Srinivas R. Chakravarthy


Department of Industrial and Manufacturing Engineering and

Business Kettering University, Flint, MI 48504, USA

[email protected]


Stefanka Chukova


School of Mathematical and Computing Sciences

Victoria University of Wellington,

Wellington, New Zealand

[email protected]





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.