Performance evaluation of a discrete-time \(Geo[X]/G/1\) retrial queue with general retrial times.

*(English)*Zbl 1189.90040Summary: We consider a discrete-time \(Geo[X]/G/1\) retrial queue with general retrial times. The system state distribution as well as the orbit size and the system size distributions are obtained in terms of their generating functions. These generating functions yield exact expressions for different performance measures. The present model is proved to have a stochastic decomposition law. Hence, a measure of the proximity between the distributions of the system size in the present model and the corresponding one without retrials is derived. A set of numerical results is presented with a focus on the effect of batch arrivals and general retrial times on the system performance. It appears that it is the mean batch size (and not the batch size distribution) that has the main effect on the system performance. Moreover, increasing the mean batch size is shown to have a noticeable effect on the size of the stability region. Finally, geometric retrial times are shown to have an overall better performance compared with two other distributions.

##### MSC:

90B22 | Queues and service in operations research |

60K25 | Queueing theory (aspects of probability theory) |

##### Keywords:

discrete-time retrial queues; general retrial times; batch arrivals; stochastic decomposition; performance evaluation
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\textit{A.-K. Aboul-Hassan} et al., Comput. Math. Appl. 58, No. 3, 548--557 (2009; Zbl 1189.90040)

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