Throughput analysis of unscheduled multicast transmissions in WDM broadcast-and-select networks

In a WDM network, in order to receive a transmission on a wavelength nodes must tune their receiver to that wavelength. If each node has only a single receiver, a transmission on one wavelength may not be received by nodes that are tuned to receive a message on another wavelength. In the absence of a scheduling algorithm to coordinate the transmissions, multiple simultaneous transmissions to the same receiver are possible, resulting in a reduction in the system throughput. This problem is similar to that of scheduling traffic in an input queued switch, for which it was shown in Karol et al. (1987) that with unicast traffic, under uniform traffic conditions, the throughput of an N×N switch is limited to 58%. Here we consider a slotted system where the size of a slot is equal to the message size. We consider two transmission protocols. With the first protocol, which we call persistent, a message is repeatedly transmitted until it has been received by all of its intended recipients. The second protocol we consider introduces a random delay between retransmissions of a message