الفهرس 
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Abstract
In Cognitive Radio (CR) networks, secondary users (SUs) exploit the spectrum holes not used by the primary users (PUs) and cease their transmissions whenever primary users reuse their spectrum bands. Many research papers study CR networks using continuous-time models, however, since periodic sensing is commonly used to protect the PU, discrete-time models are more convenient to analyze the performance of the system. Moreover, since SUs access the channels based on a search of an idle channel, multi-server-access queueing models are the best for describing the situation. To study the mean time an SU spends in the system, in this thesis we combine these two properties by proposing two novel mathematical models for the CR network. In the first, we assume a discrete-time multi-server queueing system with an infinite buffer with the server interruptions. The interruption process is characterizedby an arbitrary independent and identically distributed (i.i.d.) number of available servers during a time slot. We assume that the service time has a geometric distribution as a description for connection-based communication networks. We analyze the model and derive the Probability Generating Function (PGF) for the queue length. We successfully apply the model in CR networks with the discrete-time PU activity characterized by i.i.d. Bernoulli channel occupation to compute the mean time in system for an SU.With some adaptations in the inputs of the proposed mathematical model, we analyze the effect of imperfect sensing. Additionally, we apply the model in the case where channel aggregation is allowed for the SUs and check the effect of using channel aggregation on the SU mean time in system. In the second proposed mathematical model, we further extend the first model such that the server interruption process is characterized by Markovian discrete-time correlation. By means of two-dimensional Markov chain analysis we derive the PGF for the queue length. In the context of CR networks, we manage to apply the described mathematical model in a network that is characterized by continuous-time Markovian ON-OFF PU activity in each channel to calculate the mean time in system for an SU which is more realistic. By some additional adaptations to the model inputs, we include the cases of imperfect sensing and channel aggregation. Additionally, we use the model to optimize the sensing period of the secondary network in order to achieve the minimum mean time in system for an SU. The optimization is done for both the cases of channel aggregation allowed or not allowed.