Faz-tipli servis dağılımları ve değişik büyüklükte bekleme yerleri olan kapalı kuyruk ağlarının kronecker gösterimi ve bölmeye dayalı çözümlenmesi

This thesis extends two approximative fixed-point iterative methods basedon decomposition for closed queueing networks (QNs) with Coxian service dis-tributions and arbitrary buffer sizes from the literature to include phase-typeservice distributions. It shows how the irreducible Markov chain associated witheach subnetwork in the decomposition can be represented hierarchically usingKronecker products. The proposed methods are implemented in a software tool,which is capable of computing the steady-state probability vector of each subnet-work by a multilevel method at each fixed-point iteration. The two methods arecompared with others, one being the multilevel method for the closed QN itself,for accuracy and efficiency on a number of examples using the tool, and theirconvergence properties are discussed. Numerical results indicate that there is aniche among the problems considered which is filled by the two approximativefixed-point iterative methods.Keywords: Closed queueing networks · Phase-type service distributions · Kro-necker representations · Network decomposition · Fixed-point iteration · Multi-level methods.iii