Vaccinations without waiting times & extra hours

Barbara Bredner is a professional statistician consulting companies from industry, research and development. In a recent article she discusses a very important and current topic – vaccination logistics in Germany. With the help of iGrafx, Bredner illustrated and analyzed the necessary process steps within a vaccination center to achieve the goal of 1000 vaccinated people a day.

Finally, the first vaccines are ready for approval, but the next question already emerges: How can a large number of people who are waiting to get the vaccine be vaccinated? The RKI (Robert Koch- Institution) is currently developing a list of criteria, for the order in which population groups are invited to be vaccinated. Meanwhile, the cities and municipalities are setting up vaccination centers where many people can be vaccinated as quickly as possible.

So far, so good. The German series “WDR Lokalzeit” (broadcasted on 7th December 2020) showed the vaccination center in Herne. Soon 1000 people will be vaccinated there every day. For the educational interview with anamnesis (pre-illnesses, earlier inoculation reactions etc.) 3 minutes are planned by the cash medical federation.

Presumably, an average of 3 minutes is a good value; after all, the cash medial federation does such planning more frequently. There will certainly also be people who need less information, e.g. because they have no pre-existing conditions or have already dealt with the vaccination very intensively in advance. Then again, there will be people who simply have more questions or a variety of preexisting conditions where the education takes longer than 3 minutes. Has the spread been taken into account in the vaccination process?

It makes sense not to assume a constant value for the clarification, but for a distribution of values. One possibility is a triangular distribution with a minimum value of 30 seconds, a maximum value of 6 minutes or 360 seconds, and an average value or modal value of 180 seconds, as shown in the figure “Triangular distribution: duration of educational interview”. A value distribution is also more realistic than a constant value for other steps in the process of vaccination.

Diagram Duration Educational interview













Triangular distribution: duration of the educational interview, minimum 30 seconds, maximum 360 seconds, mostly 180 seconds



General conditions & assumptions

For each simulation, framework conditions have to be given, e.g.:

  • 1000 people are to be vaccinated per day.
  • The vaccination should take a maximum of 60 minutes in total.
  • The vaccination center is open 10 hours per day, last admission 60 minutes before closing.
  • In 9 hours, 1000 people are to be admitted, i.e. per hour 1000/9 = 111 people or every 32.4 seconds 1 person. For the simulation, the value is rounded to every 30 seconds.
  • The duration for the path of the vaccinated people from one station to the next is 20 seconds.
  • Any number of workstations can be used per process step.

The number of workstations per process step is determined according to the average or modal value. For the educational interview, the modal value is 180 seconds, i.e. at least 180/30 = 6 workstations are required for 1 person every 30 seconds.

Process steps, tasks and times

1.Check In

Task: query “Do you feel ill?”, temperature measurement, check appointment invitation

Value distribution: triangular distribution, Min=20, Max=60, Modal=40 seconds

Number of workstations: 40/30 = 1. 33, i.e. 2 workstations

2. Formalities

Task: Checking documents (e.g. vaccination certificate, health insurance card), issuing forms for vaccination (e.g. declaration of consent, procedure for second vaccination), explaining the forms

Value distribution: triangular distribution, Min=40, Max=240, Modal=70 seconds

Number of workstations: 70/30 = 2.33, i.e. 3 workstations

3. Fill in forms

Task: People willing to be vaccinated fill in forms

Value distribution: Triangular distribution, Min=60, Max=360, Modal=120 seconds

Number of workstations: 0, support for language or reading/writing difficulties if needed (not included here)

4. Informative interview

Task: educational interview including review of completed forms, medical history, pre-existing conditions, previous vaccination reactions, risks of vaccination, etc.

Value distribution: triangular distribution, Min=30, Max=360, Modal=180 seconds

Number of workstations: 180/30 = 6, i.e. 6 workstations

5. Vaccination

Task: Execution of vaccination, documentation, indication of waiting time

Value distribution: triangular distribution, Min=40, Max=80, Modal=60 seconds

Number of workstations: 60/30 = 2, i.e. 2 workstations

6. Waiting

Task: waiting time after vaccination

Value distribution: triangular distribution, Min=28, Max=36, Modal=30 minutes

Number of workstations: 0

Number of seats: 2 people per minute, 60 people in 30 minutes, i.e. at least 80 seats

7. Check Out

Task: action instructions in case of vaccination reactions, appointment for second vaccination

Value distribution: triangular distribution, min=10, max=120, modal=40 seconds

All values are example values. The simulations have been created with iGrafx PROCESS, version 17.71.1276-Origins. The simulation files and a summary of the results can be found on Github.

Results of the simulation

In the first simulation, the specifications are implemented as described above. The figure shows the process flow in the vaccination center. Blue boxes indicate active process steps, red boxes indicate overloaded ones. At the top left of each process step is indicated how many people are currently in that process step or waiting to be processed.

Simulation with first setting (v1)

Simulation vaccination center

The process step “2. Formalities” is almost always colored red, i.e. long queues form here. The steps “1. Check In”, “5. vaccination” and “7. Check Out” are also often overcrowded. Due to the many waiting times, only 577 people are vaccinated after 10 hours (i.e. one working day) instead of the planned 1000. On average, each person experienced 1:47 of avoidable waiting time and was in the vaccination center for more than 2.5 hours in total.

Table first result

Results of the first simulation (v1)
For the next simulations, the number of workstations in the first two steps is increased. Then the waiting times in the first two steps decrease, but waiting times occur in other steps because more people enter the other process steps. (They just don’t wait as long at “1. Check In” and “2. Formalities”).




Table second result Results of the second simulation (v2)

The number of vaccinated people increases to 652 and the total time in the process decreases to just over 2 hours. Unfortunately, both are still far from 1000 vaccinated and a maximum dwell time of 60 minutes. In the second simulation, as queues form before the “4. Informative Interview” and “5. vaccination” steps, more workstations are created in these two steps.




table third result

Results of the third simulation (v3)

The target of 1000 vaccinated persons is still far underachieved in the third simulation, with 680, and the average turnaround time is still over 2 hours. Almost 80 minutes of it is avoidable waiting time.The queue moves further along in the process in the third simulation to the final step, “7. Check Out”. There, each person waits almost 60 minutes to get the information they need. This would lead to people skipping the last step. This significantly                                                                                                                                                                                    increases the risk that appointments for the                                                                                                                                                                                          necessary second vaccination are not                                                                                                                                                                                                    made at all or not made at the right time.


In the fourth simulation, more workstations are set up in “1. Check In” and especially “7. Check Out”. This means that the specified targets are almost achieved.

table fourth result

Results of the fourth simulation

With the settings in the fourth simulation, with 976 vaccinated people and a mean total time of 66 minutes, the goals of 1000 vaccinated people in a maximum of 60 minutes are almost reached. More vaccinated people are possible in this setup by e.g. slightly increasing the number of appointments per hour and instead of 1 person every 30 seconds already entering the process after 28 seconds.

Simulation with fourth setting (v4)

Simulation of fourth result

The figure shows the simulation with the fourth setting. Significantly fewer red boxes appear compared to the first simulation, even though there are still waiting times. They are significantly lower for each vaccinee, totaling 22 minutes, compared to 107 minutes of avoidable waiting time in the first simulation.

The table below shows how many workstations were scheduled per process step. The distribution of values per process step has remained the same in each simulation.

table summary of results

This is how queues and overload are avoided!

It is always necessary to consider the dispersion in process steps to make a process run well enough. It does not matter if it’s an industrial manufacturing process or a vaccination process. By taking the dispersion into account, goals are reached, queues and overloads are avoided – and so can you!

Of course, I am also happy to support you with process simulation. Just make an appointment (free of charge for new customers).

Barbara Bredner


Autorin: Barbara Bredner


Telephone: +49 (0)201 9467 7787


Linkedin: Barbara Bredner





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