Title :
Stability of queueing networks and scheduling policies
Author :
Kumar, P.R. ; Meyn, Sean P.
Author_Institution :
Dept. of Electr. & Comput. Eng., Illinois Univ., Urbana, IL, USA
fDate :
2/1/1995 12:00:00 AM
Abstract :
We develop a programmatic procedure for establishing the stability of queueing networks and scheduling policies. The method uses linear or nonlinear programming to determine what is an appropriate quadratic functional to use as a Lyapunov function. If the underlying system is Markovian, our method establishes not only positive recurrence and the existence of a steady-state probability distribution, but also the geometric convergence of an exponential moment. We illustrate this method on several example problems
Keywords :
Lyapunov methods; Markov processes; convergence of numerical methods; mathematical programming; probability; production control; queueing theory; stability; Lyapunov function; Markovian system; exponential moment; geometric convergence; linear programming; machine scheduling; nonlinear programming; probability distribution; production control; quadratic functional; queueing networks; stability; Convergence; Functional programming; Linear programming; Lyapunov method; Quadratic programming; Stability; Steady-state; Stochastic processes; Telecommunication traffic; Traffic control;
Journal_Title :
Automatic Control, IEEE Transactions on
