# The busy period of the queueing system M / G /∞

@article{Stadje1985TheBP, title={The busy period of the queueing system M / G /∞}, author={Wolfgang Stadje}, journal={Journal of Applied Probability}, year={1985}, volume={22}, pages={697-704} }

For the queueing system M/G/oo some distributions connected with the associated busy periods are derived. QUEUES WITH UNLIMITED SERVICE

## 60 Citations

Busy periods in M/M/∞ systems with heterogeneous servers

- MathematicsQueueing Syst. Theory Appl.
- 2006

This note gives a solution for the problem of finding the probability density and probability distribution functions of the N-busy-period length for the M/M/∞ system where the servers are not…

M|G|∞ queue busy period with PME distribution

- Mathematics
- 2013

In this article it is shown that if the busy period of a M|G|∞ queue system is PME distributed, the service time is a random variable with a long-tail distribution. The result is obtained through…

A M/G/∞ Queue Busy Period Distribution Characterizing Parameter

- Mathematics
- 2013

In this work it is proposed a parameter, η, to characterize the M/G/∞ Queue Busy Period distribution that is a modification of the peakedness proposed in Whitt (1984). As this distribution moments…

Idle and busy periods in stable M/M/k queues

- Mathematics
- 1998

This paper finds the first and second moments of the number of arrivals in a stable M / M / k queue during an idle period , i.e. in a period when at least one server is idle. These and similar…

A M/G/inf Queue Busy Period Distribution Characterizing Parameter

- MathematicsComput. Inf. Sci.
- 2013

In this work it is proposed a parameter, ? , to characterize the M/G/ ? Queue Busy Period distribution that is a modification of the peakedness proposed in Whitt (1984). As this distribution moments…

Infinite-server M|G|$\infty$ queueing models with catastrophes

- Mathematics
- 2018

The infinite-server queueing models with homogeneous and non-homogeneous arrivals of customers and catastrophes are considered. The probability generating functions of joint distributions of numbers…

Busy Periods in a System with Heterogeneous Servers or Channels

- MathematicsProbl. Inf. Transm.
- 2005

A solution is given for the problem of finding the probability densities and probability distribution functions of the N-busy period length of a multiple communication channel system having channels with different transmission rates.

The M|M|∞ queue transient probabilities

- Mathematics
- 2018

In the theory and applications of queuing systems, transient probabilities play a key role. Often, due to the difficulty of their calculation they are replaced by the stationary probabilities. In the…

On the Convergence Rate for Queueing and Reliability Models Described by Regenerative Processes*

- Mathematics
- 2016

Convergence rates in total variation are established for some models of queueing theory and reliability theory. The analysis is based on renewal technique and asymptotic results for the renewal…

About some extended Erlang-Sevast'yanov queueing system and its convergence rate (English and Russian versions)

- Mathematics
- 2018

The upper bound for the convergence rate of the distribution of the state of a queuing system with infinitely many servers is obtained, in the case when the intensity of the incoming flow and the…

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