Disk average the mean service times are for the cpu
Performance Analysis
Peter Harrison & Giuliano Casale
▶ Lectures: Wednesdays 9:00–11:00, in 144; Tutorials: Wednesdays 11:00–12:00, in 144.
▶ 18 lectures, 9 tutorials, 2 pieces of assessed coursework.
Example 1: A simple transaction processing (TP) server
A transaction processing (TP) system accepts and processes a
service rate
Q: If both the arrival rate and service rate are doubled, what
▶ The arrival rate is 15tps
Example 3: A simple multiprocessor TP system
Consider our TP system but this time with multiple transaction processors


▶ The arrival rate is 16.5 tps
▶ The mean service time per transaction is 58.37ms
Q: By how much is the system response time reduced by adding one processor?
q
∝1
γ
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Example 5: A simple computer model
Consider an open uniprocessor CPU system with just disks


▶ Each submitted job makes 121 visits to the CPU, 70 to disk 1 and 50 to disk 2 on average
▶ The mean service times are 5ms for the CPU, 30ms for disk 1 and 37ms for disk 2Q: What is the effect of replacing the CPU with one twice the speed?
∝1


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Example 7: A multiprogramming system with virtual
▶ Each job page faults at a rate determined by the following lifetime function:
Lifetime function example


Q: What number of batch jobs keeps the system throughput at its maximum and at what point does thrashing occur?
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K 


Disk 1
Introduction
Computer systems are
We also see these characteristics in queues of customers in a bank
or supermarket, or prices on the stock exchange.
{Xt ∈ Ωt ∈ T}, each defined on some sample space Ω (the same for each) for a parameter space T. 

▶ T and Ω may be either discrete or continuous
▶ T is normally regarded as time
The Poisson process is a renewal process with renewal period
(interarrival time) having cumulative distribution function F and
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Memoryless property of the (negative) exponential distribution
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Proof.



▶ e.g. when you get to a bus stop, how long will you have to wait for the next bus?
▶ If the renewal process is Poisson, R has the same distribution as S by the memoryless property


Therefore
▶ From it we can derive the distribution function of the
interarrival times (i.e. negative exponential) and the Poisson distribution for Nt (the number of arrivals in time t)


Derivation of the interarrival time distribution
P(S > t + h) = P = P(S > t)P(no arrival in (t, t + h])�(S > t) ∧ (no arrival in (t, t + h])� 

by the memoryless property. Let G(t) = P(S > t). Then: G(t + h) = G(t)P(no arrival in (t, t + h]) = (1 − hλ)G(t) + o(h)
and so  


