"Queues are formed at movie halls, metro stations, traffic lights, etc. We would like to optimise these queues so that waiting times are as low as possible, or the number of servers is economically efficient. Longer waiting times lead to costs such as loss of productive time, higher fuel consumption, etc. For example, in Hong Kong, it was computed that a 10 minute delay each day for every worker would lead to a loss of output of about US $2.28 billion a year."
"How do we study the impact of different factors on a queue? One way to get insight is to simulate random arrivals and departures on a computer - this involves basic probability combined with "random numbers" (Ever noticed the RAND button on your scientific calculator?). The diagram shows a simulation of the changing length of a queue where arrivals are random but on average are once every 10 minutes. The service time is similarly random, but on average is one customer every 5 minutes. Note that even though the service time is - on average - quite short, the queue can still get quite long!"
Nice blog.
ReplyDeleteQueuing analysis can generate very surprising results. For instance, there's the most basic result from the simplest single server (M/M/1) queue: if the (average) inter-arrival time equals the (average) service time, the queue will become infinitely long. A nice illustration of why one shouldn't trust average-case analysis.