# 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…

## 24 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…

### Workload and busy period for $$M/GI/1$$M/GI/1 with a general impatience mechanism

- Computer ScienceQueueing Syst. Theory Appl.
- 2013

A unified approach to impatience under FCFS discipline based on the vector process of workload and busy time is presented, which covers the special cases of impatience on waiting times as well as impatient on sojourn times.

## References

SHOWING 1-10 OF 16 REFERENCES

### The Busy Period of an M/G/1 Queue with Customer Impatience

- MathematicsJournal of Applied Probability
- 2010

The busy period distribution for various choices of the patience time distribution is determined for an M/G/1 queue in which an arriving customer does not enter the system whenever its virtual waiting time, i.e. the amount of work seen upon arrival, is larger than a certain random patience time.

### Single-server queues with impatient customers

- MathematicsAdvances in Applied Probability
- 1984

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.…

### The Virtual Waiting Time of the M/G/1 Queue with Impatient Customers

- MathematicsQueueing Syst. Theory Appl.
- 2001

The M/G/1 queue with impatient customers is studied and the complete formula of the limiting distribution of the virtual waiting time is derived explicitly using a martingale argument.

### Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility

- MathematicsOper. Res. Lett.
- 2000

### Queues with Impatient Customers

- Business
- 2011

It is possible that queueing models that combine the queue with the on hand inventory, completion of service with occurrences of demand, and the impatience time with the lifetime of the product could be useful for describing some types of perishable inventory systems.

### Reneging Phenomena in Single Channel Queues

- MathematicsMath. Oper. Res.
- 1979

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.

### The M/G/1 Queue with Quasi-Restricted Accessibility

- Mathematics
- 2007

We consider single-server queues of the M/G/1 kind with a special kind of partial customer rejection called quasi-restricted accessibility (QRA). Under QRA, the actual service time assigned to an…

### The Markovian Queue with Bounded Waiting time

- Computer Science
- 1977

The single-server queueing system is studied where arrivals are rejected if their waiting plus service times would exceed a fixed amount K. Applications of this model include equipment repair…

### Queuing with Impatient Customers and Ordered Service

- Business
- 1957

Two types of customer behavior are considered: (1) if a customer is acquired for service before he has waited a time τ0, he remains in the queue until served irrespective of whether or not his total…

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

- Mathematics
- 1967

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…