# 计算机系统代写｜COMP9334 – Capacity Planning of Computer Systems and Networks

When an HTTP request arrives at the website, it is first processed by the distributor. The request is then sent to one of the two servers for processing.

With probability 0.4, the request is sent to Server 1. With probability 0.6, the request is sent to Server 2. Once a request is processed by either server, the request is completed and the HTTP response is sent to the user.

During the routine operation of the web site, the following measurements are collected:

The web site is found to process 72,000 HTTP requests in one hour.

The average number of HTTP requests in the distributor is 0.2.

For Server 1, there is on average 3.2 HTTP requests waiting in the buffer for processing, and each HTTP request requires a service time of 100 milliseconds.

For Server 2, there is on average 8.1 HTTP requests waiting in the buffer for processing, and each HTTP request requires a service time of 75 milliseconds.Question 1

Read the panel on the left and then answer the questions below.

This question consists of 3 parts: Parts (a), (b) and (c).

Part (a)

What is the utilization of Server 1?

Part (b)

What is the average waiting time of Server 1?

Part (c)

What is the average response time of Server 1?

Consider a non-preemptive priority single-server queueing system with 2 classes of jobs. The two classes of jobs will be referred to as Class A and Class B where the jobs in Class A have non-preemptive priority over the jobs in Class B. Jobs from Class A obey Poisson arrival with mean arrival rate and exponential service time distribution with mean service time . Jobs from Class B obey Poisson arrival with mean arrival rate and exponential service time distribution with mean service time . You can assume that the following 4 probability distributions are independent of each other: inter-arrival time distribution of Class A jobs, inter-arrival time distribution of Class B jobs and service time distributions of Class B jobs.

The queueing system consists of 2 queues, which will be referred to as Queue A and Queue B in this question. Each queue consists of 1 buffer space.

Assuming that Queue A is used to buffer jobs from Class A alone and Queue B is used to buffer jobs from Class B alone. This non-preemptive priority queueing system can be modelled by a continuous-time Markov chain. The state of the

Markov chain is the three tuple（nA,nB,nS）where nA is the number of jobs in Queue A,nB is the number of jobs in Queue B, and nS is number of jobs in the server.