# CS457 - System Performance Evaluation - Winter 2010

## Public Service Announcements

1. Office hours for assignment 1. (DC3549)
2. Assignment 1 revised.

# Lecture 6 - Assignment 1, Modelling Performance Metrics

## Response Time, Throughput and Utilization (pdf)

For request i:

• arrival time, a(i)
• departure time, d(i)
• response time, r(i) = d(i) - a(i)

Draw a time line

• number in system at the beginning of the time interval, n(0).
• number in system at the end of the time interval, n(L).
• number arriving between 0 and L, a(0,L)
• number departing between 0 and L, d(0,L)
• identity: n(0) + a(0,L) = n(L) + d(0,L)
• Let L -> infinity, either
• n(L) -> infinity & system is unstable (r(i) -> infinity)
or
• n(L) stays finite & system is stable
• a(0,L) - d(0,L) -> 0

Throughput is the number of requests processed per unit time. For stable systems,

• throughput = a(0,L) / L = average arrival rate = 1 / \lambda
• mean response time = (1/a(0,L)) sum_i r(i)
• total work done = total busy time = sum_i s(i) ~ S * a(0,L)
• s(i) is the amount of time the server takes to do request i on an unloaded system
• system capacity = L
• average system utilization: U = (S * a(0,L)) / L = S * throughput