Overflow in systems with two servers: the negative consequences

We investigate a system with two types of customers wherein each customer type has a dedicated server. When the corresponding dedicated server is busy, we allow customer overflow to the non-dedicated server, and the service time of each server is customer-dependent. The objective of this study is to assess the negative consequences of overflow. On the basis of the analytical stationary distribution of the proposed two-server model, we first identify the conditions under which overflow leads to improvement of throughputs. Second, we obtain customers’ overflow rates and ratios. For a symmetric system under heavy traffic, the wrong assignment ratio comes close to 50%. Third, we analyze the probability that a customer is served by a non-dedicated server. The probability that both servers are serving non-dedicated customers approaches 25% in a symmetric system under heavy traffic. Finally, we determine various overflow conditions while including the overflow costs.