Strictly Nonblocking WDM Cross-connects

Abstract

Using (WDM) technology, an optical network can route multiple signals simultaneously along a single optical fiber by encoding each signal on its own wavelength. If the network contains places where multiple fibers connect together and signals are allowed to be moved from any of the incoming fibers to any of the outgoing fibers, then the network is said to contain cross-connects. More precisely, a $k_1\,\times\,k_2$ WDM cross-connect has k1 input fibers and k2 output fibers. Each of the k1 input fibers supports the same n1 input wavelengths and each of the k2 output fibers supports the same n2 output wavelengths. Since a signal on input wavelength $\lambda$ can be routed from its input fiber to an output fiber such that it arrives on the output fiber using wavelength $\gamma$, where $\lambda \neq \gamma$, the cross-connect must be capable of performing wavelength conversion. Along any fiber in the cross-connect a device called a wavelength interchanger can be inserted to perform wavelength conversion. In other words if the path of a signal from an input fiber to an output fiber passes through a \wins, then the wavelength of the signal can be changed to any wavelength that is not already in use along the fiber leaving the wavelength interchanger. Given the high cost of \wisns, the overall cost of a \CC{k_1}{k_2} is minimized by reducing the number of \wis in the cross-connect. However, a desirable property for a cross-connect C is for C to always be able to provide a route (and wavelength conversion) for any valid demand from any pair of input and output fibers regardless of the routes of other demands currently routed in C. If C has this capability then it is said to be strictly nonblocking. For most of this paper we consider a demand to be a request for a connection from an input fiber to an output fiber such that the connection starts on a specified input wavelength and leaves the c on a second specified wavelength. Using this demand model, we consider cross-connects for which $k_1$ is not necessarily equal to $k_2$ and the number $n_1$ of supported input wavelengths can differ from the number $n_2$ of supported output wavelengths. Without loss of generality we assume that $k_1 \leq k_2$ and present a family of \snob \CCns{k_1}{k_2}s that use \Opt \wisns. For the case when $k_1 = k_2=k$ and $n_1 = n_2$, we prove that this is optimal. For cs where $n_1$ is not necessarily equal to $n_2$, we show that if there is at most one wavelength interchanger on any path from an input fiber to an output fiber, \Opt \wis are optimal. Finally, we consider a more flexible demand model where $k_1 = k_2$ but the input and output wavelengths are not specified as part of the demand. We show that $2k-1$ \wis are still necessary for any \snob \CC{k}{k}.