Question: 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

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.

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