الفهرس يوجد فقط 14 صفحة متاحة للعرض العام
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المستخلص
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In the computer and communication systems, the information and data transmis¬sion is increasing exponentially. Therefore, the analysis of the buffering services in such systems becomes a very important issue. Consequently, the queueing system, as mathematical models for such buffering systems, represent an important topic. On other side, some modem communication networks (such as the IEEE 802.11 wireless network with medium access control protocol) work in slotted time mode. Analysis
of such systems demands queueing models working in discrete time setting. For that reason, the discrete time queueing systems get the researchers’ attention. On the other hand, the retrial queue is one of the most important classes of the queueing systems, in which the customer doesn’t stay in the queue waiting for the service, rather he leaves the service area (perhaps to do another job) and tries to take the service after some random time. There are many applications for the retrial queue¬ing systems such as: the telephoning systems, the networking systems working on CBMA/CD protocol, the landing airplanes in a busy runway, and the customer try¬ing to enter a crowded store. The majority of the research papers dealing with retrial queues, concentrated on the analysis of the continuous time setting. Little number only are devoted to analyze the discrete time retrial queues. In addition, the gener¬ating function method is commonly used in the analysis of both discrete time and continuous time retrial queues. This classical method is often difficult and risky in its numerical implementation. Therefore, this thesis is devoted to enhance the field of discrete time retrial queues by applying the algorithmic approach in the analysis. The algorithmic approach in the analysis of the probabilistic models, pioneered by M. F. Neuts, is a high stable numerical method. It is based on purely probabilistic arguments which leads to fully tractable procedures. For analyzing the retrial queues, the algorithmic methodologies assume an approximated tractable model and generate the distribution for this new model.
There are two algorithmic methodologies applied in this thesis: direct truncation and generalized truncation. These methods are applied in the analysis of a dis¬crete time Geo/PH/I retrial queue and a discrete time Geo/PH/l/1 --+ .jPH/l/C tandem retrial queue with blocking. In the discrete time Geo/PH/l retrial queue, the inter-retrial time is geometrically distributed. The numerical results are issued for three special models: a discrete time Geo/Geo/l retrial queue, a discrete time Geo/D-HExp/1 retrial queue and a discrete time Geo/NBin/l retrial queue; where D - H Exp tends for discrete hyper-exponential distribution and N Bin tends for neg¬ative binomial distribution. The numerical results of the discrete time Geo/Geo/l retrial queue are compared with results obtained using the generating function tech¬nique; and the differences are negligible. For the two other special models, the distrib¬ution of the system size is generated. Moreover, a simulator program is developed for
simulating these two models, and its numerical results are compared with the results of the algorithmic methods. The execution time of all methods are also compared, which shows that the algorithmic approach is significantly faster than the simullV tion method. On the other hand, queueing networks represent an important class of queueing systems. It is the most suitable model for production lines, manufacturing systems and multiprocessor architectures. As an example of queueing networks, the thesis considers the analysis of the discrete time Geo/PH/l ---+ ./PH/l/C tandem retrial queue with blocking model. The analysis of this system is performed using the same two algorithmic approach methods. This system consists of two sub-systems connected in series: the first is a retrial queue with geometrically distributed inter¬retrial time, while the second sub-system is a regular queue with finite buffer. The arriving customer is either serviced directly or enters the orbit; after finishing the service from the first sub-system, he enters the second sub-system. H he finds the buffer of the second sub-system is full; he returns back to the server of the first sub¬system. In this case, this server becomes blocked and can not accept any new job except after a departure occurs from the system. Numerical results are presented for a discrete time Geo/Geo/l ---+ ./Geo/l/C tandem retrial queue with blocking and a discrete time Geo/NBin/l ---+ ./D - HExp/l/C tandem retrial queue with blocking. For both systems, the distribution of the system size and the orbit size are obtained. Moreover, we study the effect of changing the buffer size C on the mean system size, the mean orbit size and the utilization of the server one. A simulator program is developed for simulating each model, and its results are compared with the results of the algorithmic approaches established before.