Question

# A small parking lot has 3 spaces (bays). Vehicles arrive randomly (according to a Poisson process)...

1. 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.
1. Find the percentage of lost customers, i.e., vehicles that arrive but cannot park due to full occupancy.
2. Find the average number of vehicles in the parking lot.
3. 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).

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.

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