| In the examples of the previous sections, the intensity of the workload was specified as the rate at which transactions arrive to the system. If the overall arrival rate of transactions is 1.5 tps, the arrival rates per class are 0.675 (= 1.5 x 0.45) tps, 0.375 (= 1.5 x 0.25) tps, and 0.45 (= 1.5 x 0.30) tps for trivial, medium, and complex transactions, respectively, according to Table 2.1. A customer class that corresponds to a workload specified in this way is called an open class. An open class has the following characteristics: Workload intensity specified by an arrival rate. For each open class, the intensity of the workload is represented by the average number of requests arriving per unit time. This arrival rate is usually independent of the system state (i.e., it does not depend on the number of other customers in the system). Unbounded number of customers in the system. As the arrival rate of customers increases, the number of customers in the system modeled by the QN tend to grow without bound. Throughput is an input parameter. In equilibrium, the throughput of an open class is equal to its arrival rate, and is therefore known. This results from observing that, in equilibrium, the flow into the system (i.e., the arrival rate) must equal the flow out of the system (i.e., the system throughput).
Consider now that at night, the database server of the previous sections is not available for the execution of online transactions. Instead, it is used to execute batch jobs that produce managerial reports. A customer class that represents this type of workload is called a closed class. The characteristics of a closed class are: Workload intensity specified by the customer population. For each closed class, the workload intensity is specified by the number of concurrent requests of that class that are in execution (i.e., the customer population for that class). For example, one may say that five batch jobs are being concurrently executed to produce reports. It is typically assumed that as soon as one job finishes, another job from the queue is ready to enter and take its place, thus maintaining a (near) constant number of customers in the system. Bounded and known number of customers in the system. The number of requests in the system is an input parameter and is therefore known and bounded. Throughput is an output parameter. The throughput of a closed class is obtained when solving the QN model and is a function (among other things) of the customer population for that class.
A QN model in which all classes are open is called an open QN model and a QN model in which all classes are closed is a closed QN model. Figure 2.3 depicts a QN with a closed workload. and indicates that as soon as one job completes, another (equivalent) job is started. Thus, the number of jobs in the system remains constant. Figure 2.3. Queuing network for a database server with a closed workload.  |
