Question

Janet is planning to open a small car-wash operation, in which only one car can be washed at a time. She must decide how much space to provide for waiting cars. Janet estimates that customers would arrive randomly with a mean rate of 10 customers per hour if the waiting area is not full. If the waiting area is full, the arriving customers would take their cars elsewhere. The average time of washing a car is 12 minutes. Assuming exponential interarrival times and service times, compare the fraction of potential customers that will be lost because of inadequate waiting space if (a) no waiting spaces were provided, and (b) if 2 waiting spaces were provided. (Waiting spaces do not include the car being washed.)

Answer 1

Here we use, stochastic model.

M/M/S MODEL

1. All inter arrival time are i.i.d. exp(λ)

2. All service time are i.i.d. exp(μ)

3. The number of service is si no restriction on capacity or calling population

here we have,

and

so by, M/M/1/K Model ; K=1,3.

(A) K=1 ;

(B) 2 space

K=3,

Answer