Customers arrive at a cafe every 2 minutes on average according to a Poisson process. There...

Customers arrive at a cafe every 2 minutes on average according to a Poisson process. There are 2 employees working at the bar providing customer service, i.e., one handling customer orders and another handling payments. It takes an average of 1 minute to complete each order (exponentially distributed). Based on the above:

f. What are the service time probability density and cumulative distribution functions?

g. What percentage of customer orders will be prepared in exactly 2 minutes?

h. What are the chances it will take between 3 and 4 minutes to prepare a customer’s order?

i. What is the average service rate for completing orders?

j. What is the average number of customers waiting to order?

k. What is the average number of customers at the cafe?

l. On average, how long does it take to serve a customer?

Expert Solution

Customers arrive at cafe every 2 minutes on average according to a poisson process. There are two employees working at the bar providing customer service, that is 1 handling customer order and and another handling payments. It takes an average of one minute to complete each order,(exponentially distributed). Based on the above:

=> Solution -:

Given data -

orchestra answered 1 year ago

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