Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-17T23:25:07.973Z Has data issue: false hasContentIssue false
  • English
  • Français

Finiteness of moments of virtual work for GI/G/C queues

Published online by Cambridge University Press:  14 July 2016

Saeed Ghahramani
Saeed Ghahramani*
Affiliation:
Towson State University
*
∗ Postal address: Towson State University, Department of Mathematics, Towson, MD 21204, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

Necessary and sufficient conditions for the finiteness of moments of virtual work for GI/G/c queues are presented.

Keywords

REGENERATIVEACTUAL WORKREMAINING SERVICE TIMEFAST SINGLE-SERVER QUEUE
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 2 , June 1989 , pp. 423 - 425
Copyright
Copyright © Applied Probability Trust 1989 

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

[1] Brumelle, S. L. (1971) Some inequalities for parallel-server queues. Operat. Res. 19, 402–413.Google Scholar
[2] Ghahramani, S. (1986) Finiteness of moments of partial busy periods for M/G/c queues. J. Appl. Prob. 23, 261–264.Google Scholar
[3] Kiefer, J. and Wolfowitz, J. (1955) On the theory of queues with many servers. Trans. Amer. Math. Soc. 78, 1–18.Google Scholar
[4] Kiefer, J. and Wolfowitz, J. (1956) On the characteristics of the general queueing process with applications to random walks. Ann. Math. Statist. 27, 147–161.Google Scholar
[5] Ramalhoto, M. F. (1984) Bounds for the variance of the busy period of the M/G/8 queue. Adv. Appl. Prob. 16, 929–932.Google Scholar
[6] Takács, L. (1963) The limiting distribution of the virtual waiting time and the queueing size for a single server queue with recurrent input and general service time. Sankyha A25, 91–100.Google Scholar
[7] Thorisson, H. (1985) The queue GI/G/k: Finite moments of the cycle variables and uniform rates of convergence. Commun. Statistics-Stochastic Models, 1(2), 221–238.Google Scholar
[8] Thorisson, H. (1985) On regenerative and ergodic properties of the k-server queue with non-stationary Poisson arrivals. J. Appl. Prob. 22, 893–902.Google Scholar
[9] Whitt, W. (1972) Embedded renewal processes in the GI/G/s queue. J. Appl. Prob. 9, 650–658.Google Scholar
[10] Wolff, R. W. (1977) An upper bound for multi-channel queues. J. Appl. Prob. 14, 884–888.Google Scholar
[11] Wolff, R. W. (1984) Conditions for finite ladder height and delay moments. Operat. Res. 32.Google Scholar