Performance analysis of a discrete-time queuing system with a correlated train arrival process |
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Affiliation: | 1. Department of Industrial Engineering, North Carolina State University, Raleigh, NC 27695-7906, United States;2. Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027-6699, United States;1. Department of Management, Bar Ilan University, Ramat Gan 52900, Israel;2. Department of Statistics and Operations Research, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel |
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Abstract: | In this paper, we present an exact transient and steady-state discrete-time queuing analysis of a statistical multiplexer with a finite number of input links and whose arrival process is correlated and consists of a train of a fixed number of fixed-length packets. The functional equation describing this queuing model is manipulated and transformed into a mathematical tractable form. This allows us to derive the transient probability generating function (pgf) of the buffer occupancy. From this transient pgf, time-dependent performance measures such as transient probability of empty buffer, transient mean of buffer occupancy and instantaneous packet overflow probabilities are derived. By applying the final-value theorem, the corresponding exact expressions for the steady-state pgf of the queue length and packet arrivals are derived. We also show how the transient analysis provides insights into the derivation of the system's busy period distribution. Closed-form expressions for the mean packet and message delays are also provided. The paper presents significant results on the transient and steady-state analysis of statistical multiplexers with N input links and correlated train arrivals. |
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