Lab Assignment 1 COP 4600 Operating Systems Principles

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

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

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

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

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

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:

Example

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.

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 interarrival time (that is > 1/λ), is 0. 37, for any exponential distribution.

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

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

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 underutilized) • Calculate the same for ρ=0. 90 (system highly utilized) • Calculate the same for ρ=0. 999 (system overutilized)

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

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.

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.

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