Queueing networks with instantaneous movements: a unified approach by quasi-reversibility

2000 ◽  
Vol 32 (01) ◽  
pp. 284-313 ◽  
Author(s):  
Xiuli Chao ◽  
Masakiyo Miyazawa
Keyword(s):  
Queueing Networks ◽  
Product Form ◽  
Unified Approach ◽  
Stationary Distributions ◽  
Batch Arrivals ◽  
Unified View ◽  
Batch Services ◽  
Product Form Queueing Networks

In this paper we extend the notion of quasi-reversibility and apply it to the study of queueing networks with instantaneous movements and signals. The signals treated here are considerably more general than those in the existing literature. The approach not only provides a unified view for queueing networks with tractable stationary distributions, it also enables us to find several new classes of product form queueing networks, including networks with positive and negative signals that instantly add or remove customers from a sequence of nodes, networks with batch arrivals, batch services and assembly-transfer features, and models with concurrent batch additions and batch deletions along a fixed or a random route of the network.

Queueing networks with instantaneous movements: a unified approach by quasi-reversibility

2000 ◽  
Vol 32 (1) ◽  
pp. 284-313 ◽  
Author(s):  
Xiuli Chao ◽  
Masakiyo Miyazawa
Keyword(s):  
Queueing Networks ◽  
Product Form ◽  
Unified Approach ◽  
Stationary Distributions ◽  
Batch Arrivals ◽  
Unified View ◽  
Batch Services ◽  
Product Form Queueing Networks

In this paper we extend the notion of quasi-reversibility and apply it to the study of queueing networks with instantaneous movements and signals. The signals treated here are considerably more general than those in the existing literature. The approach not only provides a unified view for queueing networks with tractable stationary distributions, it also enables us to find several new classes of product form queueing networks, including networks with positive and negative signals that instantly add or remove customers from a sequence of nodes, networks with batch arrivals, batch services and assembly-transfer features, and models with concurrent batch additions and batch deletions along a fixed or a random route of the network.

Some new results on queueing networks with batch movement

1991 ◽  
Vol 28 (02) ◽  
pp. 409-421 ◽  
Author(s):  
W. Henderson ◽  
P. G. Taylor
Keyword(s):  
Continuous Time ◽  
Queueing Networks ◽  
Equilibrium Distribution ◽  
Product Form ◽  
Batch Arrivals ◽  
Before And After ◽  
Equilibrium Distributions ◽  
Batch Services ◽  
Independence Results ◽  
Networks Of Queues

Product-form equilibrium distributions in networks of queues in which customers move singly have been known since 1957, when Jackson derived some surprising independence results. A product-form equilibrium distribution has also recently been shown to be valid for certain queueing networks with batch arrivals, batch services and even correlated routing. This paper derives the joint equilibrium distribution of states immediately before and after a batch of customers is released into the network. The results are valid for either discrete- or continuous-time queueing networks: previously obtained results can be seen as marginal distributions within a more general framework. A generalisation of the classical ‘arrival theorem' for continuous-time networks is given, which compares the equilibrium distribution as seen by arrivals to the time-averaged equilibrium distribution.

Some new results on queueing networks with batch movement

1991 ◽  
Vol 28 (2) ◽  
pp. 409-421 ◽  
Author(s):  
W. Henderson ◽  
P. G. Taylor
Keyword(s):  
Continuous Time ◽  
Queueing Networks ◽  
Equilibrium Distribution ◽  
Product Form ◽  
Batch Arrivals ◽  
Before And After ◽  
Equilibrium Distributions ◽  
Batch Services ◽  
Independence Results ◽  
Networks Of Queues

Product-form equilibrium distributions in networks of queues in which customers move singly have been known since 1957, when Jackson derived some surprising independence results. A product-form equilibrium distribution has also recently been shown to be valid for certain queueing networks with batch arrivals, batch services and even correlated routing.This paper derives the joint equilibrium distribution of states immediately before and after a batch of customers is released into the network. The results are valid for either discrete- or continuous-time queueing networks: previously obtained results can be seen as marginal distributions within a more general framework. A generalisation of the classical ‘arrival theorem' for continuous-time networks is given, which compares the equilibrium distribution as seen by arrivals to the time-averaged equilibrium distribution.

Mean value analysis by chain of product form queueing networks

1989 ◽  
Vol 38 (3) ◽  
pp. 432-442 ◽  
Author(s):  
A.E. Conway ◽  
E. de Souza e Silva ◽  
S.S. Lavenberg
Keyword(s):  
Queueing Networks ◽  
Mean Value ◽  
Product Form ◽  
Value Analysis ◽  
Mean Value Analysis ◽  
Product Form Queueing Networks

On closed support T-Invariants and the traffic equations

1998 ◽  
Vol 35 (2) ◽  
pp. 473-481 ◽  
Author(s):  
Richard J. Boucherie ◽  
Matteo Sereno
Keyword(s):  
Petri Nets ◽  
Queueing Networks ◽  
Stochastic Petri Nets ◽  
Product Form ◽  
Approximate Analysis ◽  
Existence Of A Solution ◽  
Exact Analysis ◽  
Necessary And Sufficient ◽  
Product Form Queueing Networks

The traffic equations are the basis for the exact analysis of product form queueing networks, and the approximate analysis of non-product form queueing networks. Conditions characterising the structure of the network that guarantees the existence of a solution for the traffic equations are therefore of great importance. This note shows that the new condition stating that each transition is covered by a minimal closed support T-invariant, is necessary and sufficient for the existence of a solution for the traffic equations for batch routing queueing networks and stochastic Petri nets.

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