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Lab Assignment 1 COP 4600: Operating Systems Principles Dr. Sumi Helal Professor Computer & Information Science & Engineering Department University of Florida, Gainesville, FL

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Lecture Overview Go over Lab Assignment 1, one more time. Queuing Theory 101 Simulation 101

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Assignment λ = arrival rate, follows an arrival process μ = service rate, follows a service process ρ = utilization = λ/μ λ μ Simulate a single queue/single server system, with a FIFO queuing discipline Report on the performance of the system Compare with analytic models.

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Queuing Theory 101 Must already know: –Random Variables –Basics of Probability Today, we will study & learn: –Probabilistic Processes –Little Law –M/M/1 analytic models

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Exponential Process Suitable for describing time between successive events (e.g., arrival, service). T is a continuous Random Number

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Example Assume average time between arrival (or average inter-arrival time) is 45 sec. –Question: what is the prob. that inter-arrival time is > 60 sec.? –Answer:

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Example

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Poisson Process Poisson is suitable for describing arrivals or occurrence of events. Describes prob. of n arrivals in any time interval. If arrival process follows Poisson distribution, then the random variable representing inter-arrival time must follow the Exponential distribution.

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Quiz To make sure you follow so far, answer the following question: –Prove that the probability that inter-arrival times are greater than the average inter- arrival time (that is > 1/λ), is 0.37, for any exponential distribution.

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Definitions W = Average job wait time in the queue L = Average queue length N = Throughput (number of jobs completed per unit time)

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Little’s Law: Proof: –Shaded area is identical (=9 in example) Time in System (W) Job# (N) # in System (L) Time (T)

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Analytic Solutions Utilizing Little Law Utilization: L: W: Quiz to check if you understand the implication of ρ Calculate L and W for ρ=0.09 (system under-utilized) Calculate the same for ρ=0.90 (system highly utilized) Calculate the same for ρ=0.999 (system over- utilized)

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Effect of ρ – A Reality that Must be considered in any Operating System Design

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Simulation 101 You have two independent events At end of processing an independent event, you must re-generate it. All future events generated should be put in an event list. Simulation loop simply finds the next event that will take place sooner in the future; remove it & process it. And yes, advance the clock to that selected next event.

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Simulation 101 At each new iteration in the simulation loop you check for exist criterion. You most update your counters and statistics every time: –The Clock is changed –A new job enters the system –A job exits the system –When the simulation loop exits.

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Simulation 101 Generating exponentially distributed random variables: –Use inverse inverse transform sampling as follows: X is RV with standard Uniform distribution [0,1], then follows the exponential distribution with average arrival rate.

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