Scheduling Multicast Input-Queued Switches

The use of multicast transmissions, in which users broadcast their data (typically video or audio) to a subset of other users, is growing on the Internet. For example, in input-queued ATM (asynchronous transfer mode) multicast switches, a cell in an input queue may be broadcast to several outputs, and only the cell at the head of each input queue (the HOL, or head-of-line,, cell) is observed and is eligible for transmission. If the HOL cell of an input queue is to be broadcast to k outputs, we think of there being k identical copies of the cell each labeled with a distinct output. In each time slot at most one cell can be transmitted to each output, and a subset of the copies of the HOL cell may be transmitted. We assume that multicast destinations are independent and identically distributed (i.i.d.). We show that the optimal policy always transmits as many cells as possible, and if the HOL cell in one queue has only one copy to be transmitted, that cell should be transmitted if possible. In the model of saturated input queues, i.e., there are an innnite number of cells in each queue, the optimal policy always clears at least one of the input queues, where by clearing a queue we mean that all the copies of the HOL cell in that queue are transmitted. For three saturated input queues, the optimal policy is to fully clear as many HOL cells as possible, and if only one HOL cell can be cleared the number of remaining copies of cells at the heads of the other two queues should be as unbalanced as possible in the majorization sense. For two input queues with an arbitrary arrival process, the optimal policy clears at least one queue. If there is at most one arrival per time slot in each queue, the optimal policy is to fully clear the HOL cell of the longest input queue.