Complutense University Library

On the M/G/1 queue with D-policy

Artalejo, Jesús R. (2001) On the M/G/1 queue with D-policy. Applied Mathematical Modelling , 25 (12). pp. 1055-1069. ISSN 0307-904X

[img] PDF
Restricted to Repository staff only until 31 December 2020.

149kB

Official URL: http://www.sciencedirect.com/science/article/pii/S0307904X01000312

View download statistics for this eprint

==>>> Export to other formats

Abstract

This paper deals with the M/G/1queue with D-policy, i.e., the server is turned off at the end of a busy period and turned on when the cumulative amount of work firstly exceeds some fixed value D. We first concentrate on the computation of the steady-state probabilities. The first moments and relationships among the busy period, the number of customers served and other performance measures are investigated. Some variants of the main model and the special case of the M/M/1 are also studied.


Item Type:Article
Additional Information:

This research was supported by DGICYT grant PB98-0837 and the European Commission through INTAS 96-0828. I want to thank Professors J.H. Dshalalow, B.D. Sivazlian and H.C. Tijms for their kind cooperation.

Uncontrolled Keywords:M/G/1queues; Control of the service process; Steady-state probabilities; Moment relationships; Renewal theory
Subjects:Sciences > Mathematics > Operations research
ID Code:15802
References:

K.R. Balachandran. Control policies for a single server system. Manage. Sci., 19 (1973), pp. 1013–1018

K.R. Balachandran, H.C. Tijms. On the D-policy for the M/G/1queue. Manage. Sci., 21 (1975), pp. 1073–1076

O.J. Boxma. Note on a control problem by Balachandran and Tijms. Manage. Sci., 22 (1976), pp. 916–917

T.B. Crabill, D. Gross, M.J. Magazine. A classified bibliography of research in optimal design and control of queues. Oper. Res., 25 (1977), pp. 219–232

B.T. Doshi. Queueing systems with vacations – A survey. Queueing Syst., 1 (1986), pp. 29–66

B.T. Doshi. Single-server queues with vacations. H. Takagi (Ed.), Stochastic Analysis of Computer and Communications Systems, North-Holland, Amsterdam (1990), pp. 217–265

J.H. Dshalalow- On applications of excess level processes to (N,D)-policy bulk queueing systems. J. Appl. Math. Stochastic Anal., 9 (1996), pp. 551–562 (Corrections in: J. Appl. Math. Stochastic Anal. 10 (1997) 207–208)

J.H. Dshalalow. Queueing processes in bulk systems under D-policy. J. Appl. Probab., 35 (1998), pp. 976–989

S.W. Fuhrmann, R.B. Cooper. Stochastic decompositions in the M/G/1queue with generalized vacations. Oper. Res., 33 (1985), pp. 1117–1129

K.G. Gakis, H.K. Rhee, B.D. Sivazlian. Distributions and first moments of the busy and idle periods in controllable M/G/1 queueing models with simple and dyadic policies. Stochastic Anal. Appl., 13 (1995), pp. 47–81

W.J. Gray, P.P. Wang. A vacation queueing model with service breakdowns. Appl. Math. Modelling, 24 (2000), pp. 391–400

D.P. Heyman. The T-policy for the M/G/1queue. Manage. Sci., 23 (1977), pp. 775–778

S. Hur. The effect of different arrival rates on the N-policy of M/G/1 with server setup. Appl. Math. Modelling, 23 (1999), pp. 289–299

J. Li, S.-C. Niu. The waiting-time distribution for the GI/G/1queue under the D-policy. Probab. Eng. Informational Sciences, 6 (1992), pp. 287–308

I. Rubin, Z. Zhang. Switch-on policies for communications and queueing systems. L.F.M. De Moraes, E. de Souza, L.F.G. Soares (Eds.), Data Communication Systems and Their Performance, Elsevier, Amsterdam (1988), pp. 315–325

H. Schellhaas. Computation of the state probabilities in a class of semi-regenerative queueing models. J. Jenssen (Ed.), Semi-Markov Models: Theory and Applications, Plenum Press, New York (1986), pp. 111–130

B.D. Sivazlian. Approximate optimal solution for a D-policy in an M/G/1 queuing system. AIIE Trans., 11 (1979), pp. 341–343

L. Takács. Introduction to the Theory of QueuesOxford University Press, New York (1962)

H. Takagi, Queueing Analysis, vols. 1–3, North-Holland, Amsterdam, 1991

J. Teghem Jr. Control of the service process in a queueing system. Eur. J. Oper. Res., 23 (1986), pp. 141–158

H.C. Tijms. Optimal control of the workload in an M/G/1 queueing system with removable server. Math. Operationsforch. u. Statist., 7 (1976), pp. 933–944

H.C. Tijms, A unified steady-state analysis for controlled Markov drift processes in inventory, queueing and replacement problems, Colloquia Mathematica Societatis János Bolyai, Keszthely, 1978, pp. 359–379

H.C. Tijms. Stochastic Models: An Algorithmic ApproachWiley, Chichester (1994)

M. Yadin, P. Naor. Queueing systems with a removable server station. Oper. Res. Quart., 14 (1963), pp. 393–405

Deposited On:02 Jul 2012 11:27
Last Modified:06 Feb 2014 10:31

Repository Staff Only: item control page