Selected Examples

Batch Service III

Another variant on batch service has the transactions accumulating into a batch according to the arrival process and has service scheduled as soon as the first transaction arrives. Service on the entire batch completes at once.

Figure 9.18: Batch Service

Figure 9.18 shows a model of this batch service. When the first transaction arrives to the Server labeled "Delay" it initiates the definition of a batch. Any other transactions that arrive to that server are discarded through the balk node. When the delay is complete, the Trigger labeled "Preempt Service" terminates service on all the transactions in the MServer labeled "Batch Server." As the transactions arrive they accumulate in the MServer for batch service. This server has a deterministic service distribution with a large parameter value for example, D. Note that 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.

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

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