Performance analysis of the discrete-time GI / Geom /1/ N queue

This paper presents an analysis of the single-server discrete-time finite-buffer queue with general interarrival and geometric service time, GI/GeomIl//N. Using the supplementary variable technique, and considering the remaining interarrival time as a supplementary variable, two variations of this model, namely the late arrival system with delayed access (LAS-DA) and early arrival system (EAS), have been examined. For both cases, steady-state distributions for outside observers as well as at random and prearrival epochs have been obtained. The waiting time analysis has also been carried out. Results for the GeomIG/1/N queue with LAS-DA have been obtained from the GIIGeomIl//N queue with EAS. We also give various performance measures. An algorithm for computing state probabilities is given in an appendix.

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

[2]  Annie Gravey,et al.  On the Geo/D/1/and Geo/D/1/n Queues , 1990, Perform. Evaluation.

[3]  Mohan L. Chaudhry,et al.  On the Analysis of the Discrete-Time Geom( n)/G( n)/1/ N Queue , 1996 .

[4]  Jeffrey J. Hunter,et al.  Mathematical techniques of applied probability , 1985 .

[5]  Warren Buckler Powell,et al.  Stochastic delays in transportation terminals : new results in the theory and application of bulk queues , 1981 .

[6]  Hideaki Takagi,et al.  Queueing analysis: a foundation of performance evaluation , 1993 .

[7]  Annie Gravey,et al.  Simultaneity in Discrete-Time Single Server Queues with Bernoulli Inputs , 1992, Perform. Evaluation.

[8]  M. L. Chaudhry,et al.  Alternative Numerical Solutions of Stationary Queueing-Time Distributions in Discrete-Time Queues: GI/G/1 , 1993 .

[9]  Yoshitaka Takahashi,et al.  ON DISCRETE-TIME SINGLE-SERVER QUEUES WITH MARKOV MODULATED BATCH BERNOULLI INPUT AND FINITE CAPACITY , 1993 .

[10]  Herbert Freeman,et al.  Discrete-Time Systems , 1980 .

[11]  Jeffrey J. Hunter.  Discrete Time Models : Techniques and Applications , 1983 .

[12]  Herwig Bruneel,et al.  Performance of discrete-time queueing systems , 1993, Comput. Oper. Res..

[13]  Per Hokstad,et al.  The G/M/m queue with finite waiting room , 1975, Journal of Applied Probability.

[14]  Jan-Kees C. W. van Ommeren,et al.  The discrete-time single-server queue , 1991, Queueing Syst. Theory Appl..