2026-09-21T00:51:31Zhttps://bura.brunel.ac.uk/oai/request

oai:bura.brunel.ac.uk:2438/55402014-11-01T12:19:38Zcom_2438_23com_2438_58com_2438_8627com_2438_8620col_2438_3672col_2438_8629col_2438_235

Madan, KC Darby-Dowman, K Maraghi, Farzana Abdulla 2011-07-11T10:02:08Z 2011-07-11T10:02:08Z 2008 http://bura.brunel.ac.uk/handle/2438/5540 This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University. Queueing systems arise in modelling of many practical applications related to computer sciences, telecommunication networks, manufacturing and production, human computer interaction, and so on. The classical queueing system, even vacation queues or queues subject to breakdown, might not be sufficiently realistic. The purpose of this research is to extend the work done on vacation queues and on unreliable queues by studying queueing systems which take into consideration both phenomena. We study the behavior of a batch arrival queueing system with a single server, where the system is subject to random breakdowns which require a repair process, and on the other hand, the server is allowed to take a vacation after finishing a service. The breakdowns are assumed to occur while serving a customer, and when the system breaks down, it enters a repair process immediately while the customer whose service is interrupted comes back to the head of the queue waiting for the service to resume. Server vacations are assumed to follow a Bernoulli schedule under single vacation policy. We consider the above assumptions for different queueing models: queues with generalized service time, queues with two-stages of heterogeneous service, queues with a second optional service, and queues with two types of service. For all the models mentioned above, it is assumed that the service times, vacation times, and repair times all have general arbitrary distributions. Applying the supplementary variable technique, we obtain probability generating functions of queue size at a random epoch for different states of the system, and some performance measures such as the mean queue length, mean waiting time in the queue, proportion of server's idle time, and the utilization factor. The results obtained in this research, show the effect of vacation and breakdown parameters upon main performance measures of interest. These effects are also illustrated using some numerical examples and graphs. Submitted by Lesh Gowreesunker (lesh.gowreesunker@brunel.ac.uk) on 2011-07-11T10:01:52Z No. of bitstreams: 1 Fulltext.pdf: 16122466 bytes, checksum: 4fe58e8700831720bc05cbefb980ff1e (MD5) Approved for entry into archive by Lesh Gowreesunker(lesh.gowreesunker@brunel.ac.uk) on 2011-07-11T10:02:08Z (GMT) No. of bitstreams: 1 Fulltext.pdf: 16122466 bytes, checksum: 4fe58e8700831720bc05cbefb980ff1e (MD5) Made available in DSpace on 2011-07-11T10:02:08Z (GMT). No. of bitstreams: 1 Fulltext.pdf: 16122466 bytes, checksum: 4fe58e8700831720bc05cbefb980ff1e (MD5) This work is funded by the Ministry of Education, Kingdom of Bahrain. en Brunel University, School of Information Systems, Computing and Mathematics School of Information Systems, Computing and Mathematics http://bura.brunel.ac.uk/bitstream/2438/5540/1/FulltextThesis.pdf A study of some M[x]/G/1 type queues with random breakdowns and bernouilli schedule server vacations based on a single vacation policy Thesis