The effect of increasing service rates in a closed queueing network

1986 ◽  
Vol 23 (2) ◽  
pp. 474-483 ◽  
Author(s):  
J. George Shanthikumar ◽  
David D. Yao
Keyword(s):  
Likelihood Ratio ◽  
Queueing Network ◽  
Stochastic Ordering ◽  
Product Form ◽  
Closed Queueing Network ◽  
Equilibrium Behavior ◽  
Service Rates ◽  
Queue Lengths ◽  
Multivariate Likelihood

In this paper we study the equilibrium behavior of the queue lengths in a product-form closed queueing network when the service rates at a subset of stations (nodes) are increased. Univariate and multivariate likelihood ratio orderings as well as multivariate stochastic ordering of the queue lengths are established to indicate the effect of increasing the service rates. Relations among these orderings are also developed.

The effect of increasing service rates in a closed queueing network

1986 ◽  
Vol 23 (02) ◽  
pp. 474-483 ◽  
Author(s):  
J. George Shanthikumar ◽  
David D. Yao
Keyword(s):  
Likelihood Ratio ◽  
Queueing Network ◽  
Stochastic Ordering ◽  
Product Form ◽  
Closed Queueing Network ◽  
Equilibrium Behavior ◽  
Service Rates ◽  
Queue Lengths ◽  
Multivariate Likelihood

In this paper we study the equilibrium behavior of the queue lengths in a product-form closed queueing network when the service rates at a subset of stations (nodes) are increased. Univariate and multivariate likelihood ratio orderings as well as multivariate stochastic ordering of the queue lengths are established to indicate the effect of increasing the service rates. Relations among these orderings are also developed.

Braess's paradox in a queueing network with state-dependent routing

1997 ◽  
Vol 34 (01) ◽  
pp. 134-154 ◽  
Author(s):  
Bruce Calvert ◽  
Wiremu Solomon ◽  
Ilze Ziedins
Keyword(s):  
Queueing Network ◽  
Wheatstone Bridge ◽  
The Other ◽  
Time Of Arrival ◽  
Expected Time ◽  
Initial Network ◽  
Braess’S Paradox ◽  
State Dependent ◽  
Service Rates ◽  
Queue Lengths

We consider initially two parallel routes, each of two queues in tandem, with arriving customers choosing the route giving them the shortest expected time in the system, given the queue lengths at the customer's time of arrival. All interarrival and service times are exponential. We then augment this network to obtain a Wheatstone bridge, in which customers may cross from one route to the other between queues, again choosing the route giving the shortest expected time in the system, given the queue lengths ahead of them. We find that Braess's paradox can occur: namely in equilibrium the expected transit time in the augmented network, for some service rates, can be greater than in the initial network.

Bivariate characterization of some stochastic order relations

1991 ◽  
Vol 23 (3) ◽  
pp. 642-659 ◽  
Author(s):  
J. George Shanthikumar ◽  
David D. Yao
Keyword(s):  
Stochastic Order ◽  
Queueing Network ◽  
Stochastic Scheduling ◽  
Stochastic Ordering ◽  
Closed Queueing Network ◽  
Order Relations ◽  
Functional Representations ◽  
Hazard Rate Ordering ◽  
Stochastic Order Relations

Bivariate (and multivariate) functional representations for the following stochastic order relations are established: the likelihood ratio ordering, hazard rate ordering, and the usual stochastic ordering. The motivation of the study is (i) to provide a general approach that supports the ‘pairwise interchange' arguments widely used in various settings, and (ii) to develop new notions of stochastic order relations so that dependent random variables can be meaningfully compared. Applications are illustrated through problems in stochastic scheduling, closed queueing network and reliability.

On Generalized Networks of Queues with Positive and Negative Arrivals

1993 ◽  
Vol 7 (3) ◽  
pp. 301-334 ◽  
Author(s):  
Xiuli Chao ◽  
Michael Pinedo
Keyword(s):  
Queueing Network ◽  
Form Solution ◽  
Product Form ◽  
Current State ◽  
State Dependent ◽  
Regular Customer ◽  
Generalized Networks ◽  
Service Rates ◽  
The Individual ◽  
Departure Processes

Consider a generalized queueing network model that is subject to two types of arrivals. The first type represents the regular customers; the second type represents signals. A signal induces a regular customer already present at a node to leave. Gelenbe [5] showed that such a network possesses a product form solution when each node consists of a single exponential server. In this paper we study a number of issues concerning this class of networks. First, we explain why such networks have a product form solution. Second, we generalize existing results to include different service disciplines, state-dependent service rates, multiple job classes, and batch servicing. Finally, we establish the relationship between these networks and networks of quasi-reversible queues. We show that the product form solution of the generalized networks is a consequence of a property of the individual nodes viewed in isolation. This property is similar to the quasi-reversibility property of the nodes of a Jackson network: if the arrivals of the regular customers and of the signals at a node in isolation are independent Poisson, the departure processes of the regular customers and the signals are also independent Poisson, and the current state of the system is independent of the past departure processes.

Braess's paradox in a queueing network with state-dependent routing

1997 ◽  
Vol 34 (1) ◽  
pp. 134-154 ◽  
Author(s):  
Bruce Calvert ◽  
Wiremu Solomon ◽  
Ilze Ziedins
Keyword(s):  
Queueing Network ◽  
Wheatstone Bridge ◽  
The Other ◽  
Time Of Arrival ◽  
Expected Time ◽  
Initial Network ◽  
Braess’S Paradox ◽  
State Dependent ◽  
Service Rates ◽  
Queue Lengths

We consider initially two parallel routes, each of two queues in tandem, with arriving customers choosing the route giving them the shortest expected time in the system, given the queue lengths at the customer's time of arrival. All interarrival and service times are exponential.We then augment this network to obtain a Wheatstone bridge, in which customers may cross from one route to the other between queues, again choosing the route giving the shortest expected time in the system, given the queue lengths ahead of them.We find that Braess's paradox can occur: namely in equilibrium the expected transit time in the augmented network, for some service rates, can be greater than in the initial network.

Bivariate characterization of some stochastic order relations

1991 ◽  
Vol 23 (03) ◽  
pp. 642-659 ◽  
Author(s):  
J. George Shanthikumar ◽  
David D. Yao
Keyword(s):  
Stochastic Order ◽  
Queueing Network ◽  
Stochastic Scheduling ◽  
Stochastic Ordering ◽  
Closed Queueing Network ◽  
Order Relations ◽  
Functional Representations ◽  
Hazard Rate Ordering ◽  
Stochastic Order Relations

Bivariate (and multivariate) functional representations for the following stochastic order relations are established: the likelihood ratio ordering, hazard rate ordering, and the usual stochastic ordering. The motivation of the study is (i) to provide a general approach that supports the ‘pairwise interchange' arguments widely used in various settings, and (ii) to develop new notions of stochastic order relations so that dependent random variables can be meaningfully compared. Applications are illustrated through problems in stochastic scheduling, closed queueing network and reliability.

scholarly journals Finite Queueing Modeling and Optimization: A Selected Review

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
F. R. B. Cruz ◽  
T. van Woensel
Keyword(s):  
Performance Evaluation ◽  
Queueing Networks ◽  
Queueing Network ◽  
Expansion Method ◽  
Network Analyzer ◽  
Modeling And Optimization ◽  
Product Engineering ◽  
Service Rates

This review provides an overview of the queueing modeling issues and the related performance evaluation and optimization approaches framed in a joined manufacturing and product engineering. Such networks are represented as queueing networks. The performance of the queueing networks is evaluated using an advanced queueing network analyzer: the generalized expansion method. Secondly, different model approaches are described and optimized with regard to the key parameters in the network (e.g., buffer and server sizes, service rates, and so on).

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