Abstract
In this paper, we present an exact queuing analysis of a discrete-time queue whose arrival process is correlated and consists of a discrete autoregressive model of order 1 (DAR(1)). The functional equation describing this DAR(1)/D/1 queuing model, originally derived in Hwang and Sohraby (Queuing Systems 43 (2003)29–41), is manipulated and transformed into a mathematical tractable form. By using simple analytical transform techniques, we show how our proposed approach allows us to derive an equivalent (yet simpler) expression for the steady-state probability generating function (pgf) of the queue length, as originally derived in Hwang and Sohraby (Queuing Systems 43 (2003)29–41). From this pgf, we characterize the distribution of the packet delay. New numerical results related to packet loss ratio and mean delay of the DAR(1)/D/1 queue are also presented. The proposed approach outlines an alternate solution technique and a general framework under which more complex time-series based queuing models can be analyzed.
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G.U. Hwang and K. Sohraby, On the exact analysis of a discrete-time queuing system with autoregressive inputs. Queuing Systems 43 (2003) 29–41.
J. Davis, K. Chandra, and C. Thompson, Nonlinear time-series model for VBR video traffic. IEEE Conference on Local Computer Networks (LCN) (2000) 678–683.
A. Elwalid, D. Heyman, T.V. Laksman, D. Mitra, and A. Weiss, Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing. IEEE Journal of Selected Areas in Communications 13 (6) (1995) 1004–1016.
T.P. Chen and T. Chen, Markov modulated autoregressive processes for traffic and channel modeling. International Packet-video Workshop PV 2002 (2002).
F. Kamoun, Performance analysis of a discrete-time queuing system with a correlated train arrival process. Performance Evaluation 63 (4–5) (2006) 315–340.
H. Bruneel and B.G. Kim, Discrete-time Models for Communication Systems Including ATM (Kluwer Academic Publishers, Boston, 1993).
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J.N. Daigle, Y. Lee, and M.N. Magalhaes, Discrete time queues with phase dependent arrivals. IEEE Trans. Commun. 43 (1994) 606–614.
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Kamoun, F. The discrete-time queue with autoregressive inputs revisited. Queueing Syst 54, 185–192 (2006). https://doi.org/10.1007/s11134-006-9591-3
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DOI: https://doi.org/10.1007/s11134-006-9591-3