queuing theory shows how mathematicians are trying to model, under limited formulations, real issues of daily life.
could say that queuing theory analyzes a type of optimization problems, how to find the right balance between quality of service (ie, the patience of those waiting in a queue) and the amount of service (ie how many workers must be put to serve customers at the lowest cost)
From the arrival rate of customers to the queue, the distribution of how they get over time, the queue capacity, how to manage turn in the queue, method of care, the number of servers that serve the public, the average time each customer care, the standard deviation of these times of attention ... many factors involved in the detailed analysis of this issue. And mathematicians yummy pass it by reaching customers Poisson exponential pace, or checking workers who deal with the public as the Weibull distribution. Fascinating!
We add now the behavior of customers: we must leave the queue, savvy to slip, some who do not join the queue to see its length, other believers who do not leave the queue but it never ends ... patients and impatient.
To finish the dress, the model is obtained after putting all these factors in mathematical notation, it behaves well when it reaches a steady state, but in transient behavior is quite different from real. And in the reality of many tails abound transients, because the service tends to stick to a schedule, there may be interruptions, etc.
So mathematicians have joined the computer to address this problem and simulation tools have been scheduled. Although not a panacea, they can now better address the transient simulation of the behavior under different assumptions and experience a multitude of options quickly getting the best solution for each case.
seems easy. At least I find very interesting topic. But in fact, in most real situations this solves the queues on the fly, with the simple experience: "If I see a lot of glue and customers complain, put another worker to serve them."
Still, there are situations that are analyzed in depth by optimizing operating costs and increasing service-benefits-at the expense of putting the customer's patience limit. Applications such as the queues at customer service points of corporations or ATM lines at supermarkets, to packet flows in an enterprise messaging through a computer network dimensioning according to information flows that support.
many theories, but let's not forget that the customer knows that the Law always prevails Harper:
"No matter what line you are situated, the other always move faster"
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