Question

- A small parking lot has 3 spaces (bays). Vehicles arrive randomly (according to a Poisson process) at an average rate of 6 vehicles per hour. The parking time has an exponential distribution with a mean of 30 minutes. If a vehicle arrives when the three parking spaces are occupied, it leaves immediately without waiting or returning.

- Find the percentage of lost customers, i.e., vehicles that arrive but cannot park due to full occupancy.
- Find the average number of vehicles in the parking lot.
- To reduce the percentage of lost customers, the parking lot manager has added a “waiting zone” near the entrance, where at most one vehicle can wait for a parking lot to become vacant. Find the effect of this arrangement on the percentage of lost customers (assume that vehicles are always willing to use the waiting zone).

Answer #1

**solution:**

**given
data:**

**a)**

3 spaces parking lot

6 vechicles per hour

average of 30 minutes

( 6 per hour & average per 30 minutes)

Poisson 's distribution

Percentage of lost coustomers

35.27% is lost customers

**b)**

Average number of vechicles in parking lot

c)

Percentage of lost customers with waiting zone. X=waiting)

waiting zone

20.34% customers are lost with waiting zone.

**please give me thumb up**

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