Browsing by Subject "Retrial queues"

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    Approximation of multiserver retrial queues by means of generalized truncated models
    (Springer, 2002) Anisimov, V. V.; Artalejo, J. R.
    It is well-known that an analytical solution of multiserver retrial queues is difficult and does not lead to numerical implementation. Thus, many papers approximate the original intractable system by the so-called generalized truncated systems which are simpler and converge to the original model. Most papers assume heuristically the convergence but do not provide a rigorous mathematical proof. In this paper, we present a proof based on a synchronization procedure. To this end, we concentrate on the M/M/c retrial queue and the approximation developed by Neuts and Rao (1990). However, the methodology can be employed to establish the convergence of several generalized truncated systems and a variety of Markovian multiserver retrial queues.
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    ItemOpen Access
    Retrial queuing models of multi-wavelength FDL feedback optical buffers
    (Institute of Electrical and Electronics Engineers, 2011) Akar, N.; Sohraby, K.
    Optical buffers based on Fiber Delay Lines (FDL) have been proposed for contention resolution in optical packet/burst switching systems. In this article, we propose a retrial queuing model for FDL optical buffers in asynchronous optical switching nodes. In the considered system, the reservation model employed is of post-reservation type and optical packets are allowed to re-circulate over the FDLs in a probabilistic manner. We combine the MMPP-based overflow traffic models of the classical circuit switching literature and fixed-point iterations to devise an algorithmic procedure to accurately estimate blocking probabilities as a function of various buffer parameters in the system when packet arrivals are Poisson and packet lengths are exponentially distributed. The proposed algorithm is both accurate and fast, allowing one to use the procedure to dimension optical buffers in next-generation optical packet switching systems.