Optimal scheduling in queueing networks

1984 ◽  
Vol 16 (1) ◽  
pp. 13-13
Author(s):  
F. J. Massey ◽  
D. F. Miller
Keyword(s):  
Queueing Networks ◽  
Queueing Network ◽  
Performance Measure ◽  
Optimal Scheduling ◽  
Closed Queueing Network ◽  
Service Stations ◽  
A Performance

This paper derives an algorithm for finding a scheduling discipline for scheduling N customers at M service stations in a closed queueing network so as to optimize a performance measure which depends on the configuration of customers at the service stations.

scholarly journals Control of Fork-Join Processing Networks with Multiple Job Types and Parallel Shared Resources

2021 ◽  
Author(s):  
Erhun Özkan
Keyword(s):  
Queueing Networks ◽  
Queueing Network ◽  
Optimal Scheduling ◽  
Shared Resources ◽  
Asymptotically Optimal ◽  
Scheduling Policy ◽  
Synchronization Constraints ◽  
Processing Network ◽  
Diffusion Scale ◽  
Processing Networks

A fork-join processing network is a queueing network in which tasks associated with a job can be processed simultaneously. Fork-join processing networks are prevalent in computer systems, healthcare, manufacturing, project management, justice systems, and so on. Unlike the conventional queueing networks, fork-join processing networks have synchronization constraints that arise because of the parallel processing of tasks and can cause significant job delays. We study scheduling in fork-join processing networks with multiple job types and parallel shared resources. Jobs arriving in the system fork into arbitrary number of tasks, then those tasks are processed in parallel, and then they join and leave the network. There are shared resources processing multiple job types. We study the scheduling problem for those shared resources (i.e., which type of job to prioritize at any given time) and propose an asymptotically optimal scheduling policy in diffusion scale.

scholarly journals Analytic error bounds for approximations of queueing networks with an application to alternate routing

1990 ◽  
Vol 31 (3) ◽  
pp. 241-258 ◽  
Author(s):  
Nico M. Van Dijk
Keyword(s):  
State Space ◽  
Error Bound ◽  
Error Bounds ◽  
General Condition ◽  
Queueing Networks ◽  
Queueing Network ◽  
Space Structure ◽  
Closed Queueing Network ◽  
Alternate Routing ◽  
Markov Reward

AbstractA general condition is provided from which an error bound can be concluded for approximations of queueing networks which are based on modifications of the transition and state space structure. This condition relies upon Markov reward theory and can be verified inductively in concrete situations. The results are illustrated by estimating the accuracy of a simple throughput bound for a closed queueing network with alternate routing and a large finite source input. An explicit error bound for this example is derived which is of order M—1, where M is the number of sources.

Resource pooling in queueing networks with dynamic routing

1992 ◽  
Vol 24 (3) ◽  
pp. 699-726 ◽  
Author(s):  
C. N. Laws
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Optimal Control Problem ◽  
Queueing Networks ◽  
Heavy Traffic ◽  
Queueing Network ◽  
Original System ◽  
Dynamic Routing ◽  
Resource Pooling ◽  
Service Stations

In this paper we investigate dynamic routing in queueing networks. We show that there is a heavy traffic limiting regime in which a network model based on Brownian motion can be used to approximate and solve an optimal control problem for a queueing network with multiple customer types. Under the solution of this approximating problem the network behaves as if the service-stations of the original system are combined to form a single pooled resource. This resource pooling is a result of dynamic routing, it can be achieved by a form of shortest expected delay routing, and we find that dynamic routing can offer substantial improvements in comparison with less responsive routing strategies.

Resource pooling in queueing networks with dynamic routing

1992 ◽  
Vol 24 (03) ◽  
pp. 699-726 ◽  
Author(s):  
C. N. Laws
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Optimal Control Problem ◽  
Queueing Networks ◽  
Heavy Traffic ◽  
Queueing Network ◽  
Original System ◽  
Dynamic Routing ◽  
Resource Pooling ◽  
Service Stations

In this paper we investigate dynamic routing in queueing networks. We show that there is a heavy traffic limiting regime in which a network model based on Brownian motion can be used to approximate and solve an optimal control problem for a queueing network with multiple customer types. Under the solution of this approximating problem the network behaves as if the service-stations of the original system are combined to form a single pooled resource. This resource pooling is a result of dynamic routing, it can be achieved by a form of shortest expected delay routing, and we find that dynamic routing can offer substantial improvements in comparison with less responsive routing strategies.

scholarly journals Asymptotic expansions for large closed and loss queueing networks

2002 ◽  
Vol 8 (4-5) ◽  
pp. 323-348 ◽  
Author(s):  
Yaakov Kogan
Keyword(s):  
Partition Function ◽  
Queueing Networks ◽  
Complex Space ◽  
Queueing Network ◽  
Network Models ◽  
Saddle Point Method ◽  
Normalization Constant ◽  
Stationary Probability Distribution ◽  
Transmission Networks ◽  
Closed Queueing Network

Loss and closed queueing network models have long been of interest to telephone and computer engineers and becoming increasingly important as models of data transmission networks. This paper describes a uniform approach that has been developed during the last decade for asymptotic analysis of large capacity networks with product form of the stationary probability distribution. Such a distribution has an explicit form up to the normalization constant, or the partition function. The approach is based on representing the partition function as a contour integral in complex space and evaluating the integral using the saddle point method and theory of residues. This paper provides an introduction to the area and a review of recent work.

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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