Selected Examples

Batch Service II

Some situations demand a somewhat different approach to batch service; for example, consider a washing machine. The machine is started when enough items have arrived for service to complete the batch. However, unlike the preceding example, all the items in the batch finish at the same time. The model in Figure 9.17 accomplishes this.

Figure 9.17: Batch Service

In this model the service distribution in the MServer labeled "Batch Server" is deterministic with a large parameter value for example, D. The Server labeled "Delay" provides the actual sample of the service time for the entire batch. And the Batch Server is turned on before the Delay and off after service for the batch is complete. Since turning the server off does not pre-empt transactions currently in service, there is another Trigger labeled "Preempt" that pre-empts all the transactions in the Batch Server. Since the transactions are pre-empted, they leave the server using the balk node.

Notice the LinePlot labeled "Server Utilization.". It shows the number of transactions in service over time. It demonstrates graphically the batch service and dependent nature of the service completions.

Because of the modeling technique used here, the service time distribution is the minimum of D and X, an exponential random variable. If you want the service time distribution to be X, then use caution in choosing D so that the probability that X > D is very small and highly unlikely to occur within the number of samples planned.

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