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Queueing Networks Queueing networks consisting of several service stations are more suitable for representing the structure of many systems with a large number of resources than models consisting of a single service station. In a queueing network at least two service stations are connected to each other. A station, i.e., a node, in the network represents a resource in the real system. Jobs in principle can be transferred between any two nodes of the network; in particular, a job can be directly returned to the node it has just left. A queueing network is called open when jobs can enter the. | Queueing Networks and Markov Chains Gunter Botch Stefan Greiner Hermann de Meer Kishor S. Trivedi Copyright 1998 John Wiley Sons Inc. Print ISBN 0-471-19366-6 Online ISBN 0-471-20058-1 K 9 Queueing Networks Queueing networks consisting of several service stations are more suitable for representing the structure of many systems with a large number of resources than models consisting of a single service station. In a queueing network at least two service stations are connected to each other. A station i.e. a node in the network represents a resource in the real system. Jobs in principle can be transferred between any two nodes of the network in particular a job can be directly returned to the node it has just left. A queueing network is called open when jobs can enter the network from outside and jobs can also leave the network. Jobs can arrive from outside the network at every node and depart from the network from any node. A queueing network is said to be closed when jobs can neither enter nor leave the network. The number of jobs in a closed network is constant. A network in which a new job enters whenever a job leaves the system can be considered as a closed one. In Fig. 7.1 an open queueing network model of a simple computer system is shown. An example of a closed queueing network model is shown in Fig. 7.2. This is the central-server model a particular closed network that has been proposed by Buze71 for the investigation of the behavior of multiprogramming system with a fixed degree of multiprogramming. The node with service rate is the central-server representing the central processing unit CPU . The other nodes model the peripheral devices disk drives printers magnetic tape units etc. The number of jobs in this closed model is equal to the degree of multiprogramming. A closed tandem queueing network with two nodes is shown in Fig. 7.3. A very frequently occurring queueing network is the machine repairman model shown in Fig. 7.4. 263 264 QUEUEING NETWORKS Fig.
