# The M/G/1+G queue revisited

@article{Boxma2011TheMQ, title={The M/G/1+G queue revisited}, author={Onno J. Boxma and David Perry and Wolfgang Stadje}, journal={Queueing Systems}, year={2011}, volume={67}, pages={207-220} }

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 than a certain random patience time. We consider the number of customers in the system, the maximum workload during a busy period, and the length of a busy period. We also briefly treat the analogous model in which any customer enters the system and leaves at the end of his patience time or at the…

## 25 Citations

### On completion times in a two-class priority queue with impatience

- Mathematics, BusinessInt. J. Math. Oper. Res.
- 2014

In this note, we consider a two-class priority queueing system with Poisson arrivals, general service time distribution and one server, in which customers that are not currently being served may…

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

- Mathematics, Computer ScienceQueueing Syst. Theory Appl.
- 2015

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.

### Comparison results for M/G/1 queues with waiting and sojourn time deadlines

- MathematicsJ. Appl. Probab.
- 2019

If the service time distribution is new better than used in expectation, then the loss probability in the M/G/1+Gs queue is greater than that in theM/G-1+Gw queue.

### Comparison results for M/G/1 queues with waiting and sojourn time deadlines

- MathematicsJournal of Applied Probability
- 2019

Abstract This paper considers two variants of M/G/1 queues with impatient customers, which are denoted by M/G/1+Gw and M/G/1+Gs. In the M/G/1+Gw queue customers have deadlines for their waiting…

### Analysis of an $$M/M/1+G$$M/M/1+G queue operated under the FCFS policy with exact admission control

- MathematicsQueueing Syst. Theory Appl.
- 2013

This article provides an explicit solution to the functional equation that must be satisfied by the workload distribution, when the system reaches steady state, and derives explicit expressions for the loss ratio and the sojourn time distribution.

### Asymptotic analysis of queueing systems with reneging: A survey of results for FIFO, single class models

- Mathematics
- 2012

### Analysis of Mx/G/1 queues with impatient customers

- BusinessQueueing Syst. Theory Appl.
- 2018

This paper considers a batch arrival queue with impatient customers, and focuses on the virtual and actual waiting times, and on the loss probability of customers.

### A computational algorithm for the loss probability in the M/G/1+PH queue

- Computer Science
- 2017

A computational algorithm for the loss probability in the stationary M/G/1 queue with impatient customers whose impatience times follow a phase-type distribution is developed.

### An M/M/1/N Queueing Model with Retention of Reneged Customers and Balking

- Business
- 2012

The concept of customer balking and reneging has been exploited to a great extent in recent past by the queu- ing modelers. Economically, if we see, the customer impatience (due to balking and…

### An investigation and historical overview of the G/M and M/G queueing processes

- Mathematics
- 2012

We present a historical and theoretical overview of the more complicated and less used G/M and M/G queueing processes, which allow for non-specific arrival and service time distributions. Such a…

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