Nikolai K.Krivulin
Algebraic Models in Simulation of Tandem Queueing Systems
Proc. 1995 Summer Computer Simulation Conference,
(Tuncer I. Ören and Louis G. Birta, eds.), Simulation
Councils, Inc., 1995, 9-14.
Algebraic models of tandem single-server queueing systems with both finite
and infinite buffers are developed in terms of the max-algebra theory. The
dynamics of each system is described by a linear vector state equation
similar to those in the conventional linear system theory, and it is
determined by a transition matrix inherent in the system. We show how
transition matrices may be calculated, and present the matrices associated
with certain particular models. The representation of system performance
measures including the system time and the waiting time of customers are
also given. Finally, the application of the models to the development of
parallel simulation procedures is briefly discussed.