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Delay, queue length, and throughput are the main performance characteristics of a data transmission system with ARQ (automaticrepeat-request) error control. Various protocols which have been proposed use, as a part or as a whole, the basic selective-repeat ARQ protocol. Their performance analysis has, however, been restricted to the throughput characteristics. An easily applicable method to analyze this basic protocol has not appeared in the literature so far. In this paper, two different methods for the queue length and delay analysis are presented. The system is modeled as a discrete time queue with infinite buffer storage. Transmission errors are considered to be independent, and block arrivals may follow an arbitrary interarrival time distribution. The first method uses an exact Markov state model, on which the theory of absorbing and ergodic Markov chains is applied, and leads to a computational algorithm. The second method, which is based on a specific assumption, uses a substantially simpler stochastic model and results in equations which are easily solved by means of iterative computation. In the case of geometrically distributed interarrival times, simple analytical formulas are extracted. The results are compared to the exact ones (that is, those obtained by the first method or by extended simulation runs) and surprising agreement is observed.
Date of Publication: Feb 1986