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Guest Post: Waiting Lines and the Coronavirus

March 28, 2020

Our Guest Post today comes from Howard Weiss, Professor of Operations Management Emeritus at Temple University.

A couple of thoughts have come to my mind recently with respect to the coronavirus.

As more citizens become infected with a virus, fewer citizens are available to become infected. This is identical in principle to the arrival rate in a finite population waiting line system. Consider, Example D7 from your Heizer/Render/Munson textbook. There are 5 printers that each break down at the rate of .05 per hour. Thus, if all five computers are working, the system arrival rate is 5*.05=.25 while if all 5 are broken down the system arrival rate is 0. Over time, the arrival rate changes depending on the number of printers that are working and we can compute the weighted average arrival rate, which we term the effective arrival rate. The Excel worksheet for this example, available on MyOMLab, computes the effective arrival rate as .218 printers per hour. This effective arrival rate is similar to the effective reproductive number that epidemiologists use for viruses.

Data Results
Arrival rate (l) per customer 0.05 Average server utilization(r) 0.436048
Service rate (m) 0.5 Average number of customers in the queue(Lq) 0.203474
Number of servers 1 Average number of customers in the system(Ls) 0.639522
Population size (N) 5 Average waiting time in the queue(Wq) 0.933264
Average time in the system(Ws) 2.933264
Probability (% of time) system is empty (P0) 0.563952
Effective arrival rate 0.218024

 

An interesting graphic related to the virus spread is at this Washington Post web site.

Observation: I recently had the opportunity to attend a concert at the Amalie Arena in Tampa. At intermission, the men’s room had a long line. This is not unusual. However, the line was not for the urinals or stalls but rather for the sinks. This was unusual. The design of the bathrooms was clearly for normal use rather than for a situation like the one we currently have with increased demand for handwashing. I was wondering what an arena might do to handle the increased sink demand.

3 Comments leave one →
  1. BeauA2 permalink
    March 28, 2020 11:18 am

    I enjoyed your example, but to be clear: scientists don’t yet know if humans can be reinfected with COVID-19 as of 3/25. https://www.newscientist.com/article/mg24532754-600-can-you-catch-the-coronavirus-twice-we-dont-know-yet/

  2. March 29, 2020 4:56 pm

    Thank you for pointing that out.

  3. March 29, 2020 5:09 pm

    Still, if half the population is currently infected then the number of people who can be
    infected or re-infected is less than if one quarter are currently infected.

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