QUESTION 7 A conference is being held at a centre that has three different entra

ID: 357085 • Letter: Q

Question

QUESTION 7 A conference is being held at a centre that has three different entrances. A registration desk is being set up at each entrance. Assume that each desk will have its own queue and will see an equal portion of the expected 125 total customers per hour arriving at the conference (assume Poisson arrivals), and that customers will not line jockey between registration desks since they are significant distances apart. If each registration desk can serve one customer at a time, and the average time to serve a customer is 0.75 minutes, then what will be the average time that a customer waits in a line (in minutes) before being able to register? a. 0.13 mins b. 0.47 mins c. 0.82 mins d. 2.41 mins e. 4.98 mins QUESTION 8 Consider a large distribution centre (DC) that sees the arrival of, on average, 40 trucks per 8-hour workday (assume a Poisson distribution). The unloading of a truck at one of the unloading docks takes, on average 45 minutes (assume exponential distribution). The docks operate for 8 hours per day. If a dock is not available, trucks wait in a common line for the next available dock. The truckers charge the DC $25 per hour (or portion thereof) for waiting (not including unloading). The cost to operate a dock is $40 per hour (assume this to be a fixed cost that does not depend on utilization of the dock). Determine the total average cost (dock costs plus truck waiting costs) per hour if five docks are operated a. between $200 and $225 per hour b. between $225 and $250 per hour c. between $250 and $275 per hour d. between $275 and $300 per hour e. More than $300 per hour

Explanation / Answer

Question 7:

The center have three desk and will see an equal proportion of the expected 125 total customers arriving per hour. Thus, number of arrivals at each desk is given as 125/3 = 41.67 customers per hour.

Operating Characteristics

Each desk represents single queue and single server model

Arrival rate (Customers/hour)

? = 41.67 customers per hour

Service (minutes/customer)

0.75 minutes/customer

Service Rate (customer/hour)

µ= (60 mins/hour)/(0.75 mins./customer)

µ= 80 customers per hour

System Utilization

? = ?/µ

? = ?/µ = 35/40 = 0.875

? = 0.875

Average waiting time in the line before serving

Wq = 1/(µ - ?) – 1/µ

Wq = 1/(80 – 41.67) - 1/80

Wq = 0.0136 hour = 0.0136*60 minutes

Wq = 0.82 minutes

Average waiting time in the queue is 0.82 minutes per customer

Part 2.