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Queues and Queueing theory

Queuing theory is a branch of mathematics that is used to understand, guess what, queues! 

Queues are quite important in processes where there are flows and sequences of actions, as they can be a significant cost element (note: flowcharts do not normally show these important 'temporary storage' elements).

The simplest queue is a queue at traffic lights, where cars arrive at a given rate, they wait for a given period and then they leave. And the simplest equation of queuing is that if the arrival rate is greater than the departure rate then you've got a queue building up.

The next stage of complexity is when not only the arrival rate is variable, but the processing rate is also variable. For example, an assembly station on a manufacturing line. Queues in such situations are 'work in progress' which can add significantly to the cost of manufacture, from the tied-up capital to the cost of floor-space for stacking and buffer stations.

Things start to hot up when there are multiple queues. For example when you go the checkouts in a supermarket, there are many possible queues you can join. Any queuing will lead to some dissatisfaction, but this will increase in stages and if the queues are too long then you might just dump your basket and never come back. The supermarket can use queuing theory to manage this situation and know how many operatives to put on the tills at any one period during the day.

And beyond this, there are additional complexities, such as in complete production lines, where parts and assemblies move in all directions, or even complete value chains, where parts and products move between companies and customers. 

See also:

Kanban, Lean systems

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