Question

. A parking lot for a certain bar has space for 10 cars. Customers arrive on average every 10 minutes, and stay at the bar an average of 1 hour.

(a) Sketch the transition diagram and various arrival/serving rates

Answer 1

To sketch the transition diagram for the parking lot scenario, you can represent the states as the number of cars in the parking lot and draw arrows indicating the transition from one state to another based on the arrival and serving rates.

Step-by-step explanation:

To sketch the transition diagram for the given scenario, we can represent the states as the number of cars in the parking lot. Since the parking lot has space for 10 cars, we can have states ranging from 0 to 10. The arrival rate is 30 customers per hour, which is equivalent to 0.5 customers per minute. The serving rate is the reciprocal of the average serving time, which is 1 customer per hour or 0.0167 customers per minute. We can now draw the transition diagram with arrows indicating the transition from one state to another based on the arrival and serving rates.

Arrival rates: State 0 -> State 1 with a rate of 0.5
State 1 -> State 2 with a rate of 0.5
State 2 -> State 3 with a rate of 0.5
...

Serving rates: State 1 -> State 0 with a rate of 0.0167
State 2 -> State 1 with a rate of 0.0167
State 3 -> State 2 with a rate of 0.0167
...