Unit:
Τομέας Στατιστικής και Επιχειρησιακής ΈρευναςLibrary of the School of Science
Dissertation committee:
Οικονόμου Αντώνης Αναπλ. Καθηγ. (Επιβλέπων), Φακίνος Δημήτρης Αναπλ. Καθηγ., Μηλολιδάκης Κωνσταντίνος Αναπλ. Καθηγ.
Original Title:
H ιδιότητα της μη-ευαισθησίας σε ουρές με ομαδικές αφίξεις και μελέτη μοντέλων γεωμετρικών εγκαταλείψεων σε ουρές με απουσίες του υπηρέτη
Summary:
The thesis is organized in two parts with two sections in each of them. In the
first part, we study the M/G/k/k and M/G/. group - arrival loss systems, where
the stationary distribution is shown to exhibit the insensitivity property
under certain conditions. In the second part, we study the M/M/1 queue with
server vacations. In particular we assume that during the vacations,
abandonment opportunities occur and the number of customers in the system is
reduced according to a geometric distribution. In the various chapters, we
begin by providing the mathematical description of the models and giving a
bibliographical overview of the respective area. Subsequently, we study various
performance measures of the systems, with particular emphasis in the stationary
distribution of the number of customers (queue length). Moreover, we study
descriptors such as the waiting time distributions and distributions related to
the busy period of the models. We also provide several efficient computational
procedures (algorithms) that simplify several computations of performance
measures in special cases. Numerical experiments that illustrate the
applicability of the theoretical results are also included.
Keywords:
M/G/k/k loss system, insensitivity property, server vacations, geometric abandonments, stationary distribution
