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# Queuing Theory and Analysis

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If the cost of waiting is \$5.00 per unit per period and the service facility costs \$2.50 per unit served, what is the total system costs? If the service rate is doubled at a total cost of \$3.50 per unit served, what is the total system costs?

Note: Must use information from previous problem:
The arrival rate for a certain waiting line system obeys a Poisson distribution with a mean of 05. unit per period. It is required that the probability of one or more units in the system not exceed 0.20. What is the minimum service rate that must be provided if the service duration is to be distrubuted exponentially

https://brainmass.com/math/probability/queuing-theory-analysis-391918

#### Solution Preview

Prob(1 or more in the system) = probability that system is in utilization and is not idle

P(0) = 1 - arrival rate / service rate [this shows that system is idle]

P( >=1) = 1 - P(0)

P(>=1) = 1 - (1 - Arrival ...

#### Solution Summary

This solution contains step-by-step calculations to determine the total system costs.

\$2.19