# Free Queuing Analysis Case Study Sample

Published: 2021-07-07 03:50:05  Category: Time, Services, System, Transportation, Value, Probability, Frequency, Arrival

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GET MY ESSAY At 95% probability, considering the rate of service is constant, then at the targeted rate of five trucks will mean that the arrival rate has to be 4.75. However, there are no 0.75 trucks. So, 4 trucks will be used as the arrival rate. Having obtained the arrival and the service rate, then it is possible to determine the frequency in which a given number of trucks are in the system. As such, the frequency is the power of probability of the system being in use where the power value is the number of trucks whose frequency is being investigated. Therefore, to determine the frequency of five trucks, and then five is the power value which the probability is powered. A similar case will hold for six and seven trucks. The frequency is found to be 32%, 26% and 20% for five, six and seven trucks respectively. In order to obtain the greatest number of trucks in the system, it means that the probability is zero. However, using zero in the calculation will mean that the entire computation is equals to zero. Hence, picking a value close to zero, it is obtained that the number of trucks that can be in the system is 314 trucks. In relation to the least number, one will take the closest probability to one and the least number that is obtained is 2 trucks.
In the case of the multiple servers, the target is to have five trucks unloaded with 100% probability will mean that the arrival time and the service time are equal. In this approach, on needs to compute the probability that the system is not in use. The value is found to be 4.9*10^-3. However, this figure has a small error since 0.99 was used instead of 1 so that to avoid having a zero as a denominator. Therefore, in order to obtain the frequency of a given number of trucks are in the system at any given time, and then the probability of the system being idle is multiplied with a given some number as shown in the excel spreadsheet. From the computation in excel, it is discovered that the frequency of having five trucks, six trucks and seven trucks is 9.8*10^-3. However, determining the greatest and the least number of trucks in this approach vary with the extent of approximation. Therefore, the number varies.

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