Nikolai K.Krivulin and D.Milov
An Algebraic Model of Queueing Networks
Proc. 2nd St.Petersburg Workshop on Mathematical Methods in
Stochastic Simulation and Experimental Design, St.Petersburg,
June 18-21, 1996 (S.M. Ermakov and V.B. Melas, eds), 156-161.
A class of queueing networks is examined to derive a representation of
network dynamics in terms of the max-plus algebra. The class includes
networks with single-server fork-join nodes supplied with buffers which
may have both infinite and finite capacity. For the networks, a common
state dynamic equation is given, which relates the departure times of
customers in an explicit vector form. Since, in general, the explicit
dynamic equation may not exist, related existence conditions are
established in terms of network topology.