Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T09:41:18.006Z Has data issue: false hasContentIssue false
  • English
  • Français

MOMENTS OF THE DURATION OF BUSY PERIODS OF MX/G/1/n SYSTEMS

Published online by Cambridge University Press:  27 May 2008

António Pacheco  and
H. Ribeiro
António Pacheco
Affiliation:
Department of Mathematics and CEMATInstituto Superior Técnico—Technical University of Lisbon1049-001 Lisboa, Portugal E-mail: [email protected]
H. Ribeiro
Affiliation:
CEMAT and Instituto Politécnico de Leiria Escola Superior de Tecnologia e Gestão Morro do Lena–Alto do Vieiro 2411-901 Leiria, Portugal E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We derive a simple recursion to compute moments of arbitrary order of the duration of busy periods of MX/G/1/n systems starting with an arbitrary number of customers in the system.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 3 , July 2008 , pp. 347 - 354
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Abramov, V.M. (1997). On a property of a refusals stream. Journal of Applied Probability 34(3): 800–805.CrossRefGoogle Scholar
2Cooper, R.B. & Tilt, B. (1976). On the relationship between the distribution of maximal queue length in the M/G/1 queue and the mean busy period in the M/G/1/n queue. Journal of Applied Probability 13(1): 195–199.CrossRefGoogle Scholar
3Harris, T.J. (1971). The remaining busy period of a finite queue. Operations Research 19: 219–223.CrossRefGoogle Scholar
4Kleinrock, L. (1975). Queueing systems. Vol. 1: Theory. New York: Wiley.Google Scholar
5Kulkarni, V.G. (1995). Modeling and analysis of stochastic systems. London: Chapman and Hall.Google Scholar
6Kwiatkowska, M., Norman, G. & Pacheco, A. (2002). Model checking CSL until formulae with random time bounds. In Herman, H. & Segala, R. (eds.), Process algebra and probabilistic methods, performance modeling and verification. Berlin: Springer.Google Scholar
7Miller, L.W. (1975). A note on the busy period of an M/G/1 finite queue. Operations Research 23(6): 1179–1182.CrossRefGoogle Scholar
8Peköz, E.A., Righter, R. & Xia, C.H. (2003). Characterizing losses during busy periods in finite buffer systems. Journal of Applied Probability 40(1): 242–249.CrossRefGoogle Scholar
9Perry, D., Stadje, W. & Zacks, S. (2000). Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility. Operations Research Letters 27(4): 163–174.CrossRefGoogle Scholar
10Ribeiro, H. (2007). Customer loss probabilities and other performance measures of regular and oscillating systems. Ph.D. thesis, Instituto Superior Técnico, Technical University of Lisbon, Lisbon.Google Scholar
11Shanthikumar, J.G. & Sumita, U. (1985). On the busy-period distributions of M/G/1/K queues with state-dependent arrivals and FCFS/LCFS-P service disciplines. Journal of Applied Probability 22(4): 912–919.CrossRefGoogle Scholar
12Willmot, G.E. (1993). On recursive evaluation of mixed-Poisson probabilities and related quantities. Scandinavian Actuarial Journal 2: 114–133.Google Scholar