This project is inspired by the research work reported in the article Optimal Power Allocation in Server Farms [1]. Server farms are a common part of many corporations’ computing infrastructure but they consume a lot of energy. The key question asked in this research is: Is it possible to reduce the energy consumption of server farms while maintaining good response time of the com- puting system.
- To apply discrete event simulation to a performance analysis problem
- To use statistically sound methods to analyse simulation outputs
A typical architecture of a server farm is shown in below figure. The server farm consists of a high- speed router at the front end and a number of computing servers at the back end. A job arriving at the server farm will first reach the high-speed router. The function of the router is to send the job to one of the servers in the back end. The job will then be processed by the server and once it is completed, the job leaves the server. Most servers use Processor Sharing (PS) rather than first-come-first-serve to process the jobs. The PS in below Figure indicates the servers are using PS for job processing.
Figure: Typical architecture of a server farm. The front-end consists of a high-speed router and
the back-end has a number of computer servers. Each server uses processor sharing (PS)
A key performance issue in a server farm is its response time. In this project, we will assume that the high-speed router takes negligible time to distribute the jobs to the servers. Therefore, the response time of a job is due entirely to the processing in the server Energy cost in operating servers is high. Each server consumes typically hundreds of Watts of power. The article stated that “ Server farms today consume more than 1.5% of the total electricity in the U.S. at a cost of nearly $4.5 billion.” (Note: the article was published in 2009 so these are past figures.) Given the high operating cost of server farms, a question is whether it is possible to reduce the energy consumption while maintaining the same level of system performance in terms of response time.
Modern servers are equipped with power management technologies such as Dynamic Frequency Scaling (DFS) or Dynamic Voltage and Frequency Scaling (DVFS). These technologies allow a system administrator to operate the servers at different power levels. If the server is operating at a higher (resp. lower) power level, then it is operating at a higher (resp. lower) clock frequency or higher (resp. lower) computing speed. Figure 2 shows the relationship between clock frequency and power consumption for a particular type of server under a specific workload. You can clearly see that the clock frequency is an increasing function of the power consumption.
The power management technologies have provided us with a method to reduce the power consumption while maintaining the performance. You can approach this problem in two different ways. You can fix the performance (i.e. response time) and see how you can reduce power consumption. Alternatively, you can fix the power consumption and see how you can maximise the performance. We will take the latter approach in this project.
For example let us assume that you have a power budget of 3000W. You can operate each server at 150W, 200W and 250W, which will give you a clock frequency of 1.2 GHz, 2.7 GHz and 3 GHz. (These clock frequencies correspond roughly to the curve in Fig. 2b.) You can use your 3000W power budget in a variety of configurations, for example: Operate 20 servers at 150W at clock frequency of 1.2 GHz (the slowest speed).
Operate 15 servers at 200W at clock frequency of 2.7 GHz (the medium speed).
Operate 12 servers at 250W at clock frequency of 3.0 GHz (the highest speed).
In this simulation, we will assume that
- The server farm has n servers.
- Each server uses Processor Sharing (PS) to process the requests.
- The power budget is xxxx watts.This means that if you switch on s serveres adn leave the other (n-s)servers off then each running server is operating at a powerr level of xxxx watts.(xxxx can be any value)
- If a server is running at a power level of p Watts, then its clock frequency f (measured in GHz) is a function of p and is given by f = 1:25 + 0.31(p/200-1)
For example, if 8 servers are switched on, then each server operates at a power level of 250 Watts and its clock frequency f is 1.25 + 0:31( 250/200 - 1) = 1:3275 GHz.(assuming xxxx = 2000Watts).
Note: For simplicity, we assume in this project that the servers can operate at any power level but in reality, a server can only operate at a discrete number of power levels.
- We use{a1,a2,...,ak,...,...} to denote the inter-arrival times of the requests arriving at the high-speed router. These inter-arrival times have the following properties: (a) Each ak is the product of two random numbers a1k and a2k, i.e ak =a1k a2k ∀k= 1,2,... (b) The sequence a1k is exponentially distributed with a mean arrival rate 7.2 requests/s. (c) The sequence a2k is uniformly distributed in the interval [0.75,1.17].
Note: The easiest way to generate the inter-arrival times is to multiply an exponentially distributed random number with the given rate and a uniformly distributed random number in the given range. It would be more difficult to use the inverse transform method in this case, though it is doable.
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The high-speed router distributes the requests using round robin job assignment. For example, assuming s servers that are switched on and the servers that are on are Server 1, Server 2, ...., Server s. The round robin job assignment means tha Request 1 is assigned to Server1, Request 2 to Server 2, ..., Requests to Servers, Request (s+ 1) to Server 1, Request(s+2) to Server 2, ..., Request 2s to Server s, Request (2s+ 1) to Server 1, and so on. You can assume the time to distribute a request to a server is negligible.
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If the server is operating at 1 GHz, then the probability density function g(t) of the service time t of the requests is:
Note that t is the service time when the request is processed by a server operating at 1 GHz. You can assume that if the same job is to be processed by a server operating at fGHz, then the service time required is tf. For example, if a job requires a service time of 8 time units when processed by a server operating at 1 GHz, then the same job will take 81.86 time units to complete when it is processed by a server operating at 1.86 GHz.
Our goal is to determine the number of servers s we should operate in order to minimise the ean response time of the requests. In order to achieve this goal, some of the tasks that we need to perform are:
- Computer programs or routines that generate the required probability distributions.
- A computer program that can simulate a PS server. The simulation program will take the number of operating servers s as an input variable. By using this program, we can test the effect of different values of s in the mean response time of the server farm.This will allow us to find a suitable value of s.
We can do this project by simulating one of the s servers.This canbe done by using the arrival times of the Requests 1, (s+1), (2s+1), (3s+1) etc because each server gets one out of s requests. In general, you can choose a random integer k(where 1≤k≤s) and use Requests k, (s+k), (2s+k), (3s+k) etc.
The minimum response time will not occur at s= 1 nor s= 2. You do not have to simulate these two values of s. You will need to simulate s from 3 to n inclusively.
When there are n jobs in the server, then each job receives 1 n of the service. The events in a PS server are the arrival of a job to the server and the departure of a completed job from the server. You should convince yourselves that between two consecutive events,the number jobs in a PS server remains the same. The discrete event simulation advances from an event to the next one.The key data structure that you need to maintain is the list of jobs in the server. Each job is characterised by two attributes: the time the job arrives at the server and the remaining amount of service the jobs will still need. Each time when a job arrives or departs, this data structure should be updated. We will use an example to explain this. For this example, we consider a PS server with the following job arrival times and service times.
We will illustrate how the simulation of PS server works using “on-paper simulation”. Three of the quantities that you need to keep track of are:
Next arrival time is the time of the next arrival
Next departure time assuming no more arrivals is defined as the time of the next departure assuming that no more arrivals will come in the future. For simplicity, we will simply use the phrase next departure time. For example, if there are three jobs in the server at a certain time and these jobs still need 5, 6 and 10 units of service, then the next departure time will be 15 time units later.
The list of jobs in the server. Each job is characterised by a 2-tuple. The first element of the 2-tuple is the arrival time of the job at the server and the second element is the amount of service it still needs.
The on-paper simulation" is shown in below table. The notes in the last column explain whatupdates you need to do for each event. Please note that there are more quantities that you need to keep track of than those three that are mentioned above. A graphical representation of the PS server status over time is given in Figure 3. There are three plots in the figure, showing the arrival times, remaining amount of service for each job and the departure times. The figure is best viewed in colour because the quantities related to each job is shown in a specific colour. Note that in between two consecutive events, the remaining amount of service for each job is not a constant. What is constant in between two consecutive events is the number of jobs in the server. The number of jobs in the server determines the service rate of each job which is the slope of the remaining service curve. You will see that the slope stays constant in between two events and changes each time an event occurs.
Contributions are always welcome in the form of pull requests with explanatory comments.