Analysis of Mx/G/1 queues with impatient customers

@article{Inoue2018AnalysisOM,
  title={Analysis of Mx/G/1 queues with impatient customers},
  author={Yoshiaki Inoue and Onno J. Boxma and David Perry and Shelemyahu Zacks},
  journal={Queueing Syst. Theory Appl.},
  year={2018},
  volume={89},
  pages={303-350}
}
This paper considers a batch arrival \(\hbox {M}^{\mathrm {x}}/\hbox {G}/1\) queue with impatient customers. We consider two different model variants. In the first variant, customers in the same batch are assumed to have the same patience time, and patience times associated with batches are i.i.d. according to a general distribution. In the second variant, patience times of customers in the same batch are independent, and they follow a general distribution. Both variants are related to an M/G/1… 

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References

SHOWING 1-10 OF 30 REFERENCES

The M/G/1+G queue revisited

We consider an M/G/1 queue with the following form of customer impatience: an arriving customer balks or reneges when its virtual waiting time, i.e., the amount of work seen upon arrival, is larger

Analysis of the loss probability in the M/G/1+G queue

TLDR
It is shown that the series solution of v(x) can be interpreted as the probability density function of a random sum of dependent random variables and its dependency structure is revealed through the analysis of a last-come first-served, preemptive-resume M/G/1 queue with workload-dependent loss.

A batch arrival Mx/M/c queue with impatient customers

General customer impatience in the queue GI/G/1

  • D. Daley
  • Mathematics
    Journal of Applied Probability
  • 1965
For the queueing system GI/G/1 with both waiting-line and service-line customer impatience an integral equation for the limiting waiting-time distribution function W(x) is derived and the existence

Single-server queues with impatient customers

We consider a single-server queueing system in which a customer gives up whenever his waiting time is larger than a random threshold, his patience time. In the case of a GI/GI/1 queue with i.i.d.

Call Centers with Impatient Customers: Many-Server Asymptotics of the M/M/n + G Queue

TLDR
Empirical findings have demonstrated a robust linear relation between the fraction abandoning and average wait, and the QED and QD formulae provide excellent approximation for exact M/M/n + G performance measures.

On the M(n)/M(n)/s Queue with Impatient Calls

Reneging Phenomena in Single Channel Queues

TLDR
This work considers a GI/G/1 queueing system where the nth arrival may renege if his service does not commence before an elapsed random time Zn, and finds solutions to the integral equation for this distribution.

Abandonment versus blocking in many-server queues: asymptotic optimality in the QED regime

TLDR
In the many-server quality and efficiency-driven (QED) regime, a diffusion control problem (DCP) is formulated and used to construct asymptotically optimal controls (of the threshold type) for QCP, which captures the tradeoff between busy signals and customer abandonment.

Queuing with balking and reneging in M|G|1 systems

AM|G|1 queuing process in which units balk with a constant probability (1−β) and renege according to a negative exponential distribution has been considered. The busy period process is first