An airline is planning to open a satellite ticket desk in a new shopping plaza, staffed by one ticket agent. It is estimated that requests for tickets and information will average 15 per hour, and requests will have a Poisson distribution. Service time is assumed to be exponentially distributed. Previous experience with similar satellite operations suggests that mean service time should average about three minutes per request.
Determine each of the following:
(1) System utilization
(2) Percent of time the server (agent) will be idle
(3) The expected number of customers waiting to be served
(4) The average time customers will spend in the system
(5) The probability of zero customers in the system
(6) The probability of four customers in the system

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temmydbrain temmydbrain · Answer 1 · 2020-04-16T03:31:19+02:00

Answer:

Check the explanation

Explanation:

Following details are to be noted :

Arrival rates for tickets and information = a = 15 / hour

Service rate ( at 3 minutes/ request ) = S = 60/3 = 20 / hour

1) System utilization = a/ s x 100 = 15/20 x 100 = 75%

2) Percentage of time server will be idle = 100 – System utilization ( %) = 100 % - 75% = 25%

3) Expected number of customer waiting to be served

= a^2/ S x ( S – a)

= 15 x 15/ 20 x ( 20 – 15 )

= 225/100

= 2.25

4)Average time a customer will spend in the system

= 15/ 20 x ( 20 – 15)+ 1/20 hours

= 3/20 + 1/20 hours

= 4/20 hours

= 4 x 60/20 minutes

= 12 minutes

5) Probability of no customers in the system = Po = ( 1 – a/s ) = 1 – 15/20 = 0.25

6) Probability of 4 customers in the system = ( a/s)^4 x Po = (15/20)^4 x 0.25 = 0.75 x 0.75 x 0.75 x 0.25 = 0.1054

chamberlainuket chamberlainuket · Answer 2 · 2020-04-18T05:45:59+02:00

Answer:

1. 75%

2. 25%

3. 2.25 customers

4. 12 minutes

5. 0.25

6. 0.0791

Explanation:

See attached file

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