M.Sc Thesis
M.Sc Student Guez Dan Scheduling Time-Constrained Communication in Input Queued Switches Department of Computer Science Mr. Adi Rosen

Abstract

We consider the problem of packet-mode scheduling of input queued switches. Packets have variable lengths, being divided into cells of unit length. Each packet arrives to the switch with a given deadline by which it must traverse the switch. A packet successfully passes the switch if the sequence of cells comprising it is contiguously transmitted out of the switch before the packet's deadline expires. A packet transmission may be preempted and restarted from the beginning later.  The scheduling policy has to decide at each time unit which packets to serve. The problem is online in nature, and thus we use competitive analysis to measure the performance of our scheduling policies.

First we consider the case where the goal of the switch policy is to maximize the total number of successfully transmitted packets. We derive two algorithms achieving the competitive ratios of 2^(2*sqrt(log L)) +1) and N+1, respectively, where L is the ratio between the longest and the shortest packet length and N is the number of input/output ports. We also show that any deterministic online algorithm has competitive ratio of at least min{log L +1,N).

Then we study the general case in which each packet has an intrinsic value representing its priority, and the goal is to maximize the total value of successfully transmitted packets.  We derive an algorithm which achieves a competitive ratio of $2\kappa+2\sqrt{\kappa+1/2}+\frac{2\kappa+\sqrt{\kappa+1/2}+1}{\sqrt{\kappa+1/2}}+3$,  where $\kappa$ is the ratio between the maximum and the minimum value per cell.

We complement our results by studying the offline version of the problem, which is NP-hard. We give a pseudo-polynomial $3$-approximation algorithm for the general case and a %strongly polynomial $3$-approximation algorithm for the case of unit value packets.