6.5 Using the Model

The MS Excel workbook ClosedQN-chap6 can now be used to solve the model. The initial customer populations for classes PDF and ZIP are set at 4 and 16, respectively (see Section 6.4.1). The total Web server traffic intensity (i.e., the total customer population or the total number of concurrent downloads) can be increased (or decreased) in the model by maintaining the 1:4 ratio between the PDF and ZIP downloads.

Suppose that the manager requests to see performance results of the original configuration against a balanced I/O configuration (i.e., one in which PDF and ZIP files are stored on disks 1 through 4 in such a way that access to each category of files is evenly distributed across all four disks). The new set of service demands for this balanced configuration is easily obtained. The CPU demands are the same as those in Table 6.1. The disk demands are computed by taking, for each class, the total disk demand (i.e., 154.2 msec and 471.6 msec for PDF and ZIP files, respectively) and, instead of dividing them evenly over two disks each, dividing them both over all four disks. Thus, for PDF files instead of 77.1 (= 154.2/2) msec for two disks, 38.6 (= 154.2/4) msec of service is required for each of four disks. Similarly, for ZIP files, the average per disk demand is 117.9 (= 471.6/4) msec. Table 6.2 shows the service demands for the balanced configuration.

Table 6.2. Service Demands (in msec) for the Balanced Configuration

Resource	Class
	PDF	ZIP
CPU	39.4	120.8
Disk 1	38.6	117.9
Disk 2	38.6	117.9
Disk 3	38.6	117.9
Disk 4	38.6	117.9

The original and the balanced QN models are solved using ClosedQN-Chap6.XLS. A range of traffic intensities, varying from 20 to 180 total customers (i.e., maintaining the 1:4 ratio between PDF and ZIP customers), are considered. Figure 6.5 shows the throughput, measured in file downloads/sec, for PDF and ZIP files for both configurations. The corresponding download time results are shown in Fig. 6.6.

Figure 6.5. Throughput vs. number of concurrent users for the original file layout and for the balanced layout.

Figure 6.6. Average file download time vs. number of concurrent users for the original file layout and for the balanced layout.

Observations from the throughput results (i.e., Fig. 6.5) indicate that:

• After some point (i.e., after 20 users), the throughput saturates because the utilization of one of the Web server devices approaches 100%.

• The maximum throughput for PDF files in the original configuration is 12 files/sec. However, for the balanced configuration, the maximum throughput for PDF files is reduced to 5 files/sec.

• The maximum throughput for ZIP files in the original configuration is 4.2 files/sec. However, for the balanced configuration, the maximum throughput for PDF files is increased to 6.6 files/sec.

• The throughput of ZIP files increases and the throughput for PDF files is reduced as the configuration is changed from the original to the balanced one. The total throughput measured in files per second (i.e., considering both PDF and ZIP files) is reduced by 28% by balancing the load across the disks (i.e., maximum throughput reduces from 16.2 (= 12 + 4.2) files/sec in the original configuration to 11.6 (= 5 + 6.6) files/sec in the balanced configuration). However, since ZIP files are significantly larger than PDF files (i.e., 1155.6 KB compared to 377.7 KB), the total throughput measured in bandwidth (i.e., KB/sec) increases by 1.4% (i.e., it increases from 9384.72 (= 12 x 377.6 + 4.2 x 1155.6) KB/sec in the original configuration to 9514.96 (= 5 x 377.6 + 6.6 x 1155.6) KB/sec in the balanced configuration).

Suppose that the SLAs on download times for PDF and ZIP files are 7 seconds and 20 seconds, respectively (since ZIP files are roughly 3 times larger than PDF files, it is reasonable for the ZIP/PDF SLA ratio to be proportional). Observations from the download time results (i.e., Fig. 6.6) indicate that:

• After about 20 concurrent users, the throughput saturates for all classes (see Fig. 6.5) and, therefore, the download times increase linearly with the number of concurrent users (see Exercise 6.5).

• For 104 concurrent users, the average download time for ZIP files at the original configuration reaches its SLA of 20 seconds, while the download time for PDF files is well below its SLA of 7 seconds. Thus, the maximum number of concurrent downloads supported by the original configuration is 104.

• For the balanced configuration, the average download time for ZIP files reaches 20 seconds at 164 concurrent customers. At this point, the download times for PDF files is still below its 7-second SLA. Thus, the balanced configuration is superior to the original one and supports 58% more customers.

For 160 customers using the balanced configuration, the utilizations of all devices are nearly 100%. Specifically, the model indicates that U_CPU = 0.98, U_disk1 = U_disk2 = 0.92, and U_disk3 = U_disk4 = 0.99.