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Queueing Network Model

Queueing Network Model. Single Class Model . Open - Infinite stream of arriving customers Closed - Finite population eg Intranet users Indistinguishable customers Queuing Service Center Users compete for service. Single Class Model (cont.). Delay Service Center

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Queueing Network Model

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  1. Queueing Network Model

  2. Single Class Model • Open - Infinite stream of arriving customers • Closed - Finite population eg Intranet users • Indistinguishable customers • Queuing Service Center • Users compete for service

  3. Single Class Model (cont.) • Delay Service Center • Each customer allocated its own server • No competition for service • e.g. data transmission over a dedicated transmission line

  4. Single Class Model Inputs • Customer Description • Workload Intensity • l, the arrival Rate • Average number of requests in the system • Average number and think time • Service Center Description • Number of service centers i • Queueing or delay • Service Demands • Di = Vi times Si for service center i

  5. Single Class Model Outputs • System Measures • R Average system response time • X system throughput • Q average number in the system • Service Center Measures • Ui Utilization of resource i • Ri Average residence time at resource i • Xi Throughput of the resource i • Qi Average queue length at resource i

  6. Multiple Class Models • Multiple customer classes • Each class has its own intensity • Each class has its own service demands • Open model - all classes are open • Closed model - all classes are closed • Mixed - both open and closed classes • Input and output measure are aggregate and per class

  7. Simple Server Models • Infinite Population/Infinite Queue • Variable Service Rate • Infinite Population/Finite Queue • Variable Service Rate • Finite Population • Fixed Service Rate • Variable Service Rate

  8. Queueing Notations • Six Queueing Parameters • Arrival Process • Poisson arrivals, interarrival times are exponentially distributed M, most commonly used • Other distributions e.g. • Erlang Ek • hyperexponential Hk • Deterministic D • General G

  9. Queueing Notations • Six Queueing Parameters • Service Time Distribution • Time spent using the resource • Commonly assumed random variables • Most common distribution exponential • Number of Servers • number of processors in the system • number of I/O channels

  10. Queueing Notations • Six Queueing Parameters • System Capacity • Those waiting for service and those receiving • Finite • If too large then consider it infinite • Population Size • Total number of potential users • Finite • If too large then consider it infinite

  11. Queueing Notations • Six Queueing Parameters • Service Discipline • Order of arrival • First Come, First Served (FCFS) • Last Come, First Served (LCFS) • Round Robin (RR) • Shortest Processing Time (SPT) • Shortest Remaining Processing Time (SRPT) • Biggest In, First Served (BIFS)

  12. Queueing Notations • Kendall Notation • A/S/m/B/K/SD • IID/Service Time distribution/Number of servers/System capacity/Population size/ Service Discipline • M/M/1 • IID exponential/Service times exponential/one server/infinite service capacity/infinite population/FCFS

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