JOURNAL OF APPLIED PROBABILITY, VOL.53, PP.1098-1110, 2016.  

TITLE: Steady-state analysis of a multi-class MAP/PH/c queue 
with acyclic PH retrials   

AUTHORS: Tugrul Dayar and M. Can Orhan

ABSTRACT: A multi-class c-server retrial queueing system in 
which customers arrive according to a class-dependent Markovian 
arrival process (MAP) is considered. Service and retrial times 
follow class-dependent phase-type (PH) distributions with the 
further assumption that PH distributions of retrial times are 
acyclic. A necessary and sufficient condition for ergodicity 
is obtained from criteria based on drifts. The infinite state 
space of the model is truncated with an appropriately chosen 
Lyapunov function. The truncated model is described as a 
multi-dimensional Markov chain and a Kronecker representation 
of its generator matrix is numerically analyzed.

KEY WORDS: Markovian arrival process; phase-type service time 
distribution; acyclic phase-type retrial time distribution; 
Kronecker product; Markov chain