Open Queueing Network Algorithms f(G(V,E))$$f{\bigl (G(V,E)\bigr )}$$

2018 ◽  
pp. 181-259
Author(s):  
J. MacGregor Smith
Keyword(s):  
Queueing Network ◽  
Network Algorithms ◽  
Open Queueing Network

Dynamic Scheduling of a Four-Station Queueing Network

1990 ◽  
Vol 4 (1) ◽  
pp. 131-156 ◽  
Author(s):  
C. N. Laws ◽  
G. M. Louth
Keyword(s):  
Control Problem ◽  
Dynamic Scheduling ◽  
Dynamic Control ◽  
Queueing Network ◽  
Single Server ◽  
Scheduling Policies ◽  
Resource Pooling ◽  
Static Scheduling ◽  
Open Queueing Network ◽  
Dynamic Policy

This paper is concerned with the problem of optimally scheduling a multiclass open queueing network with four single-server stations in which dynamic control policies are permitted. Under the assumption that the system is heavily loaded, the original scheduling problem can be approximated by a dynamic control problem involving Brownian motion. We reformulate and solve this problem and, from the interpretation of the solution, we obtain two dynamic scheduling policies for our queueing network. We compare the performance of these policies with two static scheduling policies and a lower bound via simulation. Our results suggest that under either dynamic policy the system, at least when heavily loaded, exhibits the form of resource pooling given by the solution to the approximating control problem. Furthermore, even when lightly loaded the system performs better under the dynamic policies than under either static policy.

scholarly journals Laws of Little in an open queueing network

2012 ◽  
Vol 17 (3) ◽  
pp. 327-342 ◽  
Author(s):  
Saulius Minkevičius ◽  
Stasys Steišūnas
Keyword(s):  
Waiting Time ◽  
Queueing Theory ◽  
Queue Length ◽  
Heavy Traffic ◽  
Queueing Network ◽  
Fluid Limit ◽  
Fluid Approximation ◽  
Large Numbers ◽  
Virtual Waiting Time ◽  
Open Queueing Network

The object of this research in the queueing theory is theorems about the functional strong laws of large numbers (FSLLN) under the conditions of heavy traffic in an open queueing network (OQN). The FSLLN is known as a fluid limit or fluid approximation. In this paper, FSLLN are proved for the values of important probabilistic characteristics of the OQN investigated as well as the virtual waiting time of a customer and the queue length of customers. As applications of the proved theorems laws of Little in OQN are presented.

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