Application of delay differential equation in queueing theory

摘要

Queuing Theory is the mathematical theory of waiting lines, queues or traffic. The term "customer" generally implies for a person, but also refer to a lot of other examples. A car in the lane waiting at a toll plaza, a program running in queue in a processor, or an airplane waiting to take-off after the air traffic becomes normal. In the above-mentioned cases there are several queues where the customer often has a number of choices of queues to choose from. Now, in this particular study we are introducing about the symbolic structure of the differential equation of queuing theory & discuss on a model of n-lines where the data of the length of a line given to the consumer is not current, but rather a delayed one, i.e. the given data gives information about the system at a previous time. So here the equations controlling the system become what we call the delay differential equations. In particular, we are going to imply that this delay causes the oscillations in length of the queues because of n-bifurcations.