A Survey on Queueing Systems with Mathematical Models and Applications


Queuing systems consist of one or more servers that provide some sort of services to arriving customers. Almost everyone has some experience of tedious time being in a queue during several daily life activities. It is reasonable to accept that service should be provided to the one who arrives first in the queue. But this rule always may not work. Sometimes the last comer or the customer in the high priority gets service earlier than the one who is waiting in the queue for a long time. All these characteristics are the interesting areas of research in the queueing theory. In this paper, we present some of the previous works of various researchers with brief explanations. We then carry out some of the mathematical expressions which represent the different queueing behaviors. In almost all the literatures, these queueing behaviors are examined with the help of mathematical simulations. Based on the previous contributions of researchers, our specific point of attraction is to study the finite capacity queueing models in which limited number of customers are served by a single or multiple number of servers and the batch queueing models where arrival or service or both occur in a bulk. Furthermore, we present some performance measure equations of some queueing models together with necessary components used in the queueing theory. Finally, we report some applications of queueing systems in supply chain management pointing out some areas of research as further works.

Source: Sushil Ghimire, Gyan Bahadur Thapa, Ram Prasad Ghimire, and Sergei Silvestrov , http://article.sapub.org/10.5923.j.ajor.20170701.01.html
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