Lecture10 - COT 5611 Operating Systems Design Principles...

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COT 5611 Operating Systems Design Principles Spring 2012 Dan C. Marinescu Office: HEC 304 Office hours: M-Wd 5:00-6:00 PM
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Lecture 10 - Monday February 13 n Reading assignment: Chapter 8 from the on-line text n Last time: n Design principles for computer and communication systems n Interesting Properties of Networks ¨ Isochronous and Asynchronous Multiplexing ¨ Packet Forwarding; Delay ¨ Queuing models for delay determination 2/16/12 2 Lecture 10
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Today n The M/M/1 Queuing model n Store and Forward Networks n The Internet n Layering n The Link Layer ¨ Bit framing ¨ Frames ¨ Errors ¨ Link properties n Random Multiple Access 2/16/12 3 Lecture 10
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Delays and waiting time when a resource is shared n Queuing theory describes systems where you have a shared resource – a server - and customers and both the arrival of the customers and the time it takes to service them are random variables with a certain distribution. n There are two stochastic processes involved: ¨ Arrival ¨ Service 2/16/12 4 Lecture 10
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Customer arrival n The arrival process describes the pattern of the customers arrive  characterized by its probability distribution function e.g., a uniform, exponential. n The distribution can described by one or more parameters such as the average value of the random variables subject to that distribution, e.g., the arrival rate denoted as ? ¸ or the the inter-arrival time (the average time between two consecutive customer arrivals), 1/ ? . n For example, if customers arrive in average at two minutes intervals the arrival rate is 1/2 customers/minute and the inter-arrival time is 2 minutes. 2/16/12 5 Lecture 10
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Customer service n The service process  describes how customers are served. n The service processes is characterized by its probability distribution function e.g., a uniform, exponential, hyper exponential. n The distribution can described by ¨ the service rate ? or ¨ the service time (the average time between two consecutive customer departures from the system) 1/ ? n For example, if the service rate is ? = 10 customers per hour, then the service time is 1/ ? = 60minutes/10 = 5 minutes. 2/16/12 6 Lecture 10
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The pattern of customer behavior n The customer arrives in the system and joins a waiting queue. The time spent waiting is called waiting time and it is denoted as W. n When its turn arrives the customer enters service and the service time is 1/ ? n When the service is terminated the customer leaves the system. The time spent the customer is called the time in system T = W + 1/ ? . n N is the total number of customers in system, one is in service and (N-1) are waiting in the queue. 2/16/12 7 Lecture 10
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Birth and death process n pi the probability to be in state i; ∑pi = 1 n Equilibrium equation for a birth-death process pk  = pk+1 ? n Utilization  =  ρ / ? 1 pi = i (1-  ) ρ ρ E[N] = ∑ i pi=  (1-  )  ρ ∑ i ρ = (1-  )[ / (1-  )2 ρ ρ ρ ] = /(1-  ) ρ ρ n Little’s law: E[N]= ? [ E T ]  E[T]= (1/ ?) [ /(1-  )]= (1/ ρ ρ ? )[1/(1-  )] ρ n ] 2/16/12 8 Lecture 10
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average Utilization, r 0 100% 1 1 1 ρ ------------ tolerable delay rmax queuing delay maximum Queuing delays versus utilization 2/16/12 9 Lecture 10
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