1. Lab Assignment 1 COP 4600: Operating Systems Principles Dr. Sumi Helal Professor Computer & Information Science & Engineering Department University of Florida, Gainesville, FL 32611 helal@cise.ufl.edu

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

3. 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.

4. 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

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

6. 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:

7. Example

8. 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.

9. 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.

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

11. Little’s Law: Proof: –Shaded area is identical (=9 in example) 1 2 3 Time in System (W) Job# (N) 1 2 3 1 2 3 4 5 6 7 # in System (L) 1 2 3 Time (T)

12. 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)

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

14. 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.

15. 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.

16. 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.