Continuation. Items arrive to a service station according to a Poisson process N(t) with rate λ. The items are stored until m have accumulated. Then the m items are served in a batch. The service time...

Continuation. Items arrive to a service station according to a Poisson process N(t) with rate λ. The items are stored until m have accumulated. Then the m items are served in a batch. The service time is exponentially distributed with rate γ. During the service, items continue to arrive. There is a cost hi per unit time of holding i customers in the system. Assume the station is empty at time 0. Find the expected cost C₁
of holding the customers until m have arrived. Find the expected cost C₂
for holding the added arrivals in the system during the service