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Non-Poisson Queuing Models

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As one of the most important models of the queuing theory that I specifically used in health care facilities, its primary function is to find optimal level of capacity and associated staff with it. Known specifically, as the s-server model that has capacity of a finite system, this is one mode in which application is measured with the help of blocking probability measures.

In comparison to other systems, in case of this system, it is taken that arrivals are exponentially distributed in the inter-arrival times and variance assumption is reasonable only at times.

In case of this Non-Poisson Queuing Models, a high standard of blocking probability to variability can be found. Certain specific assumptions and exceptions are to be taken into consideration in this case.

Nothing can better express a procedure than examples, and here is a sum solving which will give students a better insight of the whole procedure.

Sum 1:ย  A particular beauty parlor has 4 chairs for the clients and 2 barbers to serve them. It is taken as assumption that arrival of customers is by the process of Poisson rate of 4 customers per hour. While the services of the barbers are taken to be as 18 minutes per barber as per process of exponential distribution. Also, after this, if a customer arrives again, he or she has to leave since there is no place to sit.

How should the following be calculated given that above conditions are placed:

  • What is the effective rate of arrival?
  • What is the expected number of servers who are busy?
  • What is the probability that the shop is completely empty?
  • What are the expected number of customers who would stand in a queue?

Once a student solves these questions, the specific details associated with this topic can be clarified.

 

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