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

*Continuation from previous subsection (13.2.2b)*

Figure 13.2.2.4 presents the relevant formulas of queuing theory for the average case, with references to their original sources in the literature, specifically [GrHa18], [Coop90], and [LyMi94], including page and formula numbers. For further aspects of theoretical mathematics, the reader can consult [Fers64] and [Alba77]. It is important to note, however, that for multiple-station models (s = arbitrary), the relationships based on numerical calculation only approach validity under conditions of extensive capacity utilization.

**Fig. 13.2.2.4** Summary of relevant formulas in queuing theory.

Figure 13.2.2.5 shows wait time as a function of operation time for selected values of s and CV(OT).

**Fig. 13.2.2.5** Average relative wait time as a function of capacity utilization: selected values (following an unpublished slide of Prof. Büchel, ETH Zurich).

## 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.