The response time, Rr, for class r requests in a multiclass open QN is given by (see Chapter 13)
where Di,r is the service demand of class r requests at device i, Ui is the total utilization of device i, and K is the total number of devices, as shown in Chapter 13. Note that while Di,r is load-independent and does not change as the system load varies, Ui is a function of the arrival rate of requests in each of the classes. Specifically,
where R is the number of classes, Ui,r is the utilization of device i due to class r requests, and lr is the arrival rate of requests of class r. The first summation in Eq. (8.5.16) simply states that the total utilization of a device is the sum of the utilizations due to all classes. The second summation uses the Service Demand Law to express the per class utilizations as a product of arrival rates and service demands. The computations for the multiclass open QN that solves the performance model for the auction site are in the Chap8-OpenQN.XLS MS Excel workbook.
To assess the effect on response time under various workload intensities (i.e., the original mandate posed by management), the value of the session start rate g is varied from 8 sessions/sec to 11.1 sessions/sec. The response times are computed using Chap8-OpenQN.XLS. The results are plotted as a function of g and are shown in Fig. 8.4. Values of g higher than 11.1 sessions/sec cause the system to become unstable (i.e., the utilization of one of the devices, the database disk, reaches its maximum capacity of 100%). See Exercise 8.2. Thus, the database server disk is the system bottleneck in this case. The graphs of Fig. 8.4 indicate that, except for requests to display the home page, all other requests experience a sharp increase in response time when the rate of session starts exceeds 11 sessions/sec.
Figure 8.4. Response time at the auction site vs. session start rate.
Management is interested in the value of g that will make the average response time for requests to create auctions and place bids to exceed 4 seconds. These two request classes correspond to the upper two curves in Fig. 8.4. The response time curve for the bid requests is slightly above the curve for create auctions. At 10.9 session starts/sec, the maximum acceptable level of 4.0 sec for the average response time is exceeded.
As noted, the system bottleneck is the database server disk. The model shows that when g = 10.9 session starts/sec more than 90% of the time is spent at that device. To improve system performance, a new disk could be installed at the database server in order to reduce the load on the bottleneck disk. The performance model can be easily used to analyze this situation. Another device, representing the second disk at the database server, is added. The original service demand at the database server disk is divided between the two disks. The model is solved again. The results for two disks at the database server are in the Chap8-OpenQNTwoDisks.XLS MS Excel workbook. The upgrade causes the response times for the create auction and place bid requests to reduce to 0.489 sec and 0.458 sec, respectively, for a session start rate of 10.96 sessions/sec. This is a dramatic improvement. The addition of a new disk reduces the response time to about 11% of its original value.