Semi-open problems in open and closed queueing networks

56 mins 18 secs, 262.38 MB, WebM 480x360, 25.0 fps, 44100 Hz, 636.3 kbits/sec

Share this media item:

Embed this media item:

<iframe width="_width_" height="_height_" src="https://sms.cam.ac.uk/media/849620/embed" frameborder="0" scrolling="no" allowfullscreen></iframe>

Choose size:

About this item

Available Formats

About this item

Description:	Boxma, O (Technische Universiteit Eindhoven) Wednesday 19 May 2010, 16:00-17:00

Created:

2010-05-27 15:00

Collection:

Stochastic Processes in Communication Sciences

Publisher:

Isaac Newton Institute

Boxma, O

Language:

eng (English)

Credits:

Author:

Boxma, O


Abstract:	In this talk we consider both a closed cyclic two-queue system and an open tandem two-queue system, consisting of a single server FCFS queue with general service time distribution and a single server FCFS queue with exponential service time distribution. For the closed cyclic system, the joint steady-state sojourn time distribution of a tagged customer visiting first the M queue and then the G queue was obtained in [2]. It is easily seen that this distribution is in general different from the joint steady-state sojourn time distribution in first the G queue and then the M queue; determination of the latter distribution has remained an open problem. The main goal of the talk is to demonstrate how that joint distribution can be obtained. The used methodology may have larger applicability; in the last part of the talk we shall discuss ongoing work on using the same method to determine the joint steady-state distribution of the sojourn times of a tagged customer in an M/G/1 FCFS queue followed by a ./M/1 FCFS queue. For the latter open tandem model, the joint steady-state queue length distribution has been obtained in [1] using a boundary value method. References: 1. J.P.C. Blanc, R. Iasnogorodski and Ph. Nain (1988). Analysis of the M/GI/1 -> ./M/1 queueing model. Queueing Systems 3, 129-156. O.J. Boxma (1983). The cyclic queue with one general and one exponential server. Adv. Appl. Probab. 15, 857-873. Note: This is joint work with Hans Daduna

Abstract:

In this talk we consider both a closed cyclic two-queue system and an open tandem two-queue system, consisting of a single server FCFS queue with general service time distribution and a single server FCFS queue with exponential service time distribution. For the closed cyclic system, the joint steady-state sojourn time distribution of a tagged customer visiting first the M queue and then the G queue was obtained in [2]. It is easily seen that this distribution is in general different from the joint steady-state sojourn time distribution in first the G queue and then the M queue; determination of the latter distribution has remained an open problem. The main goal of the talk is to demonstrate how that joint distribution can be obtained.
The used methodology may have larger applicability; in the last part of the talk we shall discuss ongoing work on using the same method to determine the joint steady-state distribution of the sojourn times of a tagged customer in an M/G/1 FCFS queue followed by a ./M/1 FCFS queue. For the latter open tandem model, the joint steady-state queue length distribution has been obtained in [1] using a boundary value method.

References: 1. J.P.C. Blanc, R. Iasnogorodski and Ph. Nain (1988). Analysis of the M/GI/1 -> ./M/1 queueing model. Queueing Systems 3, 129-156. O.J. Boxma (1983). The cyclic queue with one general and one exponential server. Adv. Appl. Probab. 15, 857-873. Note: This is joint work with Hans Daduna

Available Formats

Format	Quality	Bitrate	Size
MPEG-4 Video	480x360	1.84 Mbits/sec	778.29 MB	View	Download
WebM *	480x360	636.3 kbits/sec	262.38 MB	View	Download
Flash Video	480x360	804.89 kbits/sec	332.39 MB	View	Download
iPod Video	480x360	505.38 kbits/sec	208.71 MB	View	Download
QuickTime	384x288	848.46 kbits/sec	350.39 MB	View	Download
MP3	44100 Hz	125.02 kbits/sec	51.42 MB	Listen	Download
Windows Media Video		477.24 kbits/sec	197.09 MB	View	Download
Auto	(Allows browser to choose a format it supports)