OUTPUT ANALYSIS VIA STANDARD ARENA OUTPUT

9.5 OUTPUT ANALYSIS VIA STANDARD ARENA OUTPUT

In this section we review in some detail the output analysis facilities provided by the standard Arena output report via a working example, while Section 9.6 covers the Arena Output Analyzer and Section 9.7 covers the Arena Process Analyzer. The reader is encouraged to consult the Arena manual for more information.

9.5.1 W ORKING E XAMPLE :AW ORKSTATION WITH T WO T YPES OF P ARTS

Consider a single-machine finishing operation in a workstation that processes two types of parts, denoted by G 1 and G 2. We make the following assumptions:

Parts of type G 1 arrive according to iid exponential interarrival time distributions with common mean 2 hours, and each part has a fixed processing time of 1 hour. Parts of type G 2 arrive according to iid exponential interarrival time distributions with common mean 4 hours, and each part has a fixed processing time of 1.4 hours. All parts are processed in FIFO order and all part types have equal service priorities.

We wish to simulate the finishing operation for 10,000 hours in order to understand the behavior of the number of parts in the workstation buffer and the buffer delay for each type of parts. An Arena model for our simple system is depicted is in Figure 9.3.

The model consists mostly of modules from the Arena Basic Process template panel. There are two Create modules, one for each part type, so that each of these modules generates a distinct arrival stream. Each arriving part entity then proceeds to the corresponding Assign modules, called Assign Operation Time of G 1 and Assign Operation Time of G

2, where the part type is saved in its Type attribute, the arrival time is saved in its ArrTime attribute, and the operation time is saved in its Operation

Figure 9.3 Arena model of a finishing operation with two types of parts.

178 Output Analysis

Figure 9.4 Dialog box for the Assign module for part G 1.

Time attribute. Figure 9.4 displays the dialog box for the Assign module Assign Operation Time of G 1.

Next, each part entity enters a Seize module, called G 1 Seizes Finishing or G 2 Seizes Finishing, respectively, and attempts to seize the server of the finishing operation; however, if the server is busy, the current arrival is queued (FIFO) at its associated Seize module. Figure 9.5 displays the dialog box for the Seize module G 1 Seizes Finishing, which aims to seize the common resource (machine) called Finishing Operation.

Note that the model defines multiple Seize modules, all of which aim to seize the same server. Following our naming conventions, the queue in the upper Seize module is called G 1 Q and the one in the lower Seize module is called G 2 Q. Eventually, each part entity seizes the common resource Finishing Operation from the

Figure 9.5 Dialog box for the Seize module G 1 Seizes Finishing.

Output Analysis 179 corresponding Seize module. If the common resource is unavailable upon their arrival,

then part entities of type G 1 wait in queue G 1 Q, while part entities of type G 2 wait in queue G 2 Q. Departing part entities of any type enter the Record module, called Collect Delay Statistics, to tally queue delays (the tallying mechanism will be discussed in the next section). Part entities departing from the Record module enter the Delay module, called Delay Operation Time, where they are detained for the pro- cessing time specified in their Operation Time attribute. After processing is completed, the part entities proceed to the Release module, called Release Finishing, to release the resource Finishing Operation, and finally enter the Dispose module, where they are disposed of.

9.5.2 O BSERVATION C OLLECTION

Figure 9.6 displays the dialog box of the Record module, called Collect Delay Statistics, which tallies statistics of type Time Interval. Such statistics tally the time difference between the arrival time of an entity at the Record module and the time stored in a prescribed attribute of that entity. In our case, the latter is the ArrTime attribute, which stores the part entity's arrival time at the finishing operation, so that the Record module may tally queue delays for each part type.

Observe that the Record into Set checkbox in Figure 9.6 is checked, and that its Tally Set Name field specifies a Set module name (Queue Delays). This has the effect of instructing the Record module to produce a separate delay average for each part type, rather than a pooled average across all types. In order to record the corresponding statistics separately, the modeler must create the Queue Delays tally set in the Set module (from the Basic Process template panel), and Arena records the respective statistics into separate set members, based on their Type attribute specified in the Set Index field of the Record module. Figure 9.7 displays the dialog spreadsheets associated with the Set module Queue Delays.

Figure 9.6 Dialog box of the Record module Collect Delay Statistics.

180 Output Analysis

Figure 9.7 Dialog spreadsheets for the Set module to tally delay times for each part type (left) and its members (right).

Figure 9.8 Dialog spreadsheet of the Statistic module with a Tally statistic for each part-type delay.

This set was selected as type Tally (in a drop-down list in column Type), and consists of two members (the button labeled 2 rows in the Members column), one for type G 1 parts and the other for type G 2 parts. We have also declared the two delay Tally statistics in the Statistic module (even though we did not have to), whose dialog spreadsheet is displayed in Figure 9.8 for model completeness.

9.5.3 O UTPUT S UMMARY

A replication of the Arena model for the finishing operation of Figure 9.3 was run for 10,000 hours. Figure 9.9 displays the resulting summary statistics. An examination of the input data in Section 9.5.1 reveals that the finishing process was busy processing parts of type G 1 with partial utilization r 1 ¼ 1=2 ¼ 0:5, and parts of type G 2 with partial utilization r 2 ¼ 1:4=4 ¼ 0:35. Thus, the total utilization of the finishing workstation is r ¼ 0:85. Therefore, we expect the probability of the finishing machine being in the Busy state to be around 0.85. The estimated probability in Figure 9.9 is actually 0.8556 over a replication of length 10,000 hours.

Columns 2, 3, and 4 in Table 9.2 (Finishing Machine Busy, G 1 Buffer Delay, and

G 2 Buffer Delay) display the behavior of the estimates of three performance measures as functions of increasing replication length. Observe how the estimates appear to converge to respective limiting values as the simulation length increases (convergence is indicated by the fact that the values appear to stabilize and change very little for the higher range of replication lengths). Since we know the true value of machine utiliza- tion, we can take advantage of this knowledge in deciding on the smallest replication length that gives rise to sufficiently accurate estimates (high accuracy is indicated here by low variability in the estimates as function of replication length). We naturally seek the smallest value, since we would like to reduce the computational effort as much as possible. We point out that an insufficient replication length is characterized by apparent nonconvergent values of the estimates produced. As a general rule, a longer replication

Output Analysis 181

Figure 9.9 Output statistics for the finishing operation model of Figure 9.3.

has a better chance of experiencing rare events, which may significantly affect the accuracy of the observed statistics.

9.5.4 S TATISTICS S UMMARY :M ULTIPLE R EPLICATIONS

Standard Arena reports provide statistics for each replication separately, but no pooled statistics across replications. However, pooled reports can be accessed by the

182 Output Analysis

Table 9.2 Behavior of three performance measures as functions of replication length

Replication Finishing Machine

G 2 Buffer Delay Length

G 1 Buffer Delay

Table 9.3 Outputs summary statistics based on 10 replications

Performance Measure

Average Value

Half-Width

Minimum Maximum Value

Value Machine Busy

0.8315 0.8702 G 1 Buffer Delay

2.4500 4.1146 G 2 Buffer Delay

modeler by first selecting the Setup. . . option in the Run menu, and then clicking on the Reports tab, and finally selecting the option SIMAN Output Report(.out file) in the Default Report field.

Table 9.3 illustrates statistics supported by the SIMAN Output Report, corresponding to three performance aspects (machine utilization and part delays by type), based on 10 replications of length 10,000 hours each. In particular, it displays the half-width of 95% confidence intervals (at significance level a ¼ 0:05) for all performance measures for which statistics were requested in an Outputs report. Normally, these are constructed from a single replication using the batch means method (see Section 9.2.2). If, however, more than one replication is run, then Arena's standard output provides these same statistics for each replication separately. Additionally, an Outputs report would provide the corresponding pooled summary statistics based on all replications, as shown in Table 9.3, including half-widths of 95% confidence intervals, as described in Section

9.4. Note that the confidence interval estimates in Table 9.3 are tighter (for the same level of confidence) than those of Figure 9.9. This should hardly be surprising, since the former were based on considerably more information than the latter, that is, 10 replica- tions in Table 9.3 compared to a single replication in Figure 9.9.