LSA framework in lte wireless network environment as a queueing system with unreliable resource

In this paper, we consider an LTE cell with LSA framework as a queueing system with unreliable resources. Here the resources can be assumed to represent e.g. frequency spectrum, since the LSA framework implies that part of the spectrum is leased from the third party and can be seized at a random time for a random duration. A system with C servers and R_s resources is studied. The system can be found in one of s e {0,1} states. The state transitions are distributed according to the exponential law with parameters a и P , notably R₀ < R₁. The customers arrive according to the Poisson process with parameter X , and are served according to the exponential law with parameter ц . When a new customer arrives it requires a server and a random resource volume with CDF F(x) . A customer is considered lost if there is either no enough available servers in the system or there are no enough available resources to accommodate it. Thus in the considered system a customer can be lost either upon arrival or while it is being served upon the system state change. First consider a general case of continuous resources. Here we introduce a Markov process X(t) = (n(t),(r₁ (t),...,r_n (t)),s(t)) X = |(и,(г,...,г : 0 --->'"./>v · ^u - ⁿ - ^e t^u>¹/>^r- / '' ' J · However, since, unfortunately, we failed to obtain a closed form solution for this case further we consider a discrete case. But, as it is shown in the paper, applying the same process for the discrete case means that the state space is growing exponentially against the maximum number of customers in the system. And can be obtained n Л -Е nrr №+^Rs⁾ This equation considers the scenario when a new customer can require the resources in the range from 1+ n I j=1 0 to R . As one can note from the equation the state space grows extremely rapidly with the number of servers and volume of available resources, which highly affects the matrix techniques performance. Taking all this into account, we propose an approximation, where the resources allocated to the customer are reallocated when the customer leaves the system. Thus we only have to trace the volume of the allocated resources in total and not the resources allocated to each customer separately, thus greatly reducing computation difficulty. In this case the process can be obtained as Y(t) = (n (t), r(t),s (t)) . Since we consider the Poisson arrival flow and exponential service time this approximation gives us a reasonable approximation of the initial process. For the considered system evacuation and interruption probabilities are obtained as the main characteristics. Evacuation probability is a probability that when the frequency is being seized, no customer was interrupted while being served are the interruption probability is a probability that when the frequency is being seized at least one customer was interrupted while being served. As one can note, the sum of these probabilities is a constant and equals to the probability of a frequency being seized. In the last section we give a numerical example.

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