Time-dependent analysis of M/G/1 vacation models with exhaustive service
- Hideaki Takagi
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We analyze the time-dependent process in severalM/G/1 vacation models, and explicitly obtain the Laplace transform (with respect to an arbitrary point in time) of the joint distribution of server state, queue size, and elapsed time in that state. Exhaustive-serviceM/G/1 systems with multiple vacations, single vacations, an exceptional service time for the first customer in each busy period, and a combination ofN-policy and setup times are considered. The decomposition property in the steady-state joint distribution of the queue size and the remaining service time is demonstrated.
- R.B. Cooper, Queues served in cyclic order: waiting times, Bell Syst. Tech. J. 49 (1970) 399–413.
- B.T. Doshi, A note on stochastic decomposition in aGI/G/1 queue with vacations or setup times, J. Appl. Prob. 22 (1985) 419–428. CrossRef
- B.T. Doshi, Queueing systems with vacations — a survey, Queueing Systems 1 (1986) 29–66. CrossRef
- B.T. Doshi, Single-server queues with vacations, in:Stochastic Analysis of Computer and Communication Systems, H. Takagi (ed.) (Elsevier Science, Amsterdam, 1990) to appear.
- B.T. Doshi, Conditional and unconditional distributions forM/G/1 type queues with server vacations, preprint (1989).
- S.W. Fuhrmann and R.B. Cooper, Stochastic decompositions in theM/G/1 queue with generalized vacations, Oper. Res. 33 (1985) 1117–1129.
- N.K. Jaiswal,Priority Queues (Academic Press, New York, 1968).
- J. Keilson and A. Kooharian, On time dependent queueing processes, Ann. Math. Stat. 31 (1960) 104–112.
- J. Keilson and R. Ramaswamy, The backlog and depletion-time process forM/G/1 vacation models with exhaustive service discipline, J. Appl. Prob. 25 (1988) 404–412. CrossRef
- J. Keilson and L.D. Servi, Dynamics of theM/G/1 vacation model, Oper. Res. 35 (1987) 575–582.
- L. Kleinrock and M.O. Scholl, Packet switching in radio channels: new conflict-free access schemes, IEEE Trans. Commun. COM-28 (1980) 1015–1029. CrossRef
- H. Levy and L. Kleinrock, A queue with starter and a queue with vacations: delay analysis by decomposition, Oper. Res. 34 (1986) 426–436.
- Y. Levy and U. Yechiali, Utilization of idle time in anM/G/1 queueing system, Management Sci. 22 (1975) 202–211.
- D.L. Minh, Transient solutions for some exhaustiveM/G/1 queues with generalized independent vacations, Europ. J. Oper. Res. 36 (1988) 197–201. CrossRef
- M.F. Neuts, Generalizations of the Pollaczek-Khinchin integral equation in the theory of queues, Advan. Appl. Prob. 18 (1986) 952–990. CrossRef
- M. Scholl and L. Kleinrock, On theM/G/1 queue with rest periods and certain service-independent queueing disciplines, Oper. Res. 31 (1983) 705–719. CrossRef
- J.G. Shanthikumar, On stochastic decomposition inM/G/1 type queues with generalized server vacations, Oper. Res. 36 (1988) 566–569.
- C.E. Skinner, A priority queueing system with server-walking time, Oper. Res. 15 (1967) 278–285.
- B.W. Stuck and E. Arthurs,A Computer and Communications Network Performance Analysis Primer (Prentice-Hall, Englewood Cliffs, NJ, 1985).
- L. Takács,Introduction to the Theory of Queues (Oxford University Press, New York, 1962).
- H. Takagi,Analysis of Polling Systems (The MIT Press, Cambridge, MA, 1986).
- H. Takagi, Queueing analysis of polling models, ACM Computing Surveys 20 (1988) 5–28. CrossRef
- J. Teghem, Jr., Control of the service process in a queueing system, Europ. J. Oper. Res. 23 (1986) 141–158. CrossRef
- P.D. Welch, On a generalizedM/G/1 queueing process in which the first customer of each busy period receives exceptional service, Oper. Res. 12 (1964) 736–752.
- D.M.G. Wishart, An application of ergodic theorems in the theory of queues,Proc. 4th Berkeley Symp. on Mathematical Statistics and Probability, vol. 2 (University of California Press, Berkeley and Loss Angeles, 1961) pp. 581–592.
- M. Yadin and P. Naor, Queueing systems with a removable service station, Oper. Res. Quarterly 14 (1963) 393–405.
- Time-dependent analysis of M/G/1 vacation models with exhaustive service
Volume 6, Issue 1 , pp 369-389
- Cover Date
- Print ISSN
- Online ISSN
- Baltzer Science Publishers, Baarn/Kluwer Academic Publishers
- Additional Links
- Time-dependent queues
- vacation models
- exhaustive service
- multiple vacations
- single vacations
- setup times
- Industry Sectors
- Hideaki Takagi (1)
- Author Affiliations
- 1. IBM Research, Tokyo Research Laboratory, Sanbancho YS Building, 5-11 Sanban-cho, Chiyoda-ku, 102, Tokyo, Japan