Summary: Instability of FIFO in the Permanent Sessions Model at Arbitrarily
Small Network Loads
Matthew Andrews #
Abstract
We show that for any r > 0, there is a network of First­
In­First­Out servers and a fixed set of sessions such that,
. The network load is r with respect to the Perma­
nent Sessions Model with Bounded Arrivals.
. The network can be made unstable.
1 Introduction
One of the most important questions that can be
asked about any scheduling algorithm is whether or
not it ensures stability. That is, if the tra#c injected
into the network does not overload any server, do the
queue sizes remain bounded? The reason this can
happen in a network of servers is that if the scheduling
algorithm behaves badly then a server can oscillate
between periods in which it has no data to serve (i.e.
it is starved), and periods in which a lot of data arrives
at the server (thereby causing a queue buildup). For

Source: Andrews, Matthew - Mathematics of Networks and Systems, Mathematical Sciences Research Center, Bell Laboratories

Collections: Mathematics; Computer Technologies and Information Sciences