Wikipedia:Reference desk/Archives/Mathematics/2019 March 22

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March 22

Probability of congestion

Hi there. I work in a large warehouse where the staff travel up & down aisles in sequential order to pick stock to be delivered to shops. Each store order is unique. One of the things that affects the efficiency of the process is congestion: this is a busy environment and people get in each others way at certain times of the day. I'm trying to calculate the likelihood of this congestion happening in order to ascertain the average amount of time each day that is lost to congestion.

I have a dataset that shows: employee, time of day (to the nearest second) and location (given by X & Y coordinates) plus a few other details (how many cases picked etc.) How could I use a dataset like this to show the likelihood of being congested as an average over the day/shift? Thanks in advance! :) — sparklism ^hey! 10:55, 22 March 2019 (UTC)

You might find Level of service of use, also Three-phase traffic theory is about auto traffic but there could be some useful ideas there. In general one of the first steps in analyzing a dataset is to come up with operational definitions for the quantities you're interested in. You probably have an idea in your mind about what you mean by 'congestion', but you need to model that idea in terms of what is in your dataset before you can create a meaningful query. For example you might define a person to be 'delayed by congestion' if they're moving at less than 10% of their normal speed (which would also need to be defined) while traveling. Another approach might be to define hotspots where you think congestion is happening (intersections etc.) and say a person is 'delayed by congestion' if the time they spend in these spots is greater than average. No operational definition is going to be perfect since it will be based on an imperfect model of what's actually going on, and which definition to use depends on what data is available. Another thing you should probably do is use the dataset to test the assumptions you're making. For example you probably expect that everyone moves a more or less the same speed unless there's a delay, but maybe there's some slowpoke out there who never moves at more that 50% average speed; you never know what you'll find unless you actually test the assumption against the data. --RDBury (talk) 13:56, 22 March 2019 (UTC)

Thanks - I found this very useful! — sparklism ^hey! 17:56, 22 March 2019 (UTC)