Consider two M/M/1 queues with respective parameters i 1, 2.

Suppose they share a common waiting room that can hold at most 3 customers. That is, whenever an arrival finds his server busy and 3 customers in the waiting room, then he goes away. Find the limiting probability that there will be n queue 1 customers and m queue 2 customers in the system. Hint: Use the results of Exercise 28 together with the concept of truncation.