Queueing Delay in a Finite-Buffer Model with Failures and Bernoulli Feedback

摘要

In the paper a finite-capacity queueing model with server breakdowns is considered. Jobs arrive according to a Poisson process and are being served during exponentially distributed processing time under the FIFO service discipline. During the operation of the system successive exponential failure-free times are followed by generally distributed repair periods. After the processing a job may rejoin the queue (feedback) with probability q or leave the system with probability 1 - q. Applying the analytical approach based on the idea of Markov chain and the formula of total probability, a system of integral equations for the transient queueing delay distribution is built, conditioned by the initial buffer state. Algebraic method based on the idea of Korolyuk's potential is used to obtain the solution of the corresponding system written for Laplace transforms in a closed form. Numerical example is attached as well.