# 13.7.2 Scenario: Queues as an Effect of Random Load Fluctuations (2)

### Intended learning outcomes: Experience average wait time as a function of capacity utilization in a job shop environment with random arrivals, execution of operations in order of arrival as well as operation times subject to a determinate distribution with mean and coefficient of variation.

Figure 13.2.2.3 shows the average wait time as a function of capacity utilization in a job shop environment with random arrivals, execution of operations in order of arrival (or according to random selection from the queue), as well as operation times (OT) subject to a determinate distribution with mean M(OT) and coefficient of variation CV(OT). We reproduced the effect shown in Figure 13.2.2.3 by means of a simulation, which you can view at this URL:

Start the simulation by clicking on the given arrival rate and execution (service) rate on the gray button to the far left at the bottom of the figure and watch the number of elements in the system. Stop the simulation by clicking on the middle of the three buttons (or empty the system by clicking the button to the far right). Now change the input rate to bring it closer and closer to the execution rate and observe the rising number of elements in the queue. You will see the exploding number of elements in the system as soon as, for an execution rate of 60 per unit of time, the arrival rate is 58 and higher.

## Course section 13.7: Subsections and their intended learning outcomes

• ##### 13.7 Scenarios and Exercises

Intended learning outcomes: Assess queues as an effect of random load fluctuations. Calculate examples for network planning, backward scheduling, forward scheduling, the lead-time stretching factor, and probable scheduling.

• ##### 13.7.1 Exercise: Queues as an Effect of Random Load Fluctuations (1)

Intended learning outcomes: Answer a number of questions using the relevant formulas in queuing theory.

• ##### 13.7.2 Scenario: Queues as an Effect of Random Load Fluctuations (2)

Intended learning outcomes: Experience average wait time as a function of capacity utilization in a job shop environment with random arrivals, execution of operations in order of arrival as well as operation times subject to a determinate distribution with mean and coefficient of variation.

• ##### 13.7.3 Exercise: Network Planning

Intended learning outcomes: Calculate a scheduled network with incomplete data for six operations and a start operation (administration time. Determine the critical path.

• ##### 13.7.4 Exercise: Backward Scheduling and Forward Scheduling

Intended learning outcomes: Explain and solve the forward and backward scheduling problems that is calculation of start and completion dates for the order and each operation, as well as the critical path and lead-time margin.

• ##### 13.7.5 Exercise: The Lead-Time-Stretching Factor and Probable Scheduling

Intended learning outcomes: Explain and practice the use of the lead-time-stretching factor as well as probable scheduling.