MRE Analysis of Open Exponential Queueing Networks with Server Vacations and Blocking

1996 ◽  
pp. 111-122
Author(s):  
Demetres D. Kouvatsos ◽  
Charalabos A. Skianis
Keyword(s):  
Queueing Networks ◽  
Server Vacations

Routing and Singular Control for Queueing Networks in Heavy Traffic

1989 ◽  
Author(s):  
Luiz F. Martins ◽  
Harold J. Kushner
Keyword(s):  
Queueing Networks ◽  
Heavy Traffic ◽  
Singular Control

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (02) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network. This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

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