scholarly journals On dynamic scheduling of a parallel server system with complete resource pooling

2000 ◽  
pp. 49-71 ◽  
Author(s):  
R. Williams
Keyword(s):  
Dynamic Scheduling ◽  
Resource Pooling ◽  
Parallel Server ◽  
Server System

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 Large-scale join-idle-queue system with general service times

2017 ◽  
Vol 54 (4) ◽  
pp. 995-1007 ◽  
Author(s):  
S. Foss ◽  
A. L. Stolyar
Keyword(s):  
Time Distribution ◽  
Large Scale ◽  
Service Time Distribution ◽  
Input Flow ◽  
Steady State Probability ◽  
Parallel Server ◽  
General Service Times ◽  
Natural Equilibrium ◽  
General Service ◽  
Server System

Abstract A parallel server system with n identical servers is considered. The service time distribution has a finite mean 1 / μ, but otherwise is arbitrary. Arriving customers are routed to one of the servers immediately upon arrival. The join-idle-queue routeing algorithm is studied, under which an arriving customer is sent to an idle server, if such is available, and to a randomly uniformly chosen server, otherwise. We consider the asymptotic regime where n → ∞ and the customer input flow rate is λn. Under the condition λ / μ < ½, we prove that, as n → ∞, the sequence of (appropriately scaled) stationary distributions concentrates at the natural equilibrium point, with the fraction of occupied servers being constant at λ / μ. In particular, this implies that the steady-state probability of an arriving customer waiting for service vanishes.

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