Scheduling Reserved Traffic in Input-Queued Switches: New Delay Bounds via Probabilistic Techniques

We consider the problem of providing delay bounds to reserved traffic in high-speed input-queued switches. We assume that the matrix of bandwidth demands is known and we use the now standard approach of decomposing this matrix into a convex combination of permutation matrices. Our problem therefore reduces to the problem of constructing a schedule for these permutation matrices. In this paper we derive delay bounds for four algorithms that are based on probabilistic techniques. For each algorithm we first place tokens randomly in continuous time for each permutation matrix. If the $n$th token that appears corresponds to permutation matrix $M_k$ then we schedule matrix $M_k$ in the $n$th time slot. The algorithms differ in how the random token processes are defined. For two of the algorithms we are able to perform a derandomization so as to obtain deterministic schedules. We show through numerical computation that in many situations the resulting delay bounds are smaller than the previously best-known delay bounds of Chang, Chen, and Huang.