In a drug store customers arrive at the counter (with one server per counter) in a Poisson process at the rate of 48 per hour. The service time can be assumed to be exponential with an average of 1 minute and the service is provided at a counter attended by a server. The number of counters is varied depending on the number of customers waiting or being served as follows:

0–4 customers 1 counter

5–9 customers 2 counters

10–14 customers 3 counters

15 or more 4 counters

Assume that this policy is used to increase or decrease the number of servers. Determine the following:

a. Probability of system idleness.

b. How often would the store need more than one counter?

c. What is the average number of customers either waiting for service or being served?

d. What is the average waiting time in the queue?