An approximate solution method for multiclass queueing networks with state dependent routing and window flow control
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Authors
Krzesinski, AE
Issue Date
1987
Type
Language
en
Keywords
Alternative Title
Abstract
A Multidass Queueing Network (MQN) Q ( N, .M ) consisting of M centres
with index set .M and population vector N is partitioned into two subnetworks
Q ( fJ -V , .M -1) ) and Q (V , V ) . The centres in Q (V , · V ) are further partitioned in to
disjoint subnetworks called branches. A set of State Dependent Routing (SDR)
probabilities is used to admit customers from Q ( N - V , .M - V ) into the individual
branches of Q (V , V ) such that the customers are preferentially routed to the least
congested branches. The SDR probabilities are such that Q( JV, .M ) has a product
form solution .
The S D R probabilities set a n upper bound o n the number of customers that can
concurrently be present in each branch of Q (V , V ). In addition, an upper bound is
set on the total number of customers that can concurrently be present in Q (V , V ) .
Once this bound is reached, the product form SDR probabilities route customers
around Q(V, 1) ).
Exact solutions for MQNs with product form SDR are computationally intractable
unless each SDR branch consists of a single centre only. An approximate
solution method is therefore developed for MQNs with product form SDR. The approximate
solution method is next extended to admit customers in first come first served order to Q (V , 1) ) when the total number of customers in Q (V , V ) reaches its upper bound. Such a combination of SDR and blocking can be used to model adaptive routing and window flow control mechanisms in computer networks.
MQNs with SDR and blocking violate product form. Simulation solutions are
used to test the accuracy of the approximation Jn method . The accuracy of the approximation technique is found to be good. Finally, the effects of population constrained
SDR on network performance measures an investigated.
Description
Citation
Kzresinski, A.E. (1987) An approximate solution method for multiclass queueing networks with state dependent routing and window flow control. Proceedings of the 4th South African Computer Symposium, Holiday Inn, Pretoria, 1-3 July 1987, edited by P. Kritzinger (UCT).