Abstract
This paper considers a single-server queueing model with finite and infinite buffers in which customers arrive according to a discrete-time renewal process. The customers are served one at a time under discrete-time Markovian service process (D-MSP). This service process is similar to the discrete-time Markovian arrival process (D-MAP), where arrivals are replaced with service completions. Using the imbedded Markov chain technique and the matrix-geometric method, we obtain the system-length distribution at a prearrival epoch. We also provide the steady-state system-length distribution at an arbitrary epoch by using the supplementary variable technique and the classical argument based on renewal-theory. The analysis of actual-waiting-time (in the queue) distribution (measured in slots) has also been investigated. Further, we derive the coefficient of correlation of the lagged interdeparture intervals. Moreover, computational experiences with a variety of numerical results in the form of tables and graphs are discussed.
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Samanta, S.K., Gupta, U.C. & Chaudhry, M.L. Analysis of stationary discrete-time GI/D-MSP/1 queue with finite and infinite buffers. 4OR-Q J Oper Res 7, 337–361 (2009). https://doi.org/10.1007/s10288-008-0088-2
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DOI: https://doi.org/10.1007/s10288-008-0088-2
Keywords
- Discrete-time Markovian service process (D-MSP)
- Matrix-geometric method
- Queue
- Supplementary variable
- Waiting time