Approximate analysis of limited-range wavelength conversion all-optical WDM networks G. Shen * , T.H. Cheng, S.K. Bose, C. Lu, T.Y. Chai, H.M.M. Hosseini Network Technological Research Centre, Nanyang Technological University, Nanyang Avenue, Singapore, Singapore 639798 Received 3 November 1999; revised 3 May 2000; accepted 5 May 2000 Abstract We use the analytical model for multi-®bre WDM networks to approximately analyse the network performance of limited-range wave- lengthconversionWDMnetworks.Inaddition,wedevelopasimpleanalyticalmodelformulti-®brenetworkswithlimited-rangewavelength conversion capability by combining the multi-®bre network model and the limited-range wavelength conversion network model. Extensive calculations based on these models have been done for networks with a single light-path and with different wavelengths on each link. Based on the results obtained, we conclude that our analytical model is simple and yet can effectively analyse the impact of wavelength conversion range and ®bre number on the network performance. q 2001 Elsevier Science B.V. All rights reserved. Keywords: WC; NWC; PWC; Multi-®bre; Analytical model; Blocking probability; Conversion degree; Conversion percentage 1. Introduction Wavelength routed all-optical WDM network has been researchedwidelybecauseofitsbene®tssuchashugetrans- mission capacity, good routing ¯exibility and good protocol transparency [1±3]. There are a few ways to classify WDM networks.Basedonthewavelengthconversioncapabilityof the nodes, a WDM network can be classi®ed as non-wave- length continuous NWC), wavelength continuous WC) or partial wavelength conversion PWC) WDM. In an NWC network, each node is equipped with the full number of wavelength converters and each converter has the full- range wavelength conversion capability. We can assign wavelengths to a light-path link by link just like the process in a public switched telephone network. Unlike the NWC WDMnetwork,thereisnowavelengthconverterintheWC- WDM network. Therefore, the same wavelength has to be used in all the hops of a light-path from the source node to the destination node. This limitation is often called the wavelength continuity constraint. PWC is an alternative that has been proposed recently because of the high cost of wavelength converters. In this kind of network, each node only has limited wavelength conversion capability. A partial wavelength conversion network, in which the wavelength converters in each node were shared by different links, was proposed in Ref. [4]. In order to assign the wavelength converters and the wave- lengths to the links ef®ciently, a heuristic algorithm with a super-graph was proposed in Ref. [4]. Sparse converter placement is another kind of partial wavelength conversion scenario, which was initially studied in Ref. [5]. In this type of network, some nodes are equipped with the full number ofwavelengthconverters,whileothernodesdonothaveany wavelength conversion capability at all. For simplicity, we shallcallthenodesintheformercaseNWCnodesandthose in the latter case WC nodes. Consider the practical dif®cul- ties in the fabrication of high-performance wavelength converters, some researchers have proposed the limited- range wavelength conversion network, in which the wave- lengthconverterscanonlyconvertawavelengthtoalimited number of neighbouring wavelengths. In Ref. [6], an analy- tical model has been proposed to recursively compute the blockingperformanceofthiskindofnetwork.However,the author only applied the method to single light-path networks. Also, for ring and mesh networks, only simula- tions were done. Another analytical model, which can be used to analyse irregular mesh networks, was proposed in Ref.[7].Themodelisalsobasedonarecursivecomputation process and it makes use of some approximations to obtain the blocking probabilities. Another analytical model that makes use of the BPP/M/1/1 queuing model and allows Computer Communications 24 2001) 949±957 0140-3664/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII:S0140-366400)00234-6 www.elsevier.com/locate/comcom * Corresponding author. Tel.: 165-7905362; fax: 165-7926894. E-mail addresses: egxshen@ntu.edu.sg G. Shen), ethcheng@ntu.e- du.sg T.H. Cheng), eskbose@ntu.edu.sg S.K. Bose), eclu@ntu.edu.sg C. Lu).