Ergodicity of Jackson-type queueing networks

1994 ◽  
Vol 17 (1-2) ◽  
pp. 5-72 ◽  
Author(s):  
Fran�ois Baccelli ◽  
Serguei Foss
Keyword(s):  
Queueing Networks ◽  
Jackson Type

Overall station balance and decomposability for non-Markovian queueing networks

1998 ◽  
Vol 30 (03) ◽  
pp. 870-887 ◽  
Author(s):  
D. Fakinos ◽  
A. Economou
Keyword(s):  
Queueing Networks ◽  
Sufficient Conditions ◽  
Queueing Network ◽  
Necessary And Sufficient Conditions ◽  
Jackson Type ◽  
Necessary And Sufficient ◽  
Markovian Queueing Networks

Introducing the concept of overall station balance which extends the notion of station balance to non-Markovian queueing networks, several necessary and sufficient conditions are given for overall station balance to hold. Next the concept of decomposability is introduced and it is related to overall station balance. A particular case corresponding to a Jackson-type queueing network is considered in some more detail.

Overall station balance and decomposability for non-Markovian queueing networks

1998 ◽  
Vol 30 (3) ◽  
pp. 870-887 ◽  
Author(s):  
D. Fakinos ◽  
A. Economou
Keyword(s):  
Queueing Networks ◽  
Sufficient Conditions ◽  
Queueing Network ◽  
Necessary And Sufficient Conditions ◽  
Jackson Type ◽  
Necessary And Sufficient ◽  
Markovian Queueing Networks

Introducing the concept of overall station balance which extends the notion of station balance to non-Markovian queueing networks, several necessary and sufficient conditions are given for overall station balance to hold. Next the concept of decomposability is introduced and it is related to overall station balance. A particular case corresponding to a Jackson-type queueing network is considered in some more detail.

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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