Η παρούσα διπλωματική εργασία σκοπό έχει να παρουσιάσει κάποια μοντέλα ουρών ξεκινώντας από το πιο απλό όπως η ουρά Μ/Μ/1 και στη συνέχεια παρουσιάζονται αναλυτικά οι γενικεύσεις του παραπάνω μοντέλου οι ουρές M/G/1 και G/M/1. Παρουσιάζονται αναλυτικά επίσης τα μοντέλα M/M/c, Μ/Μ/c/K. Περιγράφονται μοντέλα ουρών όπως ουρές με απεριόριστη εξυπηρέτηση, ουρές με πεπερασμένη πηγή, μοντέλα με ανταλλακτικά, μοντέλα στα οποία η εξυπηρέτηση είναι εξαρτώμενη απο τον αριθμό των πελατών και ουρές με ανυπόμονους πελάτες. Τέλος στο τέταρτο και τελευταίο κεφάλαιο της εργασίας ασχολούμαστε με την μελέτη ενός συστήματος με τη χρήση της προσομοίωσης. / This thesis aims to present some queuing models, beginning from simplest as queue M/M/1 and then presents analyticaly the generalisations of the above model, M/G/1 and G/M/1 queues. Are analytically presented also models M/M/c and M/M/c/K. Are described models of queues as queues with unlimited service, queues with finite source, models with spares, models with state-dependent service and queues with impatience. Finally the fourth and final chapter of the thesis deals with the study of a system using simulation.

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Cloud computing is a general term for system architectures that involves delivering hosted services over the Internet, made possible by significant innovations in virtualization and distributed computing, as well as improved access to high-speed Internet. A cloud service differs from traditional hosting in three principal aspects. First, it is provided on demand, typically by the minute or the hour; second, it is elastic since the user can have as much or as little of a service as they want at any given time; and third, the service is fully managed by the provider -- user needs little more than computer and Internet access. Typically a contract is negotiated and agreed between a customer and a service provider; the service provider is required to execute service requests from a customer within negotiated quality of service (QoS) requirements for a given price. Due to dynamic nature of cloud environments, diversity of user's requests, resource virtualization, and time dependency of load, provides expected quality of service while avoiding over-provisioning is not a simple task. To this end, cloud provider must have efficient and accurate techniques for performance evaluation of cloud computing centers. The development of such techniques is the focus of this thesis. This thesis has two parts. In first part, Chapters 2, 3 and 4, monolithic performance models are developed for cloud computing performance analysis. We begin with Poisson task arrivals, generally distributed service times, and a large number of physical servers. Later on, we extend our model to include finite buffer capacity, batch task arrivals, and virtualized servers with a large number of virtual machines in each physical machine. However, a monolithic model may suffer from intractability and poor scalability due to large number of parameters. Therefore, in the second part of the thesis (Chapters 5 and 6) we develop and evaluate tractable functional performance sub-models for different servicing steps in a complex cloud center and the overall solution obtains by iteration over individual sub-model solutions. We also extend the proposed interacting analytical sub-models to capture other important aspects including pool management, power consumption, resource assigning process and virtual machine deployment of nowadays cloud centers. Finally, a performance model suitable for cloud computing centers with heterogeneous requests and resources using interacting stochastic models is proposed and evaluated.

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