A discrete time Geo/G/1 retrial queue with single vacation and starting failure

作者：Zhang Feng^*; Yue Dequan; Zhu Zhifeng

来源：Journal of Information and Computational Science, 2011, 8(13): 2751-2758.

• Discrete time queues
• Discrete-time
• General retrial
• Generating functions
• Markov Chain
• Numerical example
• Orbit sizes
• Performance measure
• Queueing system
• Retrial queue
• Single vacation
• Starting failures
• Stochastic decomposition
• System size
• System state

We discuss a discrete-time Geo=G=1 retrial queue with single vacation and starting failure where the retrial times follow a general distribution. As soon as the orbit is empty, the server takes a vacations immediately, while if there is at least one customer in the orbit at the end of a vacation, the server prepare to serve the coming customer from orbit or new arrivals. For this model, we firstly analyze the Markov chain underlying the considered queueing system, and derive system state probabilities. The generating functions of the orbit size and the system size are also obtained. Secondly, some performance measures such as the expected number in the orbit and the expected number of the customers in the system are given. Finally, two stochastic decomposition results and numerical examples are provided.

• 出版日期2011