The basic concepts of perturbation analysis of queueing networks with general service time distributions

1990 ◽  
Author(s):  
X.-R. Cao
Keyword(s):  
Perturbation Analysis ◽  
Service Time ◽  
Queueing Networks ◽  
Basic Concepts ◽  
General Service

Notes on the stability of closed queueing networks

1989 ◽  
Vol 26 (3) ◽  
pp. 678-682 ◽  
Author(s):  
Karl Sigman
Keyword(s):  
Service Time ◽  
Continuous Time ◽  
Queueing Networks ◽  
Queue Length ◽  
Sufficient Conditions ◽  
Time Process ◽  
Closed Queueing Networks ◽  
The Stability ◽  
General Service ◽  
Residual Service

A new proof of the stability of closed Jackson-type queueing networks (with general service-time distributions) is given and sufficient conditions are given for obtaining Cesaro, weak and total variation convergence of the continuous-time joint queue length and residual service-time process to a limiting distribution. The result weakens the sufficient conditions (for stability) of Borovkov (1986) by allowing more general service-time distributions.

Smoothed Perturbation Analysis for Single-Server Queues by Some General Service Disciplines

1997 ◽  
Vol 29 (2) ◽  
pp. 545-566 ◽  
Author(s):  
Naoto Miyoshi ◽  
Toshiharu Hasegawa
Keyword(s):  
Perturbation Analysis ◽  
Service Time ◽  
Single Server ◽  
Single Server Queues ◽  
The Family ◽  
Service Disciplines ◽  
Preemptive Resume Priority ◽  
Queueing Processes ◽  
Strongly Consistent ◽  
General Service

We consider some single-server queues with general service disciplines, where the family of the queueing processes are parameterized by the service time distributions. Through the smoothed perturbation analysis (SPA) technique, we present under some mild conditions a unified approach to give the strongly consistent estimator for the gradient of the steady-state mean sojourn time with respect to the parameter of service time distributions, provided that it exists. Although the implementation of the SPA requires the additional sub-paths in general, the derived estimator is given as suitable for single-run computation. Simulation results are presented for queues with non-preemptive and preemptive-resume priority disciplines which demonstrate the performance of our estimators.

Notes on the stability of closed queueing networks

1989 ◽  
Vol 26 (03) ◽  
pp. 678-682 ◽  
Author(s):  
Karl Sigman
Keyword(s):  
Service Time ◽  
Continuous Time ◽  
Queueing Networks ◽  
Queue Length ◽  
Sufficient Conditions ◽  
Time Process ◽  
Closed Queueing Networks ◽  
The Stability ◽  
General Service ◽  
Residual Service

A new proof of the stability of closed Jackson-type queueing networks (with general service-time distributions) is given and sufficient conditions are given for obtaining Cesaro, weak and total variation convergence of the continuous-time joint queue length and residual service-time process to a limiting distribution. The result weakens the sufficient conditions (for stability) of Borovkov (1986) by allowing more general service-time distributions.

Smoothed Perturbation Analysis for Single-Server Queues by Some General Service Disciplines

1997 ◽  
Vol 29 (02) ◽  
pp. 545-566
Author(s):  
Naoto Miyoshi ◽  
Toshiharu Hasegawa
Keyword(s):  
Perturbation Analysis ◽  
Service Time ◽  
Single Server ◽  
Single Server Queues ◽  
The Family ◽  
Service Disciplines ◽  
Preemptive Resume Priority ◽  
Queueing Processes ◽  
Strongly Consistent ◽  
General Service

We consider some single-server queues with general service disciplines, where the family of the queueing processes are parameterized by the service time distributions. Through the smoothed perturbation analysis (SPA) technique, we present under some mild conditions a unified approach to give the strongly consistent estimator for the gradient of the steady-state mean sojourn time with respect to the parameter of service time distributions, provided that it exists. Although the implementation of the SPA requires the additional sub-paths in general, the derived estimator is given as suitable for single-run computation. Simulation results are presented for queues with non-preemptive and preemptive-resume priority disciplines which demonstrate the performance of our estimators.

Some perturbation results for the single-server queue with Poisson input

1965 ◽  
Vol 2 (2) ◽  
pp. 462-466 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Service Time ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Server Queue ◽  
Image Position ◽  
General Service

In a previous paper [2] the author has studied the single-server queue with non-homogeneous Poisson input and general service time, with particular emphasis on the case when the parameter of the Poisson input is of the form

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