Problem: There are two types of customers that call in to a call centre - high priority and low priority. High priority calls occur at the rate of 100 per hour and low priority calls at the rate of 200 per hour (call inter-arrival times are exponentially distributed). The time taken for calls from high or low priority customers both are exponentially distributed with a mean time of 2 minutes per call.
The call centre has 15 customer service agents and wants to know how to distribute the agents between high priority and low priority customers so that they provide the best service possible to high priority customers while keeping both queues stable. In order to meet the goals of the call centre:
a. Allocate 14 agents to high priority customers and 1 agent to low priority customers
b. Allocate 9 agents to high priority customers and 6 agent to low priority customers
c. Allocate 8 agents to high priority customers and 7 agent to low priority customers
d. Allocate 5 agents to high priority customers and 10 agent to low priority customers
e. Allocate 4 agents to high priority customers and 11 agent to low priority customers