Performance analysis of a discrete-time queuing system with a correlated train arrival process

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 tbr 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.

[1]  Henry C. Thacher,et al.  Applied and Computational Complex Analysis. , 1988 .

[2]  Mustafa K. Mehmet Ali,et al.  A performance analysis of a discrete-time priority queueing system with correlated arrivals , 2004, Perform. Evaluation.

[3]  Chris Blondia,et al.  Statistical Multiplexing of VBR Sources: A Matrix-Analytic Approach , 1992, Perform. Evaluation.

[4]  Herwig Bruneel,et al.  An efficient solution technique for discrete-time queues fed by heterogeneous traffic. , 1997 .

[5]  Amedeo R. Odoni,et al.  An Empirical Investigation of the Transient Behavior of Stationary Queueing Systems , 1983, Oper. Res..

[6]  Herwig Bruneel.  Packet Delay and Queue Length for Statistical Multiplexers with Low-Speed Access Lines , 1993, Comput. Networks ISDN Syst..

[7]  Faouzi Kamoun,et al.  A Transient Discrete-Time Queueing Analysis of the ATM Multiplexer , 1998, Perform. Evaluation.

[8]  Herwig Bruneel.  Calculation of message delays and message waiting times in switching elements with slow access lines , 1994, IEEE Trans. Commun..

[9]  Edmund Taylor Whittaker,et al.  A Course of Modern Analysis , 2021 .

[10]  Ji Zhang,et al.  Spectral decomposition approach for transient analysis of multi-server discrete-time queues , 1992, [Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications.

[11]  Herwig Bruneel,et al.  Performance of statistical multiplexers with finite number of inputs and train arrivals , 1992, [Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications.

[12]  Y. Lee,et al.  Discrete time queues with phase dependent arrivals , 1994, IEEE Trans. Commun..

[13]  G. F. Newell,et al.  Introduction to the Theory of Queues. , 1963 .

[14]  D. Mitra,et al.  Stochastic theory of a data-handling system with multiple sources , 1982, The Bell System Technical Journal.

[15]  Herwig Bruneel,et al.  Buffer Contents and Delay for Statistical Multiplexers with Fixed-Length Packet-Train Arrivals , 1993, Perform. Evaluation.

[16]  Daniel Zwillinger,et al.  CRC standard mathematical tables and formulae; 30th edition , 1995 .

[17]  Herwig Bruneel,et al.  Discrete-time models for communication systems including ATM , 1992 .

[18]  Gunnar Karlsson,et al.  Performance models of statistical multiplexing in packet video communications , 1988, IEEE Trans. Commun..