We derive the variance constant of continuous-time level dependent quasi-birth-and-death processes by investigating the expected integral functionals of the first return times. As an application, we consider the variance constant for the M/M/c retrial queue with non-persistent customers. For this model, analytical expressions and numerical results are obtained for the cases of single server and multiple servers, respectively. We also apply the obtained result to test the M/M/c vacation model for airport security pre-board screening checkpoint services by constructing a confidence interval for the mean queue length.

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Keywords Central limit theorem, M/M/c retrial queue, M/M/c vacation model, Markov processes, quasi-birth-and-death processes
Persistent URL dx.doi.org/10.1080/15326349.2017.1376285
Journal Stochastic Models
Liu, Y. (Yuanyuan), Wang, P. (Pengfei), & Zhao, Y. (2017). The variance constant for continuous-time level dependent quasi-birth-and-death processes. Stochastic Models, 1–20. doi:10.1080/15326349.2017.1376285