JOURNAL OF APPLIED PROBABILITY, VOL.49, PP.1166-1187, 2012.  

TITLE: Kronecker-based infinite level-dependent QBD processes   

AUTHORS: Tugrul Dayar and M. Can Orhan

ABSTRACT: Markovian systems with multiple interacting subsystems 
under the influence of a control unit are considered. The state 
spaces of the subsystems are countably infinite, whereas that of 
the control unit is finite. A recent infinite level-dependent
quasi-birth-and-death (LDQBD) model for such systems is extended 
by facilitating the automatic representation and generation of 
the nonzero blocks in its underlying infinitesimal generator 
matrix with sums of Kronecker products. Experiments are performed 
on systems of stochastic chemical kinetics having two or more 
countably infinite state space subsystems. Results indicate that, 
even though more memory is consumed, there are many cases where a 
matrix analytic solution coupled with Lyapunov theory yields a 
faster and more accurate steady-state measure compared to that 
obtained with simulation.

KEY WORDS: Markov processes; numerical analysis; simulation; 
biology; queues: theory