On a resequencing model for high speed networks

In this paper we analyze the effect of fixed delay in conjunction with queueing and resequencing delay on the optimal distribution of traffic on multiple disjoint paths. We study a system of two hosts or end nodes, connected by a high speed network, communicating on two virtual channels which follow disjoint physical paths. The paths have a different number of hops and/or physical length which leads to a different amount of constant delay for each of them. The variable delay on each path is modelled by a queue with exponential service. Furthermore the destination node delivers packets in the order they arrived at the source node, which entails additional resequencing delay. We find the optimal split of traffic, so as to minimize the total average system time (including the resequencing delay). Our results show that the optimal splitting probability may be heavily dependant on the difference in the fixed delays on the two paths. Numerical examples are presented to illustrate the effect of fixed delay on the fraction of traffic routed to different paths. Performance can be further improved when we do a deterministic split of the traffic.