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In this work, we consider a discrete time Geo/G/1 retrial queue with general retrial times and balking customers. If a new arriving customer finds the server busy, he may join the orbit to retry getting the required service again or depart completely from the system. Using the supplementary variable technique, this queueing system is modelled using a Markov chain. We derive the generating functions of the steady state distribution of this Markov chain. Hence, we establish the generating functions of the orbit size and the system size distributions. This set of generating functions is used to derive various performance measures. We prove a stochastic decomposition law and use it to a derive a measure of the proximity between the distributions of the system size in the present model and the corresponding one without retrials. A set of recursive formulae is built up to facilitate computing the orbit size and the system size distributions. Numerical results are presented with a focus on the effect of balking on the system performance.

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/ ibis paper presents a method for obtaining closed form expressions for a class of nonlinear circuits of autonomous and nonamonomous types .The method depends on the theory of normal forms. It overcomes the drawbacks confronted by other methods such as harmonic balance, voiterra series and direct integration. This method also is suitable for the investigation of periodic, quasiperiodic and chaotic behaviors.