# 13.2.2b Wait Time as a Function of Capacity Utilization

### Intended learning outcomes: Explain the average wait time as a function of capacity utilization.

Continuation from previous subsection (13.2.2)

For the following discussion, Figure 13.2.2.2 sets out several definitions of variables from queuing theory.

Fig. 13.2.2.2       Definitions of queuing theory variables.

To simplify the discussion, assume the following:

• Arrivals are random; that is, they follow a Poisson distribution with the parameter λ. λ is the average number of arrivals per period under observation.
• Arrivals and the operation process are independent of one another.
• Execution proceeds either in order of arrival or according to random selection from the queue.
• The duration of the operations is independent of the order of processing and is subject to a determinate distribution with mean M(OT) and coefficient of variation CV(OT).

Figure 13.2.2.3 shows the average wait time as a function of capacity utilization for a model with one station (s = 1, where a queue feeds only one operation station, i.e., one workstation or one machine). We assume the coefficient of variation CV(OT) for the distribution to be 1, which is the case with a negative exponential distribution, for example.

Fig. 13.2.2.3       Average wait time as a function of capacity utilization: special case s = 1, CV(OT) = 1.

Exercise: Get used to the effect of queues by choosing different values for the queuing theory variables.

Continuation in next subsection (13.2.2c).

## Course section 13.2: Subsections and their intended learning outcomes

• ##### 13.2 Logistic Buffers and Logistic Queues

Intended learning outcomes: Explain wait time, buffers, the funnel model, and queues as an effect of random load fluctuations. Present conclusions for job shop production. Produce an overview on logistic operating curves.

• ##### 13.2.1 Wait Time, Logistic Buffers, and the Funnel Model

Intended learning outcomes: Describe inventory buffers to cushion disturbances in the production flow. Explain the buffer model, the reservoir model and the funnel model.

• ##### 13.2.2 Logistic Queues as an Effect of Random Load Fluctuations

Intended learning outcomes: Describe job shop production as a network with work centers as nodes.

• ##### 13.2.2b Wait Time as a Function of Capacity Utilization

Intended learning outcomes: Explain the average wait time as a function of capacity utilization.

• ##### 13.2.2c Queuing Theory: Relevant Formulas for the Average Case

Intended learning outcomes: Produce a summary of relevant formulas in queuing theory for the average case.

• ##### 13.2.3 Conclusions for Job Shop Production

Intended learning outcomes: Present qualitative findings of queuing theory for job shop production and, in part, for line production. Describe the measures indicated by the qualitative findings of queuing theory.

• ##### 13.2.4 LOC — Logistic Operating Curves

Intended learning outcomes: Produce an overview on logistic operating curves. Explain an example of logistic operating curves.