Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-24T02:57:41.136Z Has data issue: false hasContentIssue false
  • English
  • Français

The steady-state solution of the M/K2/m queue

Published online by Cambridge University Press:  01 July 2016

Per Hokstad
Per Hokstad*
Affiliation:
University of Trondheim
Get access Rights & Permissions [Opens in a new window]

Abstract

The many-server queue with service time having rational Laplace transform of order 2 is considered. An expression for the asymptotic queue-length distribution is obtained. A relatively simple formula for the mean queue length is also found. A few numerical results on the mean queue length and on the probability of having to wait are given for the case of three servers. Some approximations for these quantities are also considered.

Keywords

MANY SERVER QUEUEQUEUE LENGTH
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 3 , September 1980 , pp. 799 - 823
Copyright
Copyright © Applied Probability Trust 1980 

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

Cohen, J. W. (1979) On the M/G/2 queueing model. Math. Inst., Utrecht.Google Scholar
Cox, D. R. (1955) A use of complex probabilities in the theory of stochastic processes. Proc. Camb. Phil. Soc. 51, 313–319.CrossRefGoogle Scholar
Elldin, A. (1969) Switch Calculations. General Survey, 3rd edn. L. M. Ericsson, Stockholm.Google Scholar
Heffer, J. C. (1969) Steady-state solution of the M/EK/c (∞, FIFO) queueing system. INFOR 7, 16–30.Google Scholar
Hillier, F. S. and Lo, F. D. (1971) Tables for multiple-server queueing systems involving Erlang distributions. Technical Report No. 31, Dept. of Opns Res., Stanford University.Google Scholar
Hokstad, P. (1978) Approximations for the M/G/m queue. Operat. Res. 26, 510–523.CrossRefGoogle Scholar
Hokstad, P. (1979) On the steady state solution of the M/G/2 queue. Adv. Appl. Prob. 11, 240–255.CrossRefGoogle Scholar
Mayhugh, J. O. and McCormick, R. E. (1968) Steady state solution of the queue M/Ek/r. Management Sci. 14, 692–712.CrossRefGoogle Scholar
Shapiro, S. (1966) The M-server queue with Poisson input and gamma-distributed service of order two. Operat. Res. 14, 685–694.Google Scholar
Stoyan, D. (1977) Bounds and approximations in queueing through monotonicity and continuity. Operat. Res. 25, 851–863.CrossRefGoogle Scholar
Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
Takács, L. (1969) On Erlang's formula. Ann. Math. Statist. 40, 71–78.CrossRefGoogle Scholar