Strong Approximations of Irreducible Closed Queueing Networks

1997 ◽  
Vol 29 (2) ◽  
pp. 498-522 ◽  
Author(s):  
Hanqin Zhang
Keyword(s):  
Queueing Networks ◽  
Queue Length ◽  
Rates Of Convergence ◽  
Closed Queueing Networks ◽  
Brownian Motions ◽  
Strong Approximations ◽  
Queue Lengths

A sequence of irreducible closed queueing networks is considered in this paper. We obtain that the queue length processes can be approximated by reflected Brownian motions. Using these approximations, we get rates of convergence of the distributions of queue lengths.

Strong Approximations of Irreducible Closed Queueing Networks

1997 ◽  
Vol 29 (02) ◽  
pp. 498-522 ◽  
Author(s):  
Hanqin Zhang
Keyword(s):  
Queueing Networks ◽  
Queue Length ◽  
Rates Of Convergence ◽  
Closed Queueing Networks ◽  
Brownian Motions ◽  
Strong Approximations ◽  
Queue Lengths

A sequence of irreducible closed queueing networks is considered in this paper. We obtain that the queue length processes can be approximated by reflected Brownian motions. Using these approximations, we get rates of convergence of the distributions of queue lengths.

Notes on the stability of closed queueing networks

1989 ◽  
Vol 26 (3) ◽  
pp. 678-682 ◽  
Author(s):  
Karl Sigman
Keyword(s):  
Service Time ◽  
Continuous Time ◽  
Queueing Networks ◽  
Queue Length ◽  
Sufficient Conditions ◽  
Time Process ◽  
Closed Queueing Networks ◽  
The Stability ◽  
General Service ◽  
Residual Service

A new proof of the stability of closed Jackson-type queueing networks (with general service-time distributions) is given and sufficient conditions are given for obtaining Cesaro, weak and total variation convergence of the continuous-time joint queue length and residual service-time process to a limiting distribution. The result weakens the sufficient conditions (for stability) of Borovkov (1986) by allowing more general service-time distributions.

Notes on the stability of closed queueing networks

1989 ◽  
Vol 26 (03) ◽  
pp. 678-682 ◽  
Author(s):  
Karl Sigman
Keyword(s):  
Service Time ◽  
Continuous Time ◽  
Queueing Networks ◽  
Queue Length ◽  
Sufficient Conditions ◽  
Time Process ◽  
Closed Queueing Networks ◽  
The Stability ◽  
General Service ◽  
Residual Service

A new proof of the stability of closed Jackson-type queueing networks (with general service-time distributions) is given and sufficient conditions are given for obtaining Cesaro, weak and total variation convergence of the continuous-time joint queue length and residual service-time process to a limiting distribution. The result weakens the sufficient conditions (for stability) of Borovkov (1986) by allowing more general service-time distributions.

Queueing networks by negative customers and negative queue lengths

1993 ◽  
Vol 30 (04) ◽  
pp. 931-942 ◽  
Author(s):  
W. Henderson
Keyword(s):  
Queueing Networks ◽  
Queue Length ◽  
Equilibrium Distribution ◽  
State Dependence ◽  
Balance Equations ◽  
Negative Customers ◽  
Jackson Networks ◽  
Geometric Product ◽  
Queue Lengths ◽  
Number Of Customers

A number of papers have recently appeared in the literature in which customers, in moving from node to node in the network arrive as either a positive customer or as a batch of negative customers. A positive customer joining its queue increases the number of customers at the queue by 1 and each negative customer decreases the queue length by 1, if possible. It has been shown that the equilibrium distribution for these networks assumes a geometric product form, that certain partial balance equations prevail and that the parameters of the geometric distributions are, as in Jackson networks, the service facility throughputs of customers. In this paper the previous work is generalised by allowing state dependence into both the service and routing intensities and by allowing the possibility, although not the necessity, for negative customers to build up at the nodes.

Queueing networks by negative customers and negative queue lengths

1993 ◽  
Vol 30 (4) ◽  
pp. 931-942 ◽  
Author(s):  
W. Henderson
Keyword(s):  
Queueing Networks ◽  
Queue Length ◽  
Equilibrium Distribution ◽  
State Dependence ◽  
Balance Equations ◽  
Negative Customers ◽  
Jackson Networks ◽  
Geometric Product ◽  
Queue Lengths ◽  
Number Of Customers

A number of papers have recently appeared in the literature in which customers, in moving from node to node in the network arrive as either a positive customer or as a batch of negative customers. A positive customer joining its queue increases the number of customers at the queue by 1 and each negative customer decreases the queue length by 1, if possible. It has been shown that the equilibrium distribution for these networks assumes a geometric product form, that certain partial balance equations prevail and that the parameters of the geometric distributions are, as in Jackson networks, the service facility throughputs of customers. In this paper the previous work is generalised by allowing state dependence into both the service and routing intensities and by allowing the possibility, although not the necessity, for negative customers to build up at the nodes.

scholarly journals A Probabilistic Approach to Growth Networks

2021 ◽  
Author(s):  
Predrag Jelenković ◽  
Jané Kondev ◽  
Lishibanya Mohapatra ◽  
Petar Momčilović
Keyword(s):  
Large Deviations ◽  
Queueing Networks ◽  
Probabilistic Approach ◽  
Logarithmic Scale ◽  
Single Server ◽  
Closed Queueing Networks ◽  
Single Class ◽  
Rate Functions ◽  
Queue Lengths ◽  
Operating Regimes

Single-class closed queueing networks, consisting of infinite-server and single-server queues with exponential service times and probabilistic routing, admit product-from solutions. Such solutions, although seemingly tractable, are difficult to characterize explicitly for practically relevant problems due to the exponential combinatorial complexity of its normalization constant (partition function). In “A Probabilistic Approach to Growth Networks,” Jelenković, Kondev, Mohapatra, and Momčilović develop a novel methodology, based on a probabilistic representation of product-form solutions and large-deviations concentration inequalities, which identifies distinct operating regimes and yields explicit expressions for the marginal distributions of queue lengths. From a methodological perspective, a fundamental feature of the proposed approach is that it provides exact results for order-one probabilities, even though the analysis involves large-deviations rate functions, which characterize only vanishing probabilities on a logarithmic scale.

scholarly journals Queue Length Forecasting in Complex Manufacturing Job Shops

Forecasting ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 322-338
Author(s):  
Marvin Carl May ◽  
Alexander Albers ◽  
Marc David Fischer ◽  
Florian Mayerhofer ◽  
Louis Schäfer ◽  
...  
Keyword(s):  
Operations Management ◽  
Queue Length ◽  
Manufacturing Systems ◽  
Production Control ◽  
Data Sets ◽  
Job Shops ◽  
Static Data ◽  
Queue Lengths ◽  
Operational Excellence

Currently, manufacturing is characterized by increasing complexity both on the technical and organizational levels. Thus, more complex and intelligent production control methods are developed in order to remain competitive and achieve operational excellence. Operations management described early on the influence among target metrics, such as queuing times, queue length, and production speed. However, accurate predictions of queue lengths have long been overlooked as a means to better understanding manufacturing systems. In order to provide queue length forecasts, this paper introduced a methodology to identify queue lengths in retrospect based on transitional data, as well as a comparison of easy-to-deploy machine learning-based queue forecasting models. Forecasting, based on static data sets, as well as time series models can be shown to be successfully applied in an exemplary semiconductor case study. The main findings concluded that accurate queue length prediction, even with minimal available data, is feasible by applying a variety of techniques, which can enable further research and predictions.

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