CS457 - System Performance Evaluation - Winter 2010
Public Service Announcements
- Office hours for assignment 1. (DC3549)
- Assignment 1 revised.
- PDF in the notes.
Lecture 7 - Little's Law (pdf)
There are two ways to study the performance of systems
- stochastic, where we follow the progress of each job through the
system, and
- operational, where we measure the average flow of jobs through the
system.
Little's Law, and the other results, are results of an operational
analysis.
Reminder. Operational results depend on the assumption
that the system is stable, and average out transient effects that occur when
sudden changes occur in workload or system parameters.
Connecting the Stochastic and Operational Views
Stochastic model of interarrival times
Assumptions
- Population of users, N, goes to inifinity.
- Infinite limit is reached such that Np = \lambda is finite
- p: probability a user will make a request (submit a job) in unit
time.
- \lambda: number of requests received per unit time.
- Users are independent of one another
- They don't collude
- Not true of denial of service attacks.
- Request submission is independent of the number of requests already in
the system.
Proof - Appendix of pdf
Result
Probabilities
- Zero requests in system: exp( -\lambda*t )
- Interarrival time > t: exp( -\lambda*t )
- Interarrival time < t: 1 - exp( -\lambda*t )
Applying Little's Law
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