Analysis of Alternating-priority Queueing Models with (Cross) Correlated Switchover Times
This document analyzes a single server queueing system in which service is
alternated between two queues and the server requires a (finite) switchover
time to switch from one queue to the other. The distinction from classical
results is that the sequence of switchover times from each of the queues need
not be i.i.d. nor independent from each other; each sequence is merely
required to form a stationary ergodic sequence. With the help of stochastic
recursive equations explicit expressions are derived for a number of
performance measures, most notably for the average delay of a customer and the
average queue lengths under different service disciplines. With these
expressions a comparison is made between the service disciplines and the
influence of correlation is studied. Finally, through a number of examples it
is shown that the correlation can significantly increase the mean delay and
the average queue lengths indicating that the correlation between switchover
times should not be ignored. This has important implications for communication
systems in which a common communication channel is shared amongst various
users and where the time between consecutive data transfers is correlated (for
example in ad-hoc networks).
Philippe Nain
Last modified: Tue Mar 15 14:53:34 MET 2005