8.4 Building a Performance Model

Suppose that it is observed that there is a surge in the number of auctions created and the number of bids placed between 8 p.m. and 11 p.m. [1]. During that period, the average arrival rate of auction creation and bid placement requests is much higher than the average for the rest of the day. Management is interested in analyzing the performance of the various types of requests (i.e., home page hits, search executions, bid viewings, logins, auction creations, and bid placements) during the peak period, as the number of session increases. They want to know the maximum capacity (measured as the maximum sustainable load of new sessions arriving per second) under the current SLA, stated as a maximum of 4 seconds average response time for creating new auctions and viewing bids.

The performance model required to answer the questions posed by management is a multiclass QN model with the following six classes: home (h), search (s), view (v), login (g), create (c), and bid (b). Given that requests arrive to the e-business site from a (hopefully) infinite population, an open multiclass QN model is used (see Chapter 13). The model is illustrated in Fig. 8.3. There are two queues (i.e., devices) for the Web server (CPU and disk), two for the application server, and two for the database server. The parameters needed to solve an open QN multiclass model are: arrival rates of requests per class and service demands per request per class at each device.

Figure 8.3. QN model for the online auction site.

Let g be the total rate at which sessions are started, and let f_A and f_B be the fraction of type A and type B sessions, respectively. Thus, the arrival rate of requests for each of the eight classes is given by

Equation 8.4.9

Equation 8.4.10

Equation 8.4.11

Equation 8.4.12

Equation 8.4.13

Equation 8.4.14

where is the number of class r requests (i.e., visits) that session type T customers make to the site.

The transition probability matrices for sessions of types A and B, the visit ratio computations, and the arrival rate computations are implemented in the Chap8-CBMG.XLS MS Excel workbook. The service demands for the various types of requests are obtained by the analyst by recording and replaying scripts that submit a single type of request. Most load testing tools [2] allow for scripts to be captured, built, and parameterized to simulate loads imposed by virtual users. The service demand for a request of type r can be obtained by submitting a typically large number N of requests of that type to the site during a period of time T. Then, the utilization U_i of each device i of the site is measured during that period. The Service Demand Law is then used to compute the service demand D_i,r of class r requests at device i as U_i/(N/T). In this type of homogeneous experiments the entire utilization of device i, U_i, is attributed to the type of request that is being parameterized.

By running six controlled experiments, one per workload class, the values of the service demands for all six classes (i.e., h, s, v, g, c, and b) and for all devices (i.e., the CPU and disk at the Web, application, and database servers) are shown in Table 8.4. The first two rows correspond to the Web server devices, the next two correspond to the application server devices, and the last two to the database server devices.

Table 8.4. Service Demands (in sec) for Auction Site Queuing Model

Device	(h)	(s)	(v)	(g)	(c)	(b)
WS-CPU	0.008	0.009	0.011	0.060	0.012	0.015
WS-disk	0.030	0.010	0.010	0.010	0.010	0.010
AS-CPU	0.000	0.030	0.035	0.025	0.045	0.040
AS-disk	0.000	0.008	0.080	0.009	0.011	0.012
DS-CPU	0.000	0.010	0.009	0.015	0.070	0.045
DS-disk	0.000	0.035	0.018	0.050	0.080	0.090