Question

What can managers do with queuing theory?

Multiple Choice

• Create better marketing

• Calculate net profits

• Eat at fancy restaurants

• Measure and predict performance

Utilization is equal to which of the following?

Multiple Choice

• Arrival rate times service rate

• Service rate divided by arrival rate

• Arrival rate divided by service rate

• Service rate minus arrival rate

The second, simpler formula is only valid for which condition?

Multiple Choice

• The arrival and service rates are derived from a Beta distribution

• The arrival and service rates are derived from a Chi-Square distribution

• The arrival and service rates are derived from a Poisson distribution

• The arrival and service rates are derived from a Normal distribution

A vending machine dispenses hot chocolate or coffee. Service time is 35 seconds per cup and is constant. Customers arrive at a mean rate of 61 per hour, and this rate is Poisson-distributed.

a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.)

Average number of customer            

b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Average time             minutes

c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Average number             customers

Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of 86 seconds completing his or her transactions. Transaction time is exponentially distributed.

a. Determine the average time customers spend at the machine, including waiting in line and completing transactions. (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Average time             minutes

b. Determine the probability that a customer will not have to wait upon arriving at the automatic teller machine. (Round your answer to 2 decimal places.)

Probability            

c. Determine the average number of customers waiting to use the machine. (Round your answer to 2 decimal places.)

Average number             customers

Answer 1

The managers do with queuing theory is,

• Measure and predict performance

Utilization is equal to

• Arrival rate divided by service rate

The second, simpler formula is only valid for

• The arrival and service rates are derived from a Poisson distribution

= 61 per hour = (61/60) per minute = 1.017 per minute

= 1/35 per second = (60/35) per minute = 1.714 per minute

a.

average utilization of the system, = / = 1.017 / 1.714 = 0.5933

Average number of customer  waiting in line = / ( - ) = 0.5933 * 1.017 / (1.714 - 1.017)

= 0.87

b.

average time customers spend in the system = 1 / ( - ) = 1 / (1.714 - 1.017)

Average time     1.43 minutes

c.

average number of customers in the system = / ( - ) = 1.017 / (1.714 - 1.017)

Average number 1.46 customers