Question

Problem: A clinic has only one dentist. During working days, the traffic is uniformly busy with patients arriving at the rate of 10 patients per hour. The doctor’s service time is 5 minutes.

1. What is the probability that the clinic is empty (except for the dentist)?

2. e. What is the average time a patient spends in the waiting room if the clinic has 2 more dentists with the same service rate?

Answer 1

Solution:

a:

$\lambda=10/hour$

u = 12 hour

Hence,

$P_{0} = 1 - \frac{\lambda}{\mu} = 1-\frac{10}{12} = 0.1667$

b:

M/M/K PERFORMANCE MEASURES • Formulas much more complex e.g. 1 1/2 - XP 1/2 ku Tulku-

Hence, we have,

X = 10/hour

$\mu = 12/hour$

Hence, using the formula above we have,

Hence,

$L_{q} = L - \frac{\lambda}{\mu} = 0.8555 - \frac{10}{12} = 0.0222\ patients$

Hence, the average time spent waiting in the waiting room by patients will be,

$W_{q} = \frac{L_{q}}{\lambda} = \frac{0.022}{10} = 0.0022\ hours = 0.1332\ minutes$

Hence, the average time spent waiting in the waiting room by patients is 0.1332 minutes