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Performance Engineering Overview - Part 2…

Queuing Theory Overview

Early life-cycle performance modeling

Simple Distributed System Model

Sequence Diagrams

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- 1. Performance Engineering Overview 2 Enterprise Computing Performance Brian Wilson CS 4803 EPR
- 2. Lecture Overview <ul><li>Performance Engineering Overview - Part 2… </li></ul><ul><li>Queuing Theory Overview </li></ul><ul><li>Early life-cycle performance modeling </li></ul><ul><ul><li>Simple Distributed System Model </li></ul></ul><ul><ul><li>Sequence Diagrams </li></ul></ul>Enterprise Computing Performance - Course Overview
- 3. Queuing Theory Simplified A brief introduction to queuing theory, as it applies to computing performance
- 4. What is Queuing Theory? a collection of mathematical models of various queuing systems that take inputs based on probability or assumption, and that provide quantitative parameters describing the system performance.
- 5. Introduction <ul><li>Series of mathematical formulae </li></ul><ul><li>Calculates event probability </li></ul><ul><li>Predicts capacity </li></ul>Enterprise Computing Performance - Course Overview
- 6. What’s Queuing Theory? <ul><li>The theoretical study of waiting lines, expressed in mathematical terms </li></ul>Enterprise Computing Performance - Course Overview input output queue server residence time = wait time + service time
- 7. Types of Queues <ul><li>Markovian </li></ul><ul><ul><li>Exponential distribution </li></ul></ul><ul><li>Deterministic </li></ul><ul><ul><li>Constant arrival rates </li></ul></ul><ul><li>General </li></ul><ul><ul><li>Arbitrary or random distribution of arrival rates </li></ul></ul>Enterprise Computing Performance - Course Overview
- 8. Queuing Disciplines <ul><li>The representation of the way the queue is organized (rules of inserting and removing customers to/from the queue): </li></ul><ul><li>1) FIFO (First In First Out) also called FCFS (First Come First Serve) - orderly queue. </li></ul><ul><li>2) LIFO (Last In First Out) also called LCFS (Last Come First Serve) - stack. </li></ul><ul><li>3) SIRO (Serve In Random Order). (distributed/web) </li></ul><ul><li>4) Priority Queue, that may be viewed as a number of queues for various priorities. </li></ul><ul><li>5) Many other more complex queuing methods that typically change the customer’s position in the queue according to the time spent already in the queue, expected service duration, and/or priority. Typical for computer multi-access systems. </li></ul>Enterprise Computing Performance - Course Overview
- 9. What’s a Bottleneck? <ul><li>If the Production Rate, on average over time, exceeds Consumption Rate… </li></ul><ul><li>Performance Bottleneck! </li></ul><ul><li>What’s Job Flow Balance? </li></ul><ul><ul><li>T = A </li></ul></ul>Enterprise Computing Performance - Course Overview
- 10. QT Assumptions <ul><li>For any Queuing Theory to work on paper, averages for all numbers must be assumed </li></ul><ul><li>Cannot calc real-time (instantaneous) data-points without mechanical means </li></ul>Enterprise Computing Performance - Course Overview
- 11. Formulae Notation <ul><li>A = Arrival (Production) Rate (usually noted: ) </li></ul><ul><li>Ts = Service (Consumption) Time: Average Time it takes to service one message in the queue </li></ul><ul><li>Tq = Average Time a message spends in the queue (I.e. drop of water in the funnel) </li></ul><ul><li>T = Ts + Tq [Average response time] </li></ul><ul><li>1 = 100% Service Capacity or 1 Time Unit </li></ul><ul><li>(1/Ts) = Service Rate </li></ul><ul><li>(1/A) = Average Job Inter-arrival Time [average amount of time between job arrivals] </li></ul>Enterprise Computing Performance - Course Overview
- 12. Kendall Notation <ul><li>Queuing systems are described with 3 parameters… </li></ul><ul><li>Parameter 1 </li></ul><ul><ul><li>M = Markovian inter-arrival rates </li></ul></ul><ul><ul><li>D = Deterministic inter-arrival rates </li></ul></ul><ul><li>Parameter 2 </li></ul><ul><ul><li>M = Markovian service rates </li></ul></ul><ul><ul><li>G = General service rates </li></ul></ul><ul><ul><li>D = Deterministic service times </li></ul></ul><ul><li>Parameter 3 </li></ul><ul><ul><li>Number of servers </li></ul></ul><ul><li>Examples: </li></ul><ul><ul><li>M/M/1 - D/D/2 - M/G/3 </li></ul></ul>Enterprise Computing Performance - Course Overview
- 13. Example: The M/M/1 System Enterprise Computing Performance - Course Overview Job output queue Exponential server
- 14. Little’s Law 1 <ul><li>Sometimes called “Little’s Theorem” </li></ul><ul><li>“ Length of a queue is the product of the message arrival rate multiplied by the time they stay in the queue. ” </li></ul><ul><li>Notated: Q = ATq </li></ul>Enterprise Computing Performance - Course Overview
- 15. Little’s Law 2 <ul><li>Alternate definition: </li></ul><ul><li>“ The average number of jobs waiting in the queue ( N ) is equal to the product of the average arrival rate and the average response time . ” </li></ul><ul><li>Notated: N = AT </li></ul>Enterprise Computing Performance - Course Overview
- 16. Little’s “LAW” <ul><li>A great way to remember it: </li></ul><ul><li>If we notate the length of time spent in the queue as L the arrival rate as A and the time spent in the queue (residence or Wating time), then we can say: L = AW </li></ul>Enterprise Computing Performance - Course Overview
- 17. Web Server Queuing Model Enterprise Computing Performance - Course Overview
- 18. Review Questions <ul><li>A system is said to be stable when? </li></ul><ul><li>A > (1/Ts) means? Explain… </li></ul><ul><li>If the avg inter-arrival times (1/A) are unpredictable (no correlation to a known or trend number), the arrival rate exhibits what type of distribution? </li></ul><ul><li>What’s another name for a memoryless state? </li></ul><ul><li>Such queuing networks are called ____ if new jobs arrive from outside the network, and may eventually depart from the network. </li></ul><ul><li>__________ Theory describes discreet, yet rare events where arrival rates are randomly distributed, yet can be averaged over a given period of time. </li></ul>Enterprise Computing Performance - Course Overview
- 19. Resources <ul><li>A really good website for queuing tools and techniques: http://www.me.utexas.edu/~jensen/ORMM/index.html </li></ul><ul><li>Queuing Theory Terminology: http://www.me.utexas.edu/~jensen/ORMM/models/unit/queue/subunits/terminology/index.html </li></ul>Enterprise Computing Performance - Course Overview
- 20. Early Life-cycle Performance Modeling A brief overview
- 21. Sequence Diagram Example Enterprise Computing Performance - Course Overview
- 22. Expanded Sequence Enterprise Computing Performance - Course Overview
- 23. Distributed System Model Enterprise Computing Performance - Course Overview
- 24. Resource Requirements Enterprise Computing Performance - Course Overview See Page 38 Add requirements (in terms of time) for resources such as CPU, Disk, NetDelay, etc for each step of each scenario.
- 25. Performance Prediction Tools Enterprise Computing Performance - Course Overview <ul><li>Many new UML tools for modeling </li></ul><ul><li>Very time intensive </li></ul><ul><li>Many assumptions </li></ul><ul><li>Must be done before design finalization </li></ul><ul><li>Saves time and money in the long run </li></ul>

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