Exhaustive Vacation Queue with Dependent Arrival and Service Processes
This paper presents a more general class of MAP/MAP/1 exhaustive vacation queue, in which the Markov modulated arrival and service processes are dependent. This model class requires the evaluation of the busy period of quasi birth death process with arbitrary initial level, which is a new analysis element.
The model is analyzed by applying matrix analytic methods for the underlying quasi birth death process. The main result of the paper is the probability-generating function of the number of jobs in the system. Finally, a numerical example provides an insight into the behavior of the model.
KeywordsVacation queue MAP Dependent arrival and service process QBD Matrix analytic methods stationary analysis
Unable to display preview. Download preview PDF.
- 5.Ke, J.C., Wu, C.H., Zhang, Z.G.: Recent developments in vacation queueing models: a short survey. International Journal of Operations Research 7(4), 3–8 (2010)Google Scholar
- 6.Latouche, G., Ramaswami, V.: Introduction to matrix analytic methods in stochastic modeling, vol. 5. SIAM (1999)Google Scholar
- 7.Neuts, M.F.: A versatile markovian point process. Journal of Applied Probability, 764–779 (1979)Google Scholar
- 10.Tian, N., Zhang, Z.G.: Vacation queueing models: theory and applications, vol. 93. Springer Science & Business Media (2006)Google Scholar