Analysis of the M X /G/1 Queue Under D-Policy

Abstract We study the queue length of the M X /G/1 queue under D-policy. We derive the queue length PGF at an arbitrary point of time. Then, we derive the mean queue length. As special cases, M/G/1, M X /M/1, and M/M/1 queue under D-policy are investigated. Finally, the effects of employing D-policy are discussed.

[1]  B. D. Sivazlian.  Approximate Optimal Solution for a D-Policy in an M/G/X Queuing System , 1979 .

[2]  Jewgeni H. Dshalalow.  Queueing processes in bulk systems under the D-policy , 1998 .

[3]  O. J. Boxma,et al.  Note---Note on a Control Problem of Balachandran and Tijms , 1976 .

[4]  Jesús R. Artalejo,et al.  On the M/G/1 queue with D-policy , 2001 .

[5]  Henk Tijms,et al.  Stochastic modelling and analysis: a computational approach , 1986 .

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

[7]  Casey A. Volino,et al.  A First Course in Stochastic Models , 2005, Technometrics.

[8]  K. Chae,et al.  The queue length distribution for the M/G/1 queue under the D-policy , 2001 .

[9]  D. Bharat.  Generalizations of the stochastic decomposition results for single server queues with vacations , 1990 .

[10]  Kashi R. Balachandran,et al.  Control Policies for a Single Server System , 1973 .

[11]  V. Balachandran,et al.  Comment on “Solving the 'Marketing Mix' Problem using Geometric Programming” , 1975 .

[12]  C. D. Litton,et al.  A First Course in Bulk Queues , 1983 .

[13]  Jesus R. Artalejo,et al.  A note on the optimality of the N- and D-policies for the M/G/1 queue , 2002, Oper. Res. Lett..

[14]  C. Chree,et al.  [Letters to Editor] , 1925, Nature.

[15]  Ho Woo Lee,et al.  Queue Length Analysis of MAP/G/1 Queue Under D-Policy , 2004 .

[16]  Jewgeni H. Dshalalow.  A note on D-policy bulk queueing systems , 2001, Journal of Applied Probability.

[17]  Offer Kella,et al.  Optimality of D-Policies for an M/G/1 Queue with a Removable Server , 2002, Queueing Syst. Theory Appl..

[18]  David Frankel,et al.  brief review: Queueing Analysis: A Foundation of Performance Evaluation. Volume 1: Vacation and Priority Systems, Part 1 by H. Takagi (North-Holland, 1991) , 1991, PERV.

[19]  M. L. Chaudhry,et al.  A first course in bulk queues , 1983 .

[20]  B. D. Sivazlian,et al.  Distributions and first moments of the busy and idle periods in controllable M/G/1 Queueing Models with Simple and Dyadic Policies , 1995 .

[21]  M. Yadin,et al.  Queueing Systems with a Removable Service Station , 1963 .

[22]  Rosa E. Lillo,et al.  On optimal exhaustive policies for the M/G/1-queue , 2000, Oper. Res. Lett..

[23]  Kyung C. Chae,et al.  Workload and Waiting Time Analyses of MAP/G/1 Queue under D-policy , 2004, Queueing Syst. Theory Appl..

[24]  Henk C. Tijms,et al.  A First Course in Stochastic Models: Tijms/Stochastic Models , 2003 .

[25]  Shun-Chen Niu,et al.  The Waiting-Time Distribution for the GI/G/1 Queue under the D-Policy , 1992, Probability in the Engineering and Informational Sciences.

[26]  Daniel P. Heyman,et al.  The T-Policy for the M/G/1 Queue , 1977 .

[27]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[28]  Jim Freeman,et al.  Stochastic Processes (Second Edition) , 1996 .

[29]  Panagiotis Kasteridis,et al.  On the d-policy for the m/g/1 queue , 2001 .

[30]  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 .

[31]  Jewgeni H. Dshalalow.  On applications of excess level processes to ( N , D ) -policy bulk queueing systems , 1996 .

[32]  Kyung-Chul Chae,et al.  On the Optimal D-Policy for the M/G/1 Queue , 1999 .