A FINITE CAPACITY RESEQUENCING MODEL \WITH MARKOVIAN ARRIVALS
Srinivas R. Chakravarthy
Department of Industrial and Manufacturing Engineering and
Business Kettering University, Flint, MI 48504, USA
Stefanka Chukova
School of Mathematical and Computing Sciences
Victoria University of Wellington,
Wellington, New Zealand
Abstract
We consider a two-server finite capacity queuing
model in which messages should leave the system in the order in
which they entered the system. Messages arrive arrive according to
a Markovian arrival process (MAP) and any message finding the
buffer full is considered lost. Out-of-sequence messages are
stored in a (finite) buffer and may lead to blocking when a
processed message cannot be placed in the buffer.
Using Matrix-analytic methods, the system is
analyzed in steady state. We show that the stationary waiting time
distributions of an admitted message in the queue and in the
system as well as the time spent in the service facility follow
phase-type distributions. The departure process is characterized as a
Batch Markovian Arrival Process. The system performance measures such as
system idle probability, server idle and server blocking probabilities,
throughput, mean number of messages in primary and in resequencing
buffers, rate of departure, average batch size of departure are
derived analytically.