The response time of a request that goes through server j(j = 1, ···, Nws) of Fig. 8.5(a) is the same as the response time of the single equivalent Web server of Fig. 8.5(b) with an arrival rate equal to l/Nws. (The two models have the same service demands at the CPU and disk devices.) The response time at the single equivalent server of Fig. 8.5(b) is given by
• Table of Contents
Performance by Design: Computer Capacity Planning by Example
By Daniel A. Menascé, Virgilio A.F. Almeida, Lawrence W. Dowdy
Publisher: Prentice Hall PTR Pub Date: January 05, 2004
ISBN: 0-13-090673-5 Pages: 552
Individual organizations and society as a whole could face major breakdowns if IT systems do not meet their Quality of Service (QoS) requirements on performance, availability, security, and maintainability. Corporations stand to lose valuable income, and public interests could be put at great risk. System designers and analysts usually do not take QoS requirements into account when designing and/or analyzing computer systems, due mainly to their lack of awareness about the issues that affect
performance and the lack of a framework to reason about performance. This book describes how to map real-life systems (e.g., databases, data centers, e-commerce applications) into analytic performance models. The authors elaborate upon these models, and use them to help the reader thoroughly analyze and better understand potential performance issues.
< Day Day Up >
where K is the number of devices (i.e., CPU ands disk) and D i (i = 1, ···, K) is the service demand of a
request at device i. Note that the term (l/Nws) Di is the utilization of device i according to the Service
Demand Law. The generalization of Eq. (8.6.17) to multiple classes is
Equation 8.6.18
where R r is the average response time of class r requests, lr is the average arrival rate of requests of
class r, and D i,r is the total utilization of device i over all R classes.
As an example, consider the service demands of Table 8.4 and an overall session start rate g of 11 sessions/sec. Then, consistent with the example in Section 8.3, assume 25% of type A customers and 75% of type customers. Then, the arrival rates for each type of request are given by lhome = 11.0
requests/sec, l search = 13.71 requests/sec, lview = 2.22 requests/sec, llogin = 3.68 requests/sec, lcreate = 1.10 requests/sec, and lbid = 2.10 requests/sec.
Consider three Web servers instead of one. The utilizations of the CPU and disk at the single equivalent Web server are given by
and
Then, the response times of each of the six classes of requests at the Web server tier are computed using Eq. (8.6.18) as
< Day Day Up >
• Table of Contents
Performance by Design: Computer Capacity Planning by Example
By Daniel A. Menascé, Virgilio A.F. Almeida, Lawrence W. Dowdy
Publisher: Prentice Hall PTR Pub Date: January 05, 2004
ISBN: 0-13-090673-5 Pages: 552
Individual organizations and society as a whole could face major breakdowns if IT systems do not meet their Quality of Service (QoS) requirements on performance, availability, security, and maintainability. Corporations stand to lose valuable income, and public interests could be put at great risk. System designers and analysts usually do not take QoS requirements into account when designing and/or analyzing computer systems, due mainly to their lack of awareness about the issues that affect
performance and the lack of a framework to reason about performance. This book describes how to map real-life systems (e.g., databases, data centers, e-commerce applications) into analytic performance models. The authors elaborate upon these models, and use them to help the reader thoroughly analyze and better understand potential performance issues.
< Day Day Up >
The same approach of replacing all servers of the Web tier by a single equivalent Web server can be applied to the application and database tiers.
• Table of Contents
Performance by Design: Computer Capacity Planning by Example
By Daniel A. Menascé, Virgilio A.F. Almeida, Lawrence W. Dowdy
Publisher: Prentice Hall PTR Pub Date: January 05, 2004
ISBN: 0-13-090673-5 Pages: 552
Individual organizations and society as a whole could face major breakdowns if IT systems do not meet their Quality of Service (QoS) requirements on performance, availability, security, and maintainability. Corporations stand to lose valuable income, and public interests could be put at great risk. System designers and analysts usually do not take QoS requirements into account when designing and/or analyzing computer systems, due mainly to their lack of awareness about the issues that affect
performance and the lack of a framework to reason about performance. This book describes how to map real-life systems (e.g., databases, data centers, e-commerce applications) into analytic performance models. The authors elaborate upon these models, and use them to help the reader thoroughly analyze and better understand potential performance issues.
< Day Day Up >
8.7 Concluding Remarks
This chapter shows how multiclass open QN models can be used to analyze the scalability of multi-tiered e-business services. The workload of these services is characterized at the user level. User models such as the Customer Behavior Model Graph (CBMG) are used to characterize the way customers navigate through the various e-business functions during a typical visit to an e-commerce site. This user-level characterization can be mapped to a request-level characterization used by QN models. The models are used for capacity planning and performance prediction of various what-if scenarios.
< Day Day Up >
• Table of Contents
Performance by Design: Computer Capacity Planning by Example
By Daniel A. Menascé, Virgilio A.F. Almeida, Lawrence W. Dowdy
Publisher: Prentice Hall PTR Pub Date: January 05, 2004
ISBN: 0-13-090673-5 Pages: 552
Individual organizations and society as a whole could face major breakdowns if IT systems do not meet their Quality of Service (QoS) requirements on performance, availability, security, and maintainability. Corporations stand to lose valuable income, and public interests could be put at great risk. System designers and analysts usually do not take QoS requirements into account when designing and/or analyzing computer systems, due mainly to their lack of awareness about the issues that affect
performance and the lack of a framework to reason about performance. This book describes how to map real-life systems (e.g., databases, data centers, e-commerce applications) into analytic performance models. The authors elaborate upon these models, and use them to help the reader thoroughly analyze and better understand potential performance issues.
< Day Day Up > < Day Day Up >
8.8 Exercises
Assume that the mix of sessions of type A and B is changed to fA = 0.6 and fB = 0.4. Use Chap8- CBMG.XLS and Chap8-OpenQN.XLS to recompute the arrival rates for each class and solve the performance model again for a total arrival rate of sessions, g, varying from 8 to 12 session starts/sec.
1.
Provide an expression for the maximum theoretical value of the session start rate g as a function of the service demands, the visit ratios at each state of the CBMGs, and the fraction of sessions of each type. Compute this maximum value of g for the online auction site. (Hints: Remember that the utilization at each device cannot exceed 1. Use Eqs. (8.4.9)-(8.4.14) and Eq. (8.5.16).)
2.
Find a system of linear equations whose solution provides the visit ratios for a general CBMG. Assume that the transition probabilities pi,j between states i and j are known for all states.
3.
Assume the data of Table 8.3 and assume that 40% of the sessions are of type A and 60% of type B. What is the average number of auctions created per hour assuming that 11 sessions are started per second?
4.
Assume that 2% of all auctions created have a winner (i.e., the auctioned item is successfully sold). Assume that an auction with a winner has an average of 50 bids. Also assume that the average price of a sold item is $50.00 and that the auction site receives a 2% commission on the sales price. Given the original configuration described in this chapter, find the maximum possible revenue throughput of the auction site (i.e., the maximum possible revenue generated by the auction site per second).
5.
Repeat the previous exercise for the case of a new disk added to the database server.
6.
Assume the average visit data of Table 8.3, the service demands of Table 8.4, and a mix of 45% of sessions of type A and 55% of type B. Assume there is only one Web server and one application server.
What is the minimum number of database servers required to support a session start rate of 15 sessions/sec?
7.
The Customer Behavior Model Graph (CBMG) for an e-commerce site is shown in Fig. 8.6. As indicated in the figure, the site offers four e-business functions: access the home page (h), search the catalog (s), add to the shopping cart (a), and buy (b). The site functionality is implemented by a single machine that consists of one CPU and one disk. Table 8.5 shows the CPU and disk service demands for each of the four e-business functions offered by the site (i.e., h, s, a, and b). Assume that 10 new sessions are started at the site per second.
Find the average number of visits per session to each of the four e-business functions. What is the arrival rate of requests to execute each of the four e-business functions? What is the total utilization of the CPU and of the disk?
What are the residence times at the CPU and disk for each of the four e-business functions? What is the response time of each of the four e-business functions?
8.