Limited-Range Wavelength Conversion Modeling for Asynchronous Optical Packet-Switched Networks Raul C. Almeida Jr, Joaquin F. Martins-Filho and H. Waldman Departamento de Eletrônica e Sistemas, Universidade Federal de Pernambuco, Recife, Brazil. Abstract — Packet contention is a very important issue in optical packet switching networks. This paper analyzes asynchronous optical packet switches when wavelength conversion is used as contention resolution mechanism. A Wavelength converter can convert one wavelength to another and consequently improve the network performance. In practical systems, a wavelength converter normally has a limited range of wavelength conversion capability. In this paper we propose a Markov model that enables the calculation of packet blocking probability for asynchronous optical packet switches equipped with limited-range wavelength converters. The analytical model is based on an infinitely fine input granularity assumption and it is shown to present a good approximation with simulation results. Index Terms — Optical packet switching, contention resolution, wavelength conversion, Markov modeling. I. I NTRODUCTION In a WDM optical packet-switched network, data packets are modulated on a specific wavelength and may travel several hops before reaching their destinations. In each hop, a switching node is used to direct the packet to the correct output fiber link. Output contention occurs when arriving packets on the same wavelength are designed to be at the same output port overlapped in time. In optical packet switching, there are three ways to handle output contention: delay-line buffering [4],[5]; deflection routing [6],[7]; and wavelength conversion [8]-[10]. These techniques exploit respectively the time, space and wavelength domains [2], [3]. Such techniques may still be combined [7][13]. In this paper we study the third method: the wavelength domain exploitation. Such domain is unique in the field of optics, which is based on the fact that several wavelengths run on the same fiber link that connects two optical switches. Therefore, on the arrival of a new packet, if its wavelength is already being used on the destination output link, it may be converted to another potential free wavelength, such that the packet can still be transmitted . In the literature, it is common to assume full-range wavelength conversion capability, i.e., a packet can be converted to any available wavelength on the desired output link. However, since to be able to optically converting to the full range of wavelengths is still a costly task, as well as a wide range wavelength conversion may slow down the switching speed, it is important to investigate limited-range wavelength conversion. In the literature, the existent works that focus on studying and modeling the contending methods are usually based on synchronous networks [8]-[12]. In this paper we propose an analytical model that enables the calculation of packet blocking probability in asynchronous optical packet switches when limited-range wavelength converters are used. We also conducted simulations to validate our analytical model. The analytical model is based on an infinitely fine input granularity assumption and it is shown to approximate quite well the simulation results. Analytical models are very useful mainly for low packet blocking probability, where simulations become time expensive. The paper is structured as follows: Section II describes the basic considerations used in our analyzes. Section III exploits full and limited-range wavelength conversion capabilities and presents our analytical model. Finally, in Section VI we make our conclusions. II. BASIC C ONSIDERATIONS This Section will present the basic considerations used in our analyses. A. The Traffic Model As arriving traffic, it will be assumed that the input channels are independent of each other and that each of them has the same input load ( r ). The traffic partitioning inside the switch will be considered uniform, i.e., a packet arriving at any input fiber has the same probability of being transmitted to any output, which can be written as N p j i 1 , = ; N j i , , 2 , 1 , K = . Finally, the traffic pattern considered in this paper is unicast, which means that each packet is destined for only one output fiber. A.1 Simulations For the simulations, it will be assumed that each input channel may be in two distinct states, as illustrated in Fig. 1: a) Active state, when a packet is present in the input