The Discrete-Time Gated Vacation Queue Revisited

Abstract We consider the discrete-time gated multiple-vacation queue. Vacations are modeled as independent random variables with distributions depending on the number of the immediately preceding vacations. Using a probability generating function approach, we focus on various performance measures such as moments of queue contents and customer delay in equilibrium. These measures are functions of a constant value which we obtain numerically.

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

[2]  Ward Whitt,et al.  A review ofL=λW and extensions , 1991, Queueing Syst. Theory Appl..

[3]  Kin K. Leung,et al.  A single-server queue with vacations and gated time-limited service , 1990, IEEE Trans. Commun..

[4]  B. T. Doshi,et al.  Queueing systems with vacations — A survey , 1986, Queueing Syst. Theory Appl..

[5]  Dieter Fiems,et al.  A note on the discretization of Little's result , 2002, Oper. Res. Lett..

[6]  Dieter Fiems,et al.  Discrete-time queues with general service times and general server interruptions , 2001, SPIE Optics East.

[7]  F. A. van der Duyn Schouten,et al.  Maintenance optimization of a production system with buffer capacity , 1995 .

[8]  Yutaka Takahashi,et al.  Queueing analysis: A foundation of performance evaluation, volume 1: Vacation and priority systems, Part 1: by H. Takagi. Elsevier Science Publishers, Amsterdam, The Netherlands, April 1991. ISBN: 0-444-88910-8 , 1993 .

[9]  Dieter Fiems,et al.  The combined gated-exhaustive vacation system in discrete time , 2002, Perform. Evaluation.

[10]  Attahiru Sule Alfa.  Discrete time analysis of MAP/PH/1 vacation queue with gated time‐limited service , 1998, Queueing Syst. Theory Appl..

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

[12]  Shuichi Sumita.  Performance Analysis of Interprocessor Communications in an Electronic Switching System with Distributed Control , 1989, Perform. Evaluation.

[13]  Onno Boxma,et al.  An M/G/1 queue with multiple types of feedback and gated vacations , 1995 .

[14]  Don Towsley,et al.  On the Statistical Analysis of Queue Lengths and Waiting Times for Statistical Multiplexers with ARQ Retransmission Schemes , 1979, IEEE Trans. Commun..