# 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.

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Fig. 13.2.2.5       Average relative wait time as a function of capacity utilization: selected values (following an unpublished slide of Prof.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.