Merging Process. Two types of items arrive to a merging station at times that form two independent Poisson processes with respectiverates λ1 and λ2. The units queue up and merge into pairs (one of...

Merging Process. Two types of items arrive to a merging station at times that form two independent Poisson processes with respectiverates λ1 and λ2. The units queue up and merge into pairs (one of each type) as follows. Whenever a type 1 item arrives to the station, it either merges with a type 2 item that is waiting at the station, or it enters a queue if are no type 2 items present. Similarly, a type 2 arrival either merges with a type 1 item or it enters a queue. Let Xk(t) denote the number of type k items at the station at time t (k = 1 or 2). Note that either X1(t) or X2(t) is 0 at any time. Assume that the station can contain at most m items (which are necessarily of one type), and when this capacity is reached, additional items of the type in the queue are turned away. Examples of such a system are automatically guided vehicles meeting products to be transported, or taxis and customers pairing up at a station