Constructions of Multicast Flexible Delay Lines and Optical Multicast Switches with 100% Throughput

Optical queues, usually constructed by optical switches and fiber delay lines (SDL), are the key elements for conflict resolution in optical packet switching. It is recently shown in the work of Chang et al. (2006) that several optical queues constructed by SDL elements are indeed infinite dimensional switches in time and they can be constructed by many classical constructions in the switching theory. In particular, a (unicast) flexible delay line is a discrete-time infinite-server queue that corresponds to the nonblocking switch in the switching theory, and it can be constructed either by the three-stage Clos network or the Cantor network. In this paper, we propose two new constructions for multicast flexible delay lines that use the unicast flexible delay lines as the basic construction elements. The first one is constructed by using parallel unicast flexible delay lines. It is shown that a multicast flexible delay line with maximum delay d can be constructed by using O(radic/d) unicast flexible delay lines with maximum delay d. Our second construction is a recursive construction. We show that a multicast flexible delay line with maximum delay 2d-1 can be constructed by two unicast flexible delay lines with maximum delay d-1 and a multicast flexible delay line with maximum delay d-1. As an application, we show that multicast flexible delay lines can be used for the constructions of optical multicast switches with 100% throughput.