“Bottlenecks were classic problems of queuing theory… They occurred because there were too many customers and not enough people to serve them.”
-Lawrence Wein, Professor of Management at Stanford School of Business
Danish mathematician Agner Krarup Erlang developed Queuing Theory while studying telephone network at Copenhagen telephone exchange. Queuing Theory has lot of applications in field of computer networks, telephones, traffic management, managing queues at various places etc.
Queue theory is about relationship between customers who join queue at certain rate ( follows Poisson distribution) and servers who serve the customers ( follows exponential distribution).
Average arrival rate of customer is denoted by λ and average service rate is denoted by µ , while system utilisation factor denoted by ρ is function of λ and µ.
We will not be getting into details of Queue theory as lot of information is available on net for those interested in this subject.
Lawrence Wein a professor of management at Stanford School of Business tried to apply queue theory in a scenario where a city gets attacked by terrorist using biochemical weapons i.e. what happens when a very large population gets impacted and how such population can be served by medical system.
He gives example of anthrax attack on big US city. To reduce impact of attack antibiotics should reach everyone in city within 4 days.
According to Lawrence there are two obstacles in rescue operation-not enough people would be available to distribute antibiotics, and not enough medical personnel to treat sick. If no solution is found thousands will die.
Lawrence calculated that a 7½-fold increase in distribution capacity would eliminate waiting lines for medicine, which would halve the death toll.
And solution for eliminating waiting lines- government should scrap existing antibiotics distribution network and instead use network of US Postal Service to distribute antibiotics, as postal services serves every home.
This study by Lawrence should be of interest to Indians. Terror attacks are not new to us and we also know what happens when number of people in queue far exceed the number of servers. Demonetisation is good example of this. Millions of people stood in queues for hours just to withdraw few hundred rupees. The existing banking staff and ATMs just could not handle the crisis.
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