scholarly journals Stochastic processes in networks of queues with exponential service times and only one class of customers

2014 ◽  
Vol 8 ◽  
pp. 5497-5505
Author(s):  
M. A. M. Ferreira
Keyword(s):  
Stochastic Processes ◽  
Service Times ◽  
Networks Of Queues

Insensitivity of processes with interruptions

1989 ◽  
Vol 26 (2) ◽  
pp. 242-258 ◽  
Author(s):  
W. Henderson ◽  
P. Taylor
Keyword(s):  
Markov Processes ◽  
Vegetation Community ◽  
Distributed Service ◽  
General Distributions ◽  
The Mean ◽  
Service Times ◽  
Semi Markov Processes ◽  
Networks Of Queues

The theory of insensitivity within generalised semi-Markov processes is extended to cover classes of models in which the generally distributed lifetimes can be terminated prematurely by the deaths of negative exponentially distributed lifetimes. As a consequence of this approach it is shown that there exist classes of processes which are insensitive with respect to characteristics of the general distributions other than the mean. Two examples are given. The first is an analysis of networks of queues in which the generally distributed service times can be interrupted with resulting changes in routing probabilities. The second is a model for the effect of disturbances on the evolution of a vegetation community.

scholarly journals A simple proof of a result of Iglehart and Shedler

1985 ◽  
Vol 17 (1) ◽  
pp. 239-241
Author(s):  
Mark Berman
Keyword(s):  
Confidence Intervals ◽  
Simple Proof ◽  
Passage Time ◽  
Alternative Proof ◽  
Multiclass Networks ◽  
Simple Alternative ◽  
General Service Times ◽  
Service Times ◽  
General Service ◽  
Networks Of Queues

Iglehart and Shedler (1983) prove that the ‘labelled jobs’ method for estimation of passage-time characteristics in closed multiclass networks of queues with general service times provides asymptotically shorter confidence intervals than does the ‘marked job’ method. A simple alternative proof of this result, under slightly more restrictive conditions, is given here.

scholarly journals A simple proof of a result of Iglehart and Shedler

1985 ◽  
Vol 17 (01) ◽  
pp. 239-241
Author(s):  
Mark Berman
Keyword(s):  
Confidence Intervals ◽  
Simple Proof ◽  
Passage Time ◽  
Alternative Proof ◽  
Multiclass Networks ◽  
Simple Alternative ◽  
General Service Times ◽  
Service Times ◽  
General Service ◽  
Networks Of Queues

Iglehart and Shedler (1983) prove that the ‘labelled jobs’ method for estimation of passage-time characteristics in closed multiclass networks of queues with general service times provides asymptotically shorter confidence intervals than does the ‘marked job’ method. A simple alternative proof of this result, under slightly more restrictive conditions, is given here.

The insensitivity of stationary probabilities in networks of queues

1978 ◽  
Vol 10 (04) ◽  
pp. 906-912 ◽  
Author(s):  
R. Schassberger
Keyword(s):  
Stochastic Processes ◽  
Service Time ◽  
General Class ◽  
Special Cases ◽  
Stationary Probabilities ◽  
Networks Of Queues

The stationary probabilities for certain networks of queues as defined by Kelly [4] were recently shown by Barbour [1] to depend on the service-time distributions involved only through their means. This type of insensitivity has been studied by König and Jansen [5] for a general class of stochastic processes. Kelly's networks yield special cases of such processes. We point this out in the present paper, thus shedding new light on the insensitivity phenomenon observed in these networks and its connection with the phenomenon of local balance. As a consequence of our recent study [8] we also obtain a new insensitivity result for these networks.

The insensitivity of stationary probabilities in networks of queues

1978 ◽  
Vol 10 (4) ◽  
pp. 906-912 ◽  
Author(s):  
R. Schassberger
Keyword(s):  
Stochastic Processes ◽  
Service Time ◽  
General Class ◽  
Special Cases ◽  
Stationary Probabilities ◽  
Networks Of Queues

The stationary probabilities for certain networks of queues as defined by Kelly [4] were recently shown by Barbour [1] to depend on the service-time distributions involved only through their means. This type of insensitivity has been studied by König and Jansen [5] for a general class of stochastic processes. Kelly's networks yield special cases of such processes. We point this out in the present paper, thus shedding new light on the insensitivity phenomenon observed in these networks and its connection with the phenomenon of local balance. As a consequence of our recent study [8] we also obtain a new insensitivity result for these networks.

Insensitivity of processes with interruptions

1989 ◽  
Vol 26 (02) ◽  
pp. 242-258 ◽  
Author(s):  
W. Henderson ◽  
P. Taylor
Keyword(s):  
Markov Processes ◽  
Vegetation Community ◽  
Distributed Service ◽  
General Distributions ◽  
The Mean ◽  
Service Times ◽  
Semi Markov Processes ◽  
Networks Of Queues

The theory of insensitivity within generalised semi-Markov processes is extended to cover classes of models in which the generally distributed lifetimes can be terminated prematurely by the deaths of negative exponentially distributed lifetimes. As a consequence of this approach it is shown that there exist classes of processes which are insensitive with respect to characteristics of the general distributions other than the mean. Two examples are given. The first is an analysis of networks of queues in which the generally distributed service times can be interrupted with resulting changes in routing probabilities. The second is a model for the effect of disturbances on the evolution of a vegetation community.

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