Queueng Theory 2013 - Queuing Theory Our goals understand...

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3: Delay Models in Data Networks - 1 Queuing Theory Our goals: understand principles of queueing systems: o Poisson Process o Markov process o Little’s theorem o Network of queues Determine Performance measures o Response time o Throughput o ?
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3: Delay Models in Data Networks - 2 Introduction- Motivation How to analyze changes in network workloads? o Should I add new terminals? How much? What percentage of calls will be blocked? o Adding more lines would solve the problem? Analysis of system (network) load and performance characteristics o response time o throughput Performance tradeoffs are often not intuitive Queuing theory, although mathematically complex, often makes analysis very straightforward
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3: Delay Models in Data Networks - 3 Queueing Theory Operations Research The study of waiting Back to early twentieth century o Danish mathematician A. K. Erlang (telephone networks), why? o Russian mathematician A. A. Markov Applied in a broad variety of applications
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3: Delay Models in Data Networks - 4 Queueing Jargons Queueing system o Customers o Queue(s) (waiting room) o Server(s) Kendall’s notation o Standard notation to describe queueing containing single queue: X / Y / m / n/ y InterArrival process Service process Servers # Queue capacity Target group
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3: Delay Models in Data Networks - 5 Common distributions G = general distribution if interarrival times or service times GI = general distribution of interarrival time with the restriction that they are independent M = negative exponential distribution (Poisson arrivals) D = deterministic arrivals or fixed length service M/M/1? M/D/1?
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3: Delay Models in Data Networks - 6 General Characteristics of Network Queuing Models Item population o generally assumed to be infinite therefore, arrival rate is persistent Queue size o infinite , therefore no loss o finite, more practical, but often immaterial Dispatching discipline o FIFO , typical o LIFO o Relative/Preferential, based on QoS o Processor sharing (PS) discipline Useful for modeling multiprogramming
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3: Delay Models in Data Networks - 7 Multiserver Queue Comments: 1. Assuming N identical servers, and is the utilization of each server. 2. Then, N is the utilization of the entire system, and the maximum utilization is N x 100%. 3. Therefore, the maximum supportable arrival rate that the system can handle is: max = N / T s
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3: Delay Models in Data Networks - 8 Multiple Single-Server Queues
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3: Delay Models in Data Networks - 9 Network of Queues
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3: Delay Models in Data Networks - 10 Elements of Queuing Networks
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3: Delay Models in Data Networks - 11 Delay Components A B propagation transmission nodal processing queueing
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3: Delay Models in Data Networks - 12 Delay Components (Cont.) Packet delay the sum of delays on each link on the path traversed by the packet.
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