 
Summary: Scheduling in a Queueing System with Asynchronously
Varying Service Rates
Matthew Andrews y Krishnan Kumaran y Kavita Ramanan y
Alexander Stolyar y Rajiv Vijayakumar z Phil Whiting y
Abstract
We consider the following queueing system which arises as a model of a wireless
link shared by multiple users. There is a nite number N of input
ows served by a
server. The system operates in discrete time t = 0; 1; 2; : : : . Each input
ow can be
described as an irreducible countable Markov chain; waiting customers of each
ow are
placed in a queue. The sequence of server states m(t); t = 0; 1; 2; : : : , is a Markov chain
with nite number of states M . When server is in state m it can serve m
i customers
of
ow i (in one time slot).
The scheduling discipline is a rule that in each time slot chooses the
ow to serve
based on the server state and the state of the queues. Our main result is that a
simple online scheduling discipline, Modied Largest Weighted Delay First, along with
its generalizations, is throughput optimal, namely it ensures that the queues are stable
as long as the vector of average arrival rates is within the system maximum stability
region.
1 Introduction
