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## Self-Service Queuing System

The best queue happens when we can let the customers behave as the servers. This type of self-service queuing system produces the minimum queue length and minimum delay.

The arrival distribution of customers follows Poisson distribution and the distribution for service time follows Exponential distribution.

Use the Self-Service queuing calculator below to experiment and to give you the best solution to solve queuing problem.

The M/M/∞ queuing calculator is based on the following formulation:

Input:

• Arrival rate (number of customers/unit time)
• Service rate (number of customers/unit time)

Output:

• U= Utilization factor = percentage of the time that all servers are busy,
• P 0 = probability that there are no customers in the system,
• P n = probability that there are n customers in the system,
• W q = average time a customer spends in waiting line waiting for service,
• W = average time a customer spends in the system (in waiting line and being served),
• L q = average number of customer in waiting line for service,
• L = average number of customer in the system (in waiting line and being served),

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Preferable reference for this tutorial is

Teknomo, Kardi. (2014) Queuing Theory Tutorial
http://people.revoledu.com/kardi/tutorial/Queuing/