Toeplitz-Circulant Preconditioners for Toeplitz Systems and their Applications to Queueing Networks with Batch Arrivals

1996 ◽  
Vol 17 (3) ◽  
pp. 762-772 ◽  
Author(s):  
Raymond H. Chan ◽  
Wai-Ki Ching
Keyword(s):  
Queueing Networks ◽  
Batch Arrivals ◽  
Circulant Preconditioners ◽  
Toeplitz Systems

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.

The Best Circulant Preconditioners for Hermitian Toeplitz Systems

2000 ◽  
Vol 38 (3) ◽  
pp. 876-896 ◽  
Author(s):  
Raymond H. Chan ◽  
Andy M. Yip ◽  
Michael K. Ng
Keyword(s):  
Circulant Preconditioners ◽  
Toeplitz Systems

Poisson functionals of Markov processes and queueing networks

1989 ◽  
Vol 21 (3) ◽  
pp. 595-611 ◽  
Author(s):  
Richard F. Serfozo
Keyword(s):  
Markov Process ◽  
Point Process ◽  
Queueing Networks ◽  
Marked Point ◽  
Queueing Systems ◽  
Marked Point Process ◽  
Reverse Time ◽  
Constant Intensity ◽  
Batch Arrivals ◽  
Markovian Processes

We present conditions under which a point process of certain jump times of a Markov process is a Poisson process. The central idea is that if the Markov process is stationary and the compensator of the point process in reverse time has a constant intensity a, then the point process is Poisson with rate a. A known example is that the output flow from an M/M/1 queueing system is Poisson. We present similar Poisson characterizations of more general marked point process functionals of a Markov process. These results yield easy-to-use criteria for a collection of such processes to be multivariate Poisson, compound Poisson, or marked Poisson with a specified dependence or independence. We discuss several applications for queueing systems with batch arrivals and services and for networks of queues. We also indicate how our results extend to functionals of non-Markovian processes.

The best circulant preconditioners for Hermitian Toeplitz systems II: The multiple-zero case

2002 ◽  
Vol 92 (1) ◽  
pp. 17-40 ◽  
Author(s):  
Raymond H. Chan ◽  
Michael K. Ng ◽  
Andy M. Yip
Keyword(s):  
Multiple Zero ◽  
Circulant Preconditioners ◽  
Toeplitz Systems

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.

Poisson functionals of Markov processes and queueing networks

1989 ◽  
Vol 21 (03) ◽  
pp. 595-611 ◽  
Author(s):  
Richard F. Serfozo
Keyword(s):  
Markov Process ◽  
Point Process ◽  
Queueing Networks ◽  
Marked Point ◽  
Queueing Systems ◽  
Marked Point Process ◽  
Reverse Time ◽  
Constant Intensity ◽  
Batch Arrivals ◽  
Markovian Processes

We present conditions under which a point process of certain jump times of a Markov process is a Poisson process. The central idea is that if the Markov process is stationary and the compensator of the point process in reverse time has a constant intensitya, then the point process is Poisson with ratea.A known example is that the output flow from anM/M/1 queueing system is Poisson. We present similar Poisson characterizations of more general marked point process functionals of a Markov process. These results yield easy-to-use criteria for a collection of such processes to be multivariate Poisson, compound Poisson, or marked Poisson with a specified dependence or independence. We discuss several applications for queueing systems with batch arrivals and services and for networks of queues. We also indicate how our results extend to functionals of non-Markovian processes.

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.

A Geometric Product-Form Distribution for a Queueing Network by Non-Standard Batch Arrivals and Batch Transfers

1997 ◽  
Vol 29 (02) ◽  
pp. 523-544 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Peter G. Taylor
Keyword(s):  
Stationary Distribution ◽  
Queueing Networks ◽  
Queueing Network ◽  
Product Form ◽  
Arrival Process ◽  
Service Discipline ◽  
Batch Service ◽  
Batch Arrivals ◽  
Geometric Product ◽  
Number Of Customers

We introduce a batch service discipline, called assemble-transfer batch service, for continuous-time open queueing networks with batch movements. Under this service discipline a requested number of customers is simultaneously served at a node, and transferred to another node as, possibly, a batch of different size, if there are sufficient customers there; the node is emptied otherwise. We assume a Markovian setting for the arrival process, service times and routing, where batch sizes are generally distributed. Under the assumption that extra batches arrive while nodes are empty, and under a stability condition, it is shown that the stationary distribution of the queue length has a geometric product form over the nodes if and only if certain conditions are satisfied for the extra arrivals. This gives a new class of queueing networks which have tractable stationary distributions, and simultaneously shows that the product form provides a stochastic upper bound for the stationary distribution of the corresponding queueing network without the extra arrivals.

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