Networks of Queues

2013 ◽  
pp. 1037-1041
Author(s):  
Richard F. Serfozo
Keyword(s):  
Networks Of Queues

PROCESSOR SHARING G-QUEUES WITH INERT CUSTOMERS AND CATASTROPHES: A MODEL FOR SERVER AGING AND REJUVENATION

2017 ◽  
Vol 31 (4) ◽  
pp. 420-435 ◽  
Author(s):  
J.-M. Fourneau ◽  
Y. Ait El Majhoub
Keyword(s):  
Steady State ◽  
Product Form ◽  
Processor Sharing ◽  
Service Capacity ◽  
Steady State Distribution ◽  
State Distribution ◽  
Signal Arrival ◽  
Open Networks ◽  
Networks Of Queues

We consider open networks of queues with Processor-Sharing discipline and signals. The signals deletes all the customers present in the queues and vanish instantaneously. The customers may be usual customers or inert customers. Inert customers do not receive service but the servers still try to share the service capacity between all the customers (inert or usual). Thus a part of the service capacity is wasted. We prove that such a model has a product-form steady-state distribution when the signal arrival rates are positive.

Networks of queues

1976 ◽  
Vol 8 (2) ◽  
pp. 416-432 ◽  
Author(s):  
F. P. Kelly
Keyword(s):  
Communication Networks ◽  
The State ◽  
Machine Interference ◽  
Equilibrium Distributions ◽  
Reversible Processes ◽  
Networks Of Queues

The behaviour in equilibrium of networks of queues is studied. Equilibrium distributions are obtained and in certain cases it is shown that the state of an individual queue is independent of the state of the rest of the network. The processes considered in this paper are irreversible; however, the method used to establish equilibrium distributions is one which has previously only been used when dealing with reversible processes. Results are obtained for models of communication networks, machine interference and birth-illness-death processes.

scholarly journals Weak Convergence Limits for Closed Cyclic Networks of Queues with Multiple Bottleneck Nodes

2012 ◽  
Vol 49 (1) ◽  
pp. 60-83
Author(s):  
Ole Stenzel ◽  
Hans Daduna
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Time Distribution ◽  
Idle Time ◽  
Single Server ◽  
Sojourn Time Distribution ◽  
Cyclic Networks ◽  
Number Of Customers ◽  
Networks Of Queues ◽  
Asymptotic Behaviours

We consider a sequence of cycles of exponential single-server nodes, where the number of nodes is fixed and the number of customers grows unboundedly. We prove a central limit theorem for the cycle time distribution. We investigate the idle time structure of the bottleneck nodes and the joint sojourn time distribution that a test customer observes at the nonbottleneck nodes during a cycle. Furthermore, we study the filling behaviour of the bottleneck nodes, and show that the single bottleneck and multiple bottleneck cases lead to different asymptotic behaviours.

Insensitivity with age-dependent routing

1989 ◽  
Vol 21 (02) ◽  
pp. 398-408 ◽  
Author(s):  
M. Rumsewicz ◽  
W. Henderson
Keyword(s):  
Age Dependent ◽  
Networks Of Queues

The theory of insensitivity is extended to include processes where some of the routing probabilities of the process are made dependent upon the length of time the generally distributed variables have been alive. Examples of such systems are given, including networks of queues with age-dependent routing.

Insensitive average residence times in generalized semi-Markov processes

1981 ◽  
Vol 13 (04) ◽  
pp. 720-735 ◽  
Author(s):  
A. D. Barbour ◽  
R. Schassberger
Keyword(s):  
Steady State ◽  
Markov Processes ◽  
Broad Class ◽  
Residence Times ◽  
Steady State Distribution ◽  
State Distribution ◽  
Lifetime Distributions ◽  
Definition Of ◽  
Semi Markov Processes ◽  
Networks Of Queues

For a broad class of stochastic processes, the generalized semi-Markov processes, conditions are known which imply that the steady state distribution of the process, when it exists, depends only on the means, and not the exact shapes, of certain lifetime distributions entering the definition of the process. It is shown in the present paper that this insensitivity extends to certain average and conditional average residence times. Particularly interesting applications can be found in the field of networks of queues.

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