TY - JOUR
T1 - Iterative methods for overflow queueing models I
AU - Chan, R. H.
PY - 1987/3
Y1 - 1987/3
N2 - Markovian queueing networks having overflow capacity are discussed. The Kolmogorov balance equations result in a linear homogeneous system, where the right null-vector is the steady-state probability distribution for the network. Preconditioned conjugate gradient methods are employed to find the null-vector. The preconditioner is a singular matrix which can be handled by separation of variables. The resulting preconditioned system is nonsingular. Numerical results show that the number of iterations required for convergence is roughly constant independent of the queue sizes. Analytic results are given to explain this fast convergence.
AB - Markovian queueing networks having overflow capacity are discussed. The Kolmogorov balance equations result in a linear homogeneous system, where the right null-vector is the steady-state probability distribution for the network. Preconditioned conjugate gradient methods are employed to find the null-vector. The preconditioner is a singular matrix which can be handled by separation of variables. The resulting preconditioned system is nonsingular. Numerical results show that the number of iterations required for convergence is roughly constant independent of the queue sizes. Analytic results are given to explain this fast convergence.
KW - AMS(MOS): 65N20
KW - 65F10
KW - 60K25
KW - CR: G1.3
UR - http://www.scopus.com/inward/record.url?scp=0000592564&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0000592564&origin=recordpage
U2 - 10.1007/BF01396747
DO - 10.1007/BF01396747
M3 - RGC 21 - Publication in refereed journal
VL - 51
SP - 143
EP - 180
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 2
ER -