Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
  • Home
Hostname: page-component-54cdcc668b-zz2mb Total loading time: 0.221 Render date: 2021-03-08T17:24:09.587Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }
EnglishFrançais
Journal of Applied Probability Journal of Applied Probability

Article contents

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

Part of: Computer system organization Special processes

Published online by Cambridge University Press:  30 July 2019

Yoshiaki Inoue
Yoshiaki Inoue
Affiliation:
Osaka University
Corresponding
E-mail address:
yoshiaki@comm.eng.osaka-u.ac.jp
Get access
Rights & Permissions[Opens in a new window]

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 times, and they leave the system immediately if their services do not start before the expiration of their deadlines. On the other hand, in the M/G/1+Gs queue customers have deadlines for their sojourn times, where customers in service also immediately leave the system when their deadlines expire. In this paper we derive comparison results for performance measures of these models. In particular, we show that 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 the M/G/1+Gw queue.

Keywords

M/G/1 queue impatient customer virtual waiting time loss probability stochastic order

MSC classification

Primary: 60K25: Queueing theory
Secondary: 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 2 , June 2019 , pp. 524 - 532
Copyright
© Applied Probability Trust 2019 

Access options

Get access to the full version of this content by using one of the access options below.
If you should have access and can't see this content please contact technical support.

References

Baccelli, F., Boyer, P., and Hebuterne, G. (1984). Single-server queues with impatient customers. Adv. Appl. Prob. 16, 887–905.CrossRefGoogle Scholar
Bekker, R., Borst., S. C., and Boxma, O. J. (2004). Queues with workload-dependent arrival and service rates. Queueing Systems 46, 537–556.CrossRefGoogle Scholar
Boxma, O., Perry, D., and Stadje, W. (2011). The M/G/1+G queue revisited. Queueing Systems 67, 207–220.CrossRefGoogle Scholar
Brandt, A. and BRANDT, M. (2013). Workload and busy period for M/G/1 with a general impatience mechanism. Queueing Systems 75, 189–209.CrossRefGoogle Scholar
Brill, P.H. and Posner, M. J. M. (1977). Level crossings in point processes applied to queues: Single- server case. Operat. Res. 25, 662–674.CrossRefGoogle Scholar
Browne, S. and Sigman, K. (1992). Work-modulated queues with applications to storage processes. J. Appl. Prob. 29, 699–712.CrossRefGoogle Scholar
Cohen, J. W. (1977). On up- and downcrossings. J. Appl. Prob. 14, 405–410.CrossRefGoogle Scholar
Daley, D. J. (1965). General customer impatience in the queue GI/G/1. J. Appl. Prob. 2, 186–205.CrossRefGoogle Scholar
Inoue, Y. and Takine, T. (2015). Analysis of the loss probability in the M/G/1+G queue, Queueing Systems 80, 363–386.CrossRefGoogle Scholar
Inoue, Y. and Takine, T. (2015). The M/D/1+D queue has the minimum loss probability among M/G/1+G queues. Operat. Res. Lett. 43, 629–632.CrossRefGoogle Scholar
Kovalenko, I. N. (1961). Some queueing problems with restrictions. Theory Prob. Appl. 6, 205–208.CrossRefGoogle Scholar
Mθller, A. and Stoyan, D. (2002). Comparison Methods for Stochastic Models and Risks, John Wiley, Chichester, UK.Google Scholar
Perry, D. and Asmussen, S. (1995). Rejection rules in the M/G/1 queue. Queueing Systems 19, 105–130.CrossRefGoogle Scholar
Pipkin, A. C. (1991). A Course on Integral Equations, Springer, New York, NY.CrossRefGoogle Scholar
Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders, Springer, New York, NY.CrossRefGoogle Scholar
STANFORD, R. E. (1979). Reneging phenomena in single channel queues. Math. Operat. Res. 4, 162–178.CrossRefGoogle Scholar
Van Houdt, B., Lenin, R.B., and Blondia, C. (2003). Delay distribution of (im)patient customers in a discrete time D-MAP/PH/1 queue with age-dependent service times. Queueing Systems 45, 59–73.CrossRefGoogle Scholar
Van Velthoven, J., Van Houdt, B. and Blondia, C. (2005). Response time distribution in a D-MAP/PH/1 queue with general impatience. Stoch. Models 21, 745–765.CrossRefGoogle Scholar
Van Velthoven, J., Van Houdt, B. and Blondia, C. (2006). On the probability of abandonment in queues with limited sojourn and waiting times. Operat. Res. Lett. 34, 333–338.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 10
Total number of PDF views: 74 *
View data table for this chart

* Views captured on Cambridge Core between 30th July 2019 - 8th March 2021. This data will be updated every 24 hours.

1 Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Comparison results for M/G/1 queues with waiting and sojourn time deadlines
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Comparison results for M/G/1 queues with waiting and sojourn time deadlines
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Comparison results for M/G/1 queues with waiting and sojourn time deadlines
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *