09. Queueing Networks - CS4 Modelling and Simulation LN-9 9...

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CS4 Modelling and Simulation LN-9 9 Queueing Networks 9.1 Introduction Mathematicians have studied queues for approximately 100 years, and one of their Frst applications was to telephone exchanges ( Erlang’s loss formula ). However they gained popularity with Computer Scientists about 35 years ago when it was realised that sin- gle queues, and networks of queues could be used as performance models of computer systems. More recently, developments in many of those systems have grown beyond the expressiveness of queueing networks. Nevertheless, for many people performance analysis is synonymous with queueing theory . Queueing theory was Frst used in the late 1960s to model time-sharing computer sys- tems. In particular single queues were used to study allocation policies for CPUs. Analysis of the single queues led to a new qualitative, as well as quantitative, understanding of some aspects of operating system and disk management system design. However, these single queue models were too restrictive to represent systems of interacting computing devices, as computers came to be viewed. Later developments in queueing theory therefore studied the interaction between service centres or queues— queueing networks . Contemporary computers at the time could be viewed as a set of loosely coupled hardware components through which weakly interacting jobs or transactions were circulating. The success of queueing theory as a performance modelling paradigm relied on this view of computers. Computer and communication systems today do not Ft into this model so readily; however, queueing networks remain a useful performance modelling paradigm, in some circumstances. 9.2 Single queues The basic scenario for a single queue is that customers , who belong to some population arrive at the service facility . The service facility has one or more servers who are capable of performing the service required by customers. If a customer cannot gain access to a server it must join a queue, in a buFer , until a server is available. When service is complete the customer departs, and the server selects the next customer from the bu±er according to the service discipline . ? to queue arrivals ? from queue departures * buFer Y server - - ²igure 18: A Simple Queue 61
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CS4 Modelling and Simulation LN-9 In order to describe a service facility accurately we need to know details about each of the terms emphasised above: Arrival Pattern of Customers The ability of the service facility to provide service for an arriving stream of customers depends not only on the mean arrival rate λ , but also on the pattern in which they arrive, i.e. the distribution function of the inter- arrival times. In this course we will only be considering queues in which the times between arrivals are assumed to be exponentially distributed 1 . However, you should be aware that there are other possibilities.
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This note was uploaded on 04/08/2010 for the course COMPUTER E 409232 taught by Professor Mohammadabdolahiazgomiph.d during the Spring '10 term at Islamic University.

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09. Queueing Networks - CS4 Modelling and Simulation LN-9 9...

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