4 Beedle runs a small shop that only has room for two custom

4. Beedle runs a small shop that only has room for two customers at once. While one customer is at the counter being served, another customer may wait. Customers arrive at a rate of 5 per hour and Beedle takes 10 minutes on average to serve a customer. Use a Bernoulli Single-Server Queuing Process with 1 minute frames to model the number of customers at Beedle’s shop.

a. Set up the transition probability matrix.

b. Find the steady-state distribution, then specify the proportion of time Beedle has customers.

Solution

a)

[ 1/4 1/4 1/2 1/10 ]

b)

proportion of time

5/60 * 10 = 0.833