned according to the procedures illustrated in [18]- [20].
First of all we show in Fig. 4 the Packet Loss Probability P noise loss due to MAI, Primary Beat Noise (PBN) and Secondary Beat Noise (SBN) versus the number F of OCs supported on each wavelength. Notice that P noise loss is the probability that at least a bit of a packet is affected by an error due to MAI and beat noise [15]. We have evaluated P noise loss for offered traffic p varying from 0,3 to 0,9 and packet length H equal to 500 bytes. The code length L is chosen to be 511. For each value yes I i =∪ j I i,j I i ≠{∅} and Λ i ≠{∅} and r a ≠0 •Select randomly a channel (i,λ j ,OC k )∈ Λ i • Select randomly a packet a∈ I i of traffic we report two curves: the first one is obtained when the receiver threshold th (s) i (i = 2, · · · , F ), depending on the number i of packets carried on each wavelength, is evaluated according to the procedure illustrated in [15], the second one reports the results when the threshold th (OT ) i (i = 2, · · · , F ) is chosen according to the procedure illustrated in [18]. From Fig. 4 you can notice how, when a given P noise loss is fixed, a higher number of codes can be carried on each wavelength if the receiver threshold optimization is performed. For instance, when p equals 0,5 and P noise loss is around 10 −7 , we have that 4 and 10 codes can be carried on each wavelength in the cases in which the thresholds th (s) i and th (OT ) i (i = 2, · · · , F ) are used respectively.
The choice of an optimized receiver threshold impacts on the OCDM/WDM switch performance allowing for a reduction of the Packet Loss Probability P opc loss due to output packet contentions [15]. P opc loss is reported in Fig. 5 as a function of the number r of used WCs for H=500 bytes, N =8, M =16, L=511 and p=0,3, 0,5, 0,7. The number F of used OCs for each wavelength is chosen so that the threshold Packet Loss Probability P noise loss due to MAI and beat noise is not greater than 10 −9 . For each value of traffic, we report P opc loss when the receiver threshold th (i = 2, · · · , F ) are used. We can notice that better performance is obtained when the threshold is chosen according to the procedure illustrated in [15]. For instance when p=0,7 and r=28, P opc loss equals 9, 58 * 10 −7 and 3, 87 * 10 −10 in the cases in which the receiver thresholds th (i = 2, · · · , F ) are used respectively. Obviously the better performance is due to the higher number of codes that is possible to carry on each wavelength and consequently a higher probability in solving  a function of the number r of used WCs. The curves labeled with OT report V. CONCLUSION The WDM/OCDM optical packet switch performance has been analytically investigated by introducing an analytical model to dimension the optical codes carried on each wavelength. The dimensioning has been performed in the cases in which a simple and an optimized receiver threshold are used. We have shown that the switch can reach acceptable performance, in particular for offered traffic p equal to 0,5, the packet loss probability equals 10 −9 when the number M of wavelengths equals 16, the code length L is 511 and only 24 wavelength converters are used.