Assume that the mix of sessions of type A and B is changed to f_{A} = 0.6 and f_{B} = 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.
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).)
Find a system of linear equations whose solution provides the visit ratios for a general CBMG. Assume that the transition probabilities p_{i,j} between states i and j are known for all states.
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?
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).
Repeat the previous exercise for the case of a new disk added to the database server.
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?
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?
Figure 8.6. Customer Behavior Model Graph (CBMG) for Exercise 8.8.
Table 8.5. Service Demands (in sec) for Exercise 8.8